Surface Imaging Introduction to Applied Geophysics 지반구조영상화 Week 15: Revision Gravity Survey Measures variations in Earth’s gravitational field due to subsurface density contrasts => Actually, measures variations in gravitational acceleration (g) Historically: widely used in oil & gas exploration (early 20th century) Units: Unit of acceleration due to gravity (1cm/s2) = Gal SI unit of gravity: m/s² Geophysical unit: Gal (cm/s²), usually expressed in mGal or µ Gal for small variations. acceleration due to gravity = μm/s² = Gravity unit = g.u. = 0.1mGal 10 g.u. = 1mGal https://quizlet.com/gb/454092692/gravitational-fields-key-terms-ch-21-aqa-a2-physics-diagram/ https://vocal.media/earth/the-truth-of-about-law-of-gravity Mg = megagram Kg = kilogram mGal = milliGal μGal = microGal 1Mg = 1000 kg Gal = 1cms-2 1mGal = 10-3Gal 1μGal = 10-6Gal 1g.u.= 0.1mGal (10g.u. = 1mGal) 1g.u. = 10-6ms-2 Theory Gravity method is based on Newton’s ‘Universal Law of Gravitation’ and ‘Second Law of Motion’ 1) Newton’s Universal Law of Gravitation 𝐹𝑜𝑟𝑐𝑒 = 𝑔𝑟𝑎𝑣𝑖𝑡𝑎𝑖𝑜𝑛𝑎𝑙 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 × 𝐺×𝑀×𝑚 𝐹= 𝑅2 𝑚𝑎𝑠𝑠 𝑜𝑓 𝐸𝑎𝑟𝑡ℎ 𝑀 × 𝑚𝑎𝑠𝑠 𝑚 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑚𝑎𝑠𝑠𝑒𝑠 2 (equation 1) 𝑊ℎ𝑒𝑟𝑒 𝑡ℎ𝑒 𝑔𝑟𝑎𝑣𝑖𝑡𝑎𝑡𝑖𝑜𝑛𝑎𝑙 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝐺 = 6.67 × 10−11 𝑁𝑚2 𝑘𝑔−2 https://www.youtube.com/watch?v=kxDvDgwsltM Theory 2) Newton’s Second Law of Motion 𝐹𝑜𝑟𝑐𝑒 = 𝑚𝑎𝑠𝑠 𝑚 × 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 𝑔 𝐹 = 𝑚×𝑔 https://clenta.com/newtons-laws-of-motion/ https://www1.grc.nasa.gov/beginners-guide-to-aeronautics/newtons-laws-of-motion/ (equation 2) Theory Equation (1) and (2) can be combined to obtain another simple relationship: (equation 1) 𝐹= (equation 2) 𝐺×𝑀×𝑚 𝑅2 𝐹 = 𝑚×𝑔 𝐺×𝑀×𝑚 𝐹= =𝑚×𝑔 𝑅2 𝑔= 𝐺×𝑀 𝑅2 (equation 3) 𝐺=𝑔𝑟𝑎𝑣𝑖𝑡𝑎𝑡𝑖𝑜𝑛𝑎𝑙 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑀= 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑡ℎ𝑒 𝐸𝑎𝑟𝑡ℎ 𝑅= 𝐸𝑎𝑟𝑡ℎ′ 𝑠 𝑟𝑎𝑑𝑖𝑢𝑠 https://brighterly.com/math/radius-of-a-circle/ However… Gravity is not uniform across the globe because of: • Earth’s shape → oblate spheroid (flattened at poles, bulging at equator) • Rotation → centrifugal force reduces gravity at the equator • Surface topography → mountains, valleys, oceans alter local gravity • Mass distribution → density variations in crust & mantle https://www.brainkart.com/article/Shape-and-size-of-the-Earth_33761/ Geopotential and Geoid Shape of the Earth • Result of balance between gravity & centrifugal acceleration • Causes slight flattening at poles → Earth is an oblate spheroid • Described by geopotential = gravitational potential + centrifugal acceleration • Gravity dominates What is the Geoid? • Undisturbed sea-level surface • Defined as: • Always perpendicular to gravity • Equipotential surface of Earth’s gravitational field • Irregular due to: • Mountains & valleys • Crustal density differences • Mantle variations • Used as the zero-reference surface for elevations (geodesy & GPS) • Geoid =/= mean sea level • Because geopotential values at sea level are not equal https://www.ngs.noaa.gov/research/geopotential-datums/evaluation-dov.shtml Variation of Gravity with Latitude Value of acceleration due to gravity varies over the surface of the Earth for a number of reasons, 1) Earth’s shape Radius at the poles < radius at the equator Gravity at the poles > gravity at the equator 𝑔= 𝐺×𝑀 𝑅2 2) Centrifugal acceleration Equator = rotational velocity largest Gravity at the poles > gravity at the equator & gravity varies systematically with latitude in between. International Gravity Formula (IGF) for gravity (g) at a given latitude (φ) IGF80 https://www.geeksforgeeks.org/physics/variation-in-acceleration-due-to-gravity/ Densities of Rocks Sedimentary Rocks • Least dense compared to igneous & metamorphic rocks • Factors affecting density: • Composition & cementation • Age & depth of burial • Tectonic processes • Porosity & pore-fluid type • Variations: • Sandstones / Limestones → pores filled by natural cement • Shales / Clays → compaction & recrystallization → higher density Igneous Rocks • Denser than sedimentary rocks • Density ↑ as silica content decreases • Basic igneous rocks (e.g., basalt) → denser • Acid igneous rocks (e.g., granite) → less dense https://sciencenotes.org/category/geology/page/4/ Metamorphic Rocks • Density increases with: • Decreasing acidity • Higher metamorphic grade (more intense pressure & temperature) Measurement of Gravity Absolute Gravity • Normally measured under laboratory conditions • Establishes a network of gravity stations • Provides absolute reference values (e.g., IGSN71 – International Gravity Standardization Net 1971) Relative Gravity • Most common in gravity exploration • Procedure: • Select a base station (IGSN71 reference) • Establish secondary network of survey stations • All survey data are measured relative to the base station • Used for field surveys since it is faster & more practical than absolute measurements Gravimeters Geophysicists measure variations in gravity using a gravimeter From early designs to modern instruments → basic principle remains the same → based on Hooke’s Law: • A spring stretches/compresses in proportion to the applied force • Tiny changes in gravitational acceleration cause measurable spring deflection 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑔𝑟𝑎𝑣𝑖𝑡𝑦 𝐸𝑥𝑡𝑒𝑛𝑠𝑖𝑜𝑛 𝑡𝑜 𝑠𝑝𝑟𝑖𝑛𝑔 = 𝑚𝑎𝑠𝑠 × 𝑠𝑝𝑟𝑖𝑛𝑔 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑚𝛿𝑔 𝛿𝑙 = 𝑘 𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑔𝑟𝑎𝑣𝑖𝑡𝑦 = 𝑠𝑝𝑟𝑖𝑛𝑔 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 × 𝑒𝑥𝑡𝑛𝑒𝑠𝑖𝑜𝑛 𝑚𝑎𝑠𝑠 𝑘𝛿𝑙 𝛿𝑔 = 𝑚 https://www.sciencedirect.com/topics/earth-and-planetary-sciences/gravimeter Corrections to Gravity Observations Gravimeter Measurements • Gravimeters do not directly measure gravity • Provide a meter reading → converted to observed gravity (gobs) using an instrument calibration factor • Raw data must be corrected to a common datum (e.g., sea level / geoid) • Correction process = gravity data reduction or reduction to the geoid Gravity Anomalies • Observed gravity (gobs) is compared with: • International Gravity Formula / Geodetic Reference System • Or a local base station value • The difference = gravity anomaly • Anomalies reveal subsurface density variations → geological interpretation Corrections Corrections to Gravity Observations Corrections to gravity data: • Instrument drift • Earth tides • Eötvös • Latitude • Elevation – Free-air correction • Elevation – Bouguer correction • Terrain • Isostatic Corrections: Instrumental Drift Gravimeter Limitations • Use metal springs → affected by: • Temperature changes • Constant tension from weight • Results in instrument drift → changes in gravity measurements Solutions to Drift • Repeat measurements for consistency • Use two gravimeters for cross-checking • Data correction → remove drift during processing https://mg.m.wikipedia.org/wiki/Sary:Springs_009.jpg https://www.sciencedirect.com/topics/earth-and-planetary-sciences/gravimeter An Introduction to Applied and Environmental Geophysics by John M. Reynolds https://tum.wikipedia.org/wiki/Geographic_coordinate_system https://www.britannica.com/science/meridian-geography Corrections: Latitude (Polar Flattening) Latitude Effect on Gravity • Earth is an oblate spheroid: 𝐺×𝑀 • Flatter at the poles 𝑔= 2 𝑅 • Bulges at the equator • Radius (R) shorter at poles → gravity stronger at poles Formulas for Surveys • Large N–S surveys (> 100 km) → use IGF80 formula • Smaller surveys → use equation: Δ 𝑔𝐿 = −8.108sin2ϕ g.u. per km N Φ = latitude of the base station Latitude Correction Rule • If station is north of the base → correction is negative • If station is south of the base → correction is positive Corrections: Latitude (Polar Flattening) Δ 𝑔𝐿 = −8.108sin2ϕ g.u. per km N Φ = latitude of the base station Example Measurement 3 (10km N) Measurement 2 (1km N) Measurement 1 (0Km) Measurement 4 (5km S) Base station Φ= 37˚N Δ 𝑔𝐿 = -7.15 g.u. per km N Measurement 1 = no correction Measurement 2 = g – 7.15 Measurement 3 = g – (7.15)x10 = g – 71.5 Measurement 4 = g + (7.15)x5 = g + 35.75 Corrections: Free-Air Correction (Elevation) • Not required if readings are taken at mean sea level (MSL) • At elevations below MSL: • Closer to Earth → stronger gravity • Apply negative correction • At elevations above MSL: • Further from Earth → weaker gravity • Apply positive correction Corrections: Free-Air Correction (Elevation) Measurement 1 h=20m msl h=10m Measurement 2 Measurement 1 = g + 3.086x20 = g + 61.72 Measurement 2 = g – 3.086x10 = g – 30.86 Corrections: Bouguer Correction • Accounts for gravitational effect of material (rock, soil, etc.) between the station and mean sea level (MSL) • Different from Free-Air Correction: • Free-Air → only distance above/below MSL • Bouguer → effect of intervening mass When Bouguer Correction is Needed • Not needed if: • Station at MSL • Readings in open air (airborne, or below MSL with no material above) • Needed when material lies between station and MSL Correction Rule • Station above MSL: • Rock/soil mass is below station • Increases gravity → apply negative correction • Station below MSL: • Rock/soil mass is above station • Upward gravitational pull opposes Earth’s → apply positive correction no correction Negative correction rock no correction msl Positive correction Corrections: Bouguer Correction Bouguer Correction: Assumes infinitely wide rock/soil slab and forgets about effects of local topography. Correction Rule • Station above MSL: • Rock/soil mass is below station • Increases gravity → apply negative correction • Station below MSL: • Rock/soil mass is above station • Upward gravitational pull opposes Earth’s → apply positive correction ↑h 𝜌𝑏 ↑h 𝜌𝑏 Corrections: Terrain Correction Bouguer Correction: • Assumes a semi-infinite horizontal slab of rock/soil between the measuring station and MSL • Ignores effects of local topography Terrain Correction: • Adds back the effect of hills & valleys (local topography) • Applied after Bouguer correction • Always apply positive correction value Valley • Empty space (non-existent part) inside the Bouguer plate • Not exerting additional downward force • The measured gravity is slightly smaller Hill • Extra mass above the Bouguer plate • Upward gravitational force • The net gravitational force is slightly smaller ↑h 𝜌𝑏 hill valley ↑h 𝜌𝑏 valley Corrections: Terrain Correction Tool to calculate the correction: Hammer terrain correction chart Overlay the chart on you map and centre your station. Calculate the average topographic relief of the area. An Introduction to Applied and Environmental Geophysics by John M. Reynolds Corrections: Terrain Correction Example Hill Average 4m height Occupy around ½ of the area Average relief is around 1.9m The rest of the area is level ground Correction value = 0.01 g.u. Your gravity = g(reading)+0.01 An Introduction to Applied and Environmental Geophysics by John M. Reynolds Corrections: Building Correction • Building can reduce readings by 0.10~0.30 g.u. • Recommended that gravimeter be positioned at least 2.5m away to limit influence of buildings to 0.05 g.u. http://users.uoa.gr/~jalexopoulos/papers_pdf/071%20Calculation%20of%20Building% 20Correction%20for%20urban%20gravity%20surveys%20...%20.pdf Corrections: Tides Earth–Moon–Sun system: • Changing distances cause gravity variations of up to ±3 g.u. • Predictable from gravitational tide charts Practical Approach • In surveys, tides + drift + diurnal changes are treated together • Corrected via drift correction methods, e.g.: • Re-occupying previous stations • Using a second gravimeter at base station • Provides convenient correction for all combined effects https://www.britannica.com/science/Earth-tide Corrections: Eötvös Correction https://flatearth.ws/eotvos Corrections: Eötvös Correction Geopotential = combined effect of gravity + centrifugal force On moving vehicles (ships, airplanes): • Motion at significant velocities can add to or cancel the centrifugal component • Produces errors in measured gravity values Calculation Need to know the latitude, azimuth and speed of the vehicle An azimuth degree is a horizontal angle, measured in degrees, that specifies a direction on a compass, with 0° representing North, 90° East, 180° South, and 270° West https://en.wikipedia.org/wiki/E%C3%B6tv%C3%B6s_effect An Introduction to Applied and Environmental Geophysics by John M. Reynolds Final Product: Bouguer Anomaly Final corrected anomaly after: • All data corrections applied • Subtraction of base station (relative measurement) Note: Bouguer anomaly ≠ Bouguer correction Negative anomalies (−): Subsurface is less dense than surroundings Examples: caves, salt domes in country rock, sedimentary basin surrounded by basement rock etc. Positive anomalies (+): Subsurface is denser than surroundings Examples: intrusive bodies, buried metallic objects, vintage bombs etc. An Introduction to Applied and Environmental Geophysics by John M. Reynolds Rock Density Gravity anomalies result from the difference in density, or density contrast, between a body of rock and its surroundings. For a body of density ρ1 embedded in material of density ρ2 , the density contrast △ρ is given by The sign of the density contrast determines the sign of the gravity anomaly. △ρ = ρ1 - ρ2 Rock densities are among the least variable of all geophysical parameters. Most common rock types have densities in the range between 1.60 and 3.20Mgm-3. Average rock density is around 2.65Mg/m3 The density of a rock is dependent on both its mineral composition and porosity. An Introduction to Applied and Environmental Geophysics by John M. Reynolds Gravity Survey: Simple Explanation https://bigthink.com/strange-maps/gravity-anomalies/ Interpretation Regionals and Residuals Regional trend = large-scale variations e.g., km-scale dipping geological formation Residuals = local variations e.g., small lenses within a formation Interpretation depends on the scale of target object Extracting Regionals & Residuals • No single “correct” method — several approaches: • Fourier transform • Polynomial fitting • Manual trend-line fitting (often sufficient in practice) • Both regional & residual = patterns with non-unique interpretations Principles of applied geophysics by D.S. PARASNIS Manual trend-line fitting Regional value= Line that approximates the regional trend Principles of applied geophysics by D.S. PARASNIS Map Profile 𝑑𝑦 = 𝑚𝑥 + 𝑐 𝑚 = 𝑠𝑙𝑜𝑝𝑒 c = y intercept Regional Residual value= Anomaly profile – regional value Residual Regionals and Residuals • Regionals and residuals are simply patterns with no unique interpretation, and the extraction and interpretation of it should be always supported by another data set such as geologic data. • regionals and residuals are simply patterns with no unique interpretation Applications of Residuals • Enable further quantitative analysis, e.g.: • Half-Width Method → depth estimation • Gauss’s Theorem → volume estimation (useful in ore body evaluation and resource estimation) Principles of applied geophysics by D.S. PARASNIS Anomalies of Different Bodies • Different 3D shapes (sphere, cylinder, slab, etc.) produce predictable residual gravity anomaly patterns • Patterns are based on theoretical gravity field calculations • Used to estimate depth of the center of mass (not exact top depth) g.u. distance Spherical ore body If density of the object is: Known (from drillings, samples) Or estimated (from outcrops, geologic maps) Then we can calculate: True depth of the body Volume of the object Key equation: Object shape + Residual anomaly + Object Density → True Depth + Object Volume An Introduction to Applied and Environmental Geophysics by John M. Reynolds Principles of applied geophysics by D.S. PARASNIS https://youtu.be/Vk3qk9sGVUU?si=6xpvYOC2rnL1fk25 Anomalies of Different Bodies Gravity anomalies associated with geometric forms An Introduction to Applied and Environmental Geophysics by John M. Reynolds Depth Determination Determine depth to the center of mass and/or depth to the top of the causative body Limiting depth = maximum possible depth of the body’s top Methods • Use direct / forward methods → anomaly data used to estimate depth & mass • Most common: Half-Width Method • Measure half-width (x½ ) of the anomaly at half the peak amplitude • Different definitions exist (half of anomaly vs full width at half maximum) • Formulae differ depending on definition Limitations & Cautions • Estimates often overestimate true depth • Body has finite size, not a point mass • Works best if all density contrasts have same sign (all positive or all negative) • Not effective for compact mineral bodies • Always check results against geological constraints Depth Determination Smith Rules (Limiting Depth Estimation) widely used in gravity interpretation. Aim: Estimate the limiting depth (d) to the top of a geological body. Gradient–Amplitude Ratio Method (1, 2 in Box 2.21) • Works on an isolated anomaly (all positive or all negative) • Based on relationship between: • Maximum anomaly amplitude (Δgmax) • Maximum horizontal gradient (Δg′max) • Formulae (Box 2.21) give depth-to-top estimates using this ratio Second-Derivative Method (3 in Box 2.21) • Uses the rate of change of the gravity gradient along the profile • Thought to yield more accurate depth estimates • Relies on curvature of the anomaly shape (concavity/convexity) • It is thought that second-derivative methods produce more accurate estimates of limiting depths. An Introduction to Applied and Environmental Geophysics by John M. Reynolds Mass determination Anomalous Mass: Concept • = Difference in mass between a geological body and its host rock • Two cases: • Excess mass → high-density body (e.g., ore deposit) • Mass deficiency → low-density body (e.g., cave, salt dome) Method 1 – Half-Width & Geometric Assumptions • Based on the gravity anomaly half-width (x½ ) • Body assumed to be a simple geometry (sphere, cylinder, slab) • Mass = density × volume – compared against gravityderived estimate • Example: air-filled cavity → negligible mass → calculated deficiency = missing rock Mass determination Method 2 – Gauss’s Theorem • From potential theory (Grant & West, 1965) • Advantages: • No assumptions about shape or size • Can calculate total anomalous mass directly from anomaly • Steps: • Remove regional gravity field • Divide anomaly area into rings & segments (δA) • Sum contributions → total mass Surface Imaging Introduction to Applied Geophysics 지반구조영상화 Geomagnetic Method Types of Geophysical Methods: Magnetic Survey • Measures and maps variations in Earth’s magnetic field associated with magnetic minerals in crustal rocks • Earth’s magnetic field is not uniform → influenced by subsurface materials • Different minerals have their own magnetic characteristics. • Variations in the measurements reveal the magnetic properties of rocks • The method can be applied to mineral exploration, mapping, locating buried objects Earth’s magnetic field = Magnetosphere Subsurface material’s magnetic fields https://physics.aps.org/articles/v9/91 https://www.researchgate.net/figure/Figure-R1-Skewnessof-a-magnetic-anomaly-due-to-a-uniform-arbitrarilymagnetized-source_fig1_257140351 https://www.wikiwand.com/ms/map/Bijih_besi Applications of Magnetic Surveys Small-scale (near-surface): • Locating pipes, cables. • Engineering site investigations. Large-scale (regional): • Geological mapping. • Hydrocarbon exploration. • Mineral exploration. Magnetic surveys now detect a wide range of subsurface features • Mineral exploration: Magnetite ore. • Structural geology: Buried hills, geological faults, igneous intrusions. • Energy exploration: Salt domes linked with oil fields. • Other targets: Concealed meteorites, buried magnetic objects (pipelines, infrastructure). An Introduction to Applied and Environmental Geophysics by John M. Reynolds Complementary Methods • Magnetic + Gravity surveys: • Used together before seismic surveys. • Help define basement structures and subsurface geology. • Seismic reflection: • Provides detailed subsurface imaging after magnetic/gravity surveys. Basic Concepts • • • • A bar magnet produces a magnetic field shown by flux lines. Flux lines converge near the ends of the magnet = magnetic poles. Magnetic poles always exist in pairs (dipole). A monopole = an isolated pole (theoretical, not real in nature). Magnetic pole Force Between Magnetic Poles • If two poles of strength m₁ and m₂ are separated by distance r: • Like poles repel (S S/N N). • Opposite poles attract (S→←N). • • Formula for force is similar to gravitational attraction. Both gravity and magnetism are potential fields, described by the same type of theory. Flux line Magnetic pole An Introduction to Applied and Environmental Geophysics by John M. Reynolds Magnetic Flux Density (B) – Magnetic Induction Magnetic flux density (B) describes the strength and direction of a magnetic field at a point in space. It tells you how much magnetic “force” passes through a given area. • Flux density (B): flux per unit area. • Unit: Tesla (T) = Weber/m². • Vector quantity (magnitude & direction) • Older unit: Gauss (G) • 1 T = 10,000 Gauss. • For geophysics: • Nanotesla (nT) is used. • 1 nT = 10⁻⁹ T = 10⁻⁵ Gauss. • Also called gamma in older literature. • Magnetometers measure B (magnetic flux density) in nT. • In surveys, anomalies are measured as changes in nT (nanoTesla) against the background Earth’s field (~30,000–60,000 nT). https://www.studyforfe.com/blog/fundamentals-of-magnetic-flux-and-reluctance/ Magnetic Field Strength (H) • • • A magnetic field is also created by electric currents. Magnetic field strength describes the intensity of the external magnetic field source It tells us how strong the applied field is before the material’s response is added in. • Defined using Biot–Savart’s Law: • At the center of a loop of radius r carrying current, H = 1 / (2r). • • H = magnetising field strength (magnetising force) Units: Amperes per metre (A/m). • The magnetic field can be described in two ways: • 𝑯= magnetic field strength (depends only on current or source). • 𝑩= magnetic flux density (includes effect of medium). They are related by: 𝐵 = 𝜇𝐻 where • 𝝁= magnetic permeability of the medium (how easily the material supports magnetic field lines). • In free space: 𝜇0 = 4𝜋 × 10−7 H/m. • • Imagine wind blowing: •𝐻= how hard the wind is blowing (strength). •𝐵= how many wind “gusts” are actually hitting a sail (depends on both wind and the sail’s material). This means: • In air/vacuum, 𝐵and 𝐻are almost the same (just scaled by 𝜇0 ) • In rocks, minerals with high magnetic susceptibility can increase B by concentrating magnetic field lines. Magnetic Susceptibility (κ ,χ) • A measure of how easily a material becomes magnetised when placed in a magnetic field. • • Expressed as κ (kappa). Dimensionless (no units). • Relationship to flux density (B) and magnetizing field (H): B = 𝜇H • • • • • 𝜇r = 1 + κ Key idea: Higher κ → stronger induced magnetization. Relative permeability (μᵣ) tells us how much more (or less) permeable a material is compared to free space (vacuum). Positive κ: • Materials that enhance the magnetic field (e.g. magnetite, hematite). Negative κ: • Materials that oppose the magnetic field (diamagnetic substances like quartz, calcite, copper). Geological importance: • Identifying rock/mineral types. • Distinguishing archaeological features (burnt soil, building stone, etc.). An Introduction to Applied and Environmental Geophysics by John M. Reynolds Vacuum: Relative permeability μr = 1 Susceptibility κ = 0 Air & water: Very close to vacuum values. Rocks & soils: κ varies depending on mineral content (especially magnetic minerals like magnetite). Intensity of Magnetisation (J) • • • • • • • • Shows how strongly a material becomes magnetized when exposed to a magnetic field. Fundamental property in describing the magnetic state of rocks. Units: Amperes per metre (A/m). Stronger κ → stronger induced J. J = κH Intensity of magnetisation (J) helps us: • Describe the magnetic state of any rock body. • Predict how rocks interact with Earth’s field. • Interpret anomalies in magnetic survey data. Key in distinguishing between weakly magnetic sediments vs. strongly magnetic igneous rocks or archaeological features. If a body of volume V is uniformly magnetized with intensity J: • Magnetic Moment (M) = pole strength (m) × pole separation (l) In simple terms: J= • M V Magnetic moment per unit volume = intensity of magnetisation. An Introduction to Applied and Environmental Geophysics by John M. Reynolds Summary of the Basic Terms Magnetic flux density (B) [nT] Describes the strength and direction of a magnetic field at a point in space It tells us how much magnetic “force” passes through a given area. Magnetic field strength/Magnetizing force (H) [A/m] Describes the intensity of the external magnetic field source It tells us how strong the applied field is before the material’s response is added in. Magnetic Susceptibility (κ, χ) [-] Measures how easy a material becomes magnetised when placed in a magnetic field Intensity of Magnetisation (J) [A/m] Shows how strongly a material becomes magnetized when exposed to a magnetic field Magnetic permeability (μ) [H/m] how easily the material supports magnetic field lines Relative permeability (μᵣ) [-] tells us how much more (or less) permeable a material is compared to free space (vacuum). Induced and Remanent Magnetisation (J) Induced Magnetisation (Ji): Temporary magnetisation caused by the Earth’s present magnetic field. • Caused by an external magnetic field (H). • Disappears when the external field is removed. • Proportional to magnetic susceptibility (κ). Remanent Magnetisation (Jr): Permanent magnetisation locked into a rock from the past. • Permanent magnetisation retained by minerals. • Exists even without an external field. • Results from past geological/thermal events. Rocks Contain Both • Most rocks with magnetic minerals have: • Ji (induced) – aligns with today’s Earth field. • Jr (remanent) – “locked in” from past fields/events. • Resultant Magnetisation (J): • Vector sum of Ji + Jr. • Has its own direction and magnitude. Induced magnetisation • Think of the Earth as a giant bar magnet (it has a magnetic field). • When a rock is placed in this field, its magnetic minerals (like magnetite) act a bit like little compass needles. • They line up with the Earth’s magnetic field right now. • This effect disappears or changes if the Earth’s magnetic field changes. Remanent magnetisation • Some rocks can “lock in” magnetism when they form. • For example, when lava cools, tiny magnetic minerals inside align with the Earth’s field at that time. Once the lava hardens, the alignment gets “frozen in.” • Even if the Earth’s magnetic field later changes direction, the rock keeps its original magnetisation. Induced and Remanent Magnetisation Why it Matters in Magnetic Survey • The orientation & strength of J determine: • Amplitude of the anomaly. • Shape of the anomaly. • Unlike gravity, which depends mainly on density, magnetics has more variables (κ, Ji, Jr, mineral type, etc.). • This adds both complexity and opportunity in interpretation. • Induced magnetisation: • Helps detect contrasts between soils and rock bodies. • Remanent magnetisation: • Crucial in identifying burned features (kilns, hearths, pottery). • Preserves a record of Earth’s magnetic field at time of cooling → useful in archaeomagnetism. • • • • Always consider both Ji and Jr in data interpretation. Remanent magnetisation may dominate in volcanic or fired materials. Induced magnetisation often dominates in sediments and unburnt soils. Result: magnetic anomalies are not always straightforward → multiple possible sources. Diamagnetism, Paramagnetism, Ferrimagnetism, Ferromagnetism Rocks and minerals can respond to magnetic fields in different ways, depending on the arrangement of their electrons and magnetic moments. Origin of Magnetism in Atoms • Magnetic moments come from: • Orbital motion of electrons • Spin of electrons • Paired electrons → cancel each other’s spin moment • Unpaired electrons → create a net magnetic moment Type Strength Alignment Memory? Example minerals/materials Diamagnetism Very weak Opposes field No Quartz, calcite, water Paramagnetism Weak With field No Olivine, pyroxene Ferromagnetism Very strong All parallel Yes Iron, cobalt Ferrimagnetism Strong Opposite, unequal Yes Magnetite, ferrites https://www.vedantu.com/question-answer/the-primary-origin-of-magnetism-lies-in-the-a-class-12-physics-cbse-5f7da4519a8d2a355d51e0de https://www.sciencedirect.com/topics/medicine-and-dentistry/ferromagnetic-material Diamagnetism, Paramagnetism, Ferrimagnetism, Ferromagnetism Diamagnetism • All electron shells complete → no unpaired electrons • Weak, negative susceptibility (κ < 0) • Induced magnetisation opposes applied field • Electrons in the mineral create a tiny magnetic field opposite to the applied field. • This means diamagnetic materials are slightly repelled by a magnet. • Very weak effect → often negligible in geology Paramagnetism • Caused by unpaired electrons in incomplete shells • Weak, positive susceptibility (κ > 0) • Some minerals have unpaired electrons → they behave like tiny magnets. • In the presence of an external magnetic field, they weakly align with it. • The effect disappears when the field is gone (no memory). • Magnetic moments align with applied field, but… • Random thermal motion reduces alignment • Curie–Weiss Law: susceptibility decreases with ↑ temperature https://www.sciencedirect.com/topics/medicine-and-dentistry/ferromagnetic-material Diamagnetism, Paramagnetism, Ferrimagnetism, Ferromagnetism Ferromagnetism & Magnetic Domains • Very strong magnetism. • Strong susceptibility, large spontaneous magnetisation • Due to strong coupling of unpaired electron spins • Forms magnetic domains (~1 μm) • Vanishes above Curie Temperature (Tc) → becomes paramagnetic • Magnetic moments of atoms align parallel to each other, creating a large net magnetisation. • Can stay magnetised even after the external field is removed. • Rare in nature, but pure iron and some alloys show this. Antiferromagnetism • Spins align antiparallel and equal strength → cancel each other • Net effect: very weak magnetisation (sometimes parasitic/defect-related) Ferrimagnetism (Most Important in Geophysics) • Unequal anti-parallel alignment of spins → net magnetisation • Very large susceptibilities + strong remanent magnetisation • Strong (but slightly less than ferromagnetism). • Common in many magnetic minerals (like magnetite). • Dominant source of magnetic anomalies in rocks & soils • Very important in geophysics, because many rocks owe their magnetism to ferrimagnetic minerals. https://www.sciencedirect.com/topics/medicine-and-dentistry/ferromagnetic-material Curie Temperature & Key Implications for Geophysics Curie Temperature (Tc): threshold above which permanent magnetism is lost • Magnetite: 550–580 °C • Haematite: 650–680 °C • Titanomagnetite: ~100–200 °C Oxidation effects: • Titanomagnetite → titanomaghemite → magnetite → haematite • Raises Tc, but reduces magnetisation strength Key Implications for Geophysics • Most magnetic anomalies come from ferrimagnetic minerals (esp. magnetite). • Rock magnetism depends on: • Mineralogy • Grain size & domain structure • Oxidation & alteration history • Curie Temperature defines limits for remanence in volcanic/igneous rocks. • Understanding hysteresis → explains why susceptibility values are not unique. Susceptibility of Rocks and Minerals Magnetic susceptibility (κ) = how easily a rock can be magnetised. • In magnetics, κ plays the same role as density in gravity surveys. • High κ → stronger magnetic anomaly. • Controlled by the presence of ferro- & ferrimagnetic minerals. General Susceptibility Trends (Values vary widely – only rough guidelines.) • Basic / ultrabasic igneous rocks → highest κ (lots of magnetite). • Acidic igneous & metamorphic rocks → intermediate to low κ. • Sedimentary rocks → very low κ (exceptions: iron-rich layers). Factors Controlling Susceptibility • Mineralogy – main control (magnetite, ilmenite, pyrrhotite). • Grain alignment & shape – orientation affects κ. • Magnetic fabric – anisotropy of susceptibility (AMS). • Alteration – oxidation/reduction changes magnetic properties. An Introduction to Applied and Environmental Geophysics by John M. Reynolds Remanent magnetisation and Königsberger Ratio Induced magnetisation (Ji): • Temporary, aligns with the present Earth’s magnetic field. • Magnitude depends on susceptibility κ × field strength H. Remanent magnetisation (Jr ): • Permanent, “locked in” when the rock formed. • Independent of today’s field. • Definition: The magnetisation a rock keeps after the external magnetic field is removed. • Caused by magnetic minerals (mainly magnetite, hematite, maghemite). • Acts as a “magnetic memory” of the Earth’s field at the time of rock formation. Remanent magnetisation can be different in direction from today’s Earth field. • Resultant Magnetisation (J): • Vector sum of Ji + Jr. • Has its own direction and magnitude. Remanent magnetisation and Königsberger Ratio Types of Remanence 1. NRM – Natural Remanent Magnetisation (NRM): • Permanent magnetisation that remains when external field (H) = 0. • Acquired through several processes (TRM, DRM, CRM, VRM, etc.). • Can dominate over induced magnetisation (Ji), especially in igneous rocks. 2. TRM – Thermal Remanent Magnetisation • Cooling below Curie temp • Lava cools through the Curie temperature → grains lock in Earth’s field direction. 3. DRM – Detrital Remanent Magnetisation • Alignment during deposition. • Sediment grains align with the field as they settle. 4. CRM – Chemical Remanent Magnetisation • Mineral alteration/formation • New magnetic minerals grow during chemical changes. 5. VRM – Viscous Remanent Magnetisation • Slow acquisition in weak field • Very slow acquisition of magnetisation over time in Earth’s field. 6. PDRM – Post-Depositional Remanent Magnetisation. An Introduction to Applied and Environmental Geophysics by John M. Reynolds Remanent magnetisation and Königsberger Ratio Kö nigsberger Ratio (Q) Indicates dominance of permanent vs. induced effects in rocks. 𝐽𝑟 𝑄= 𝐽𝑖 𝐽𝑟 =remanent magnetisation 𝐽𝑖 =induced magnetisation Interpretation of Q Q < 1 → induced dominates. Anomalies are aligned with today’s field. Common in sediments. Sedimentary & metamorphic rocks (except iron-rich). Q ≈ 1 → both contribute equally Slowly crystallised igneous & thermally metamorphosed rocks. Q > 1 → remanent dominates. Anomalies may appear shifted, reversed, or unexpected. Common in volcanic rocks (e.g., basalts). Q ≈ 10 → Volcanic rocks. Q ≈ 30-50 → Rapidly quenched basalts. quench: to cool (something, such as Kö nigsberger Ratio (Q) can be expressed in terms of the Earth’s magnetic field at a given locality and the susceptibility of the rocks heated metal) suddenly by immersion In surveys: Low Q → anomalies are predictable. High Q → anomalies may be misleading unless remanence is considered. An Introduction to Applied and Environmental Geophysics by John M. Reynolds The Earth’s magnetic field • Earth’s magnetic field: ~25,000–65,000 nT (depending on latitude). • Geological/archaeological anomalies: a few nT to hundreds of nT. → The anomalies are tiny “wiggles” on top of the huge background field. • To detect them, we must know the Earth’s normal field at that place and time. We need to know the Earth’s magnetic field because: • It is the background field on which anomalies are superimposed. • It controls the direction and shape of induced anomalies. • It helps distinguish induced vs remanent magnetisation. • It must be removed during data reduction to isolate anomalies. • It varies with latitude, longitude, and time, so we must correct for it. https://physics.aps.org/articles/v9/91 The Earth’s magnetic field Main Source (Internal): • Generated by fluid motion in Earth’s outer core (geodynamo effect). • Accounts for ~90–95% of the total field at the surface. Secondary Contributions: • External Currents – in the ionosphere & magnetosphere. • Induced Currents – generated in the Earth by external field variations. • Crustal Magnetisation – remanent and steady-state induced magnetisations of crustal rocks. Magnetosphere: • Shields Earth from solar wind & harmful cosmic radiation. • Crucial for maintaining life on the planet. Relevance for Exploration Geophysics: • Variations in geomagnetic components can influence survey accuracy. • Requires correction & data reduction for reliable anomaly interpretation. https://en.wikipedia.org/wiki/Earth%27s_magnetic_field Ionosphere & Magnetosphere Ionosphere • A region of the upper atmosphere where solar radiation ionises atoms and molecules → producing free electrons and ions. • Key features: • Electrically charged → can conduct currents. • Affects radio wave propagation (ex. GPS signals). • Varies daily (stronger in daytime due to solar radiation). • Why important in magnetics: • Electrical currents in the ionosphere create short-term fluctuations in the Earth’s magnetic field. • These fluctuations cause diurnal variations in magnetometer readings, which we must correct. https://www.britannica.com/science/ionosphere-and-magnetosphere Ionosphere & Magnetosphere Magnetosphere • The vast region of space around Earth where the planet’s magnetic field dominates over the solar wind. • Key features: • Shaped like a “teardrop” → compressed on the sun-facing side, stretched into a long tail away from the Sun. • Protects Earth from charged particles from the Sun (solar wind). • Disturbances here create geomagnetic storms and auroras. • Why important in magnetics: • Magnetic storms in the magnetosphere can cause sudden large changes in Earth’s field (hundreds of nT). • These affect ground surveys and must be accounted for (using base stations, IGRF models). An Introduction to Applied and Environmental Geophysics by John M. Reynolds https://www.britannica.com/science/ionosphere-and-magnetosphere The Earth’s magnetic field 1. The main dipole field 2. The non-dipolar field • Earth’s field = Dipole (~90%) + Non-dipole (~10%). • Dipole: • simple, bar-magnet-like, stable, global. • the large background we always subtract (using IGRF). • Non-dipole: • irregular, complex, regional, changes more quickly. • explains regional variations and why anomalies differ from a simple dipole model. • Both are important because we must remove them before interpreting anomalies from rocks. • (both must be understood to reduce data properly and isolate local geological anomalies.) An Introduction to Applied and Environmental Geophysics by John M. Reynolds The Main Dipole Field Dipolar Nature • The Earth’s main magnetic field behaves like a tilted dipole electromagnet. • Inclined at ~11.5° to Earth’s rotational axis. • Produced by electric currents in the liquid outer core → geodynamo effect. Geomagnetic vs. Dip Poles • Geomagnetic poles = where the axis of the best-fit dipole intersects Earth’s surface. • Dip (magnetic) poles = where the magnetic field points vertically. • Positions of both shift over time (secular variation). Field Variation • Intensity: ~30,000 nT at magnetic equator / ~60,000 nT at poles. • Field changes slowly (secular variation) and occasionally reverses polarity. • Reversals studied in palaeomagnetism; used in magnetostratigraphy for dating geological events. Vector Description • Field defined by: • Declination (D) → angle between magnetic north & true north. • Inclination (I) → angle of field relative to horizontal (90° at poles, 0° at magnetic equator). • Total intensity (F) → strength of field vector. An Introduction to Applied and Environmental Geophysics by John M. Reynolds Geomagnetic Poles & Dip Poles • Geomagnetic poles • where the axis of the best-fit dipole intersects Earth’s surface. • the points on Earth’s surface where the axis of the best-fit dipole (the simplified bar-magnet model of Earth’s field) intersects. • Dip (magnetic) poles • The points where the magnetic field vector is vertical (inclination = ±90°). • A dip pole is simply the place where a compass needle, would point straight down into the Earth (north pole) or straight up out of the Earth (south pole). • Because Earth’s field isn’t a perfect dipole, the dip poles wander around and are not exactly opposite each other. Earth’s magnetic field doesn’t just point north — it also tilts downward into the ground (in the Northern Hemisphere) or upward out of the ground (in the Southern Hemisphere). •This tilt angle = inclination (I). •At the magnetic equator, I = 0° (field is horizontal). •At mid-latitudes, I is between 0° and 90°. •At the dip poles, I = ±90° (field is vertical). An Introduction to Applied and Environmental Geophysics by John M. Reynolds https://www.researchgate.net/publication/288162460_Magnetic_Orientation_in_Migratory_Songbirds An Introduction to Applied and Environmental Geophysics by John M. Reynolds The Non-Dipolar Field • • • The Earth’s magnetic field is not a perfect bar magnet (dipole). About 90% of the field comes from the main dipole. The remaining ~10% is from non-dipole components → irregular variations that cannot be explained by a simple dipole. What Causes It? • Generated by the same geodynamo in the liquid outer core. • But the flow of molten iron is complex → produces extra field components besides the dipole. Characteristics • Much weaker than the dipole, but still important. • Changes more quickly in time than the dipole • Explains why the actual magnetic poles (dip poles) wander and why the geomagnetic field isn’t perfectly symmetric. • Amplitudes: up to 20,000 nT (~⅓ of Earth’s total field). • Large-scale features span thousands of km. Why It Matters in Geophysics • Magnetic survey data are corrected using global field models (e.g., IGRF), which include both dipole + non-dipole terms. • Helps explain regional differences in Earth’s field. • For surveys: if you don’t subtract the full reference field (dipole + non-dipole), your anomaly map will be misleading. The Non-Dipolar Field • Earth’s magnetic field ≠ perfect dipole. • Spherical harmonic analysis shows it can be modelled by 8–12 fictitious dipoles near the liquid core. Why Spherical Harmonics? • Powerful mathematical tool for breaking complex fields into simpler components. • Provides a way to calculate global magnetic field distribution and intensity. • Helps distinguish main field (core-generated) from local anomalies (crustal sources). International Geomagnetic Reference Field (IGRF) • Standard global model of Earth’s magnetic field. • The IGRF model is built using spherical harmonics (mathematical expansion). • The first term = dipole field. • The higher-order terms (quadrupole, octupole, etc.) = non-dipole field. • Updated every 5 years to account for secular variation (slow field drift). • Used worldwide in magnetic survey data reduction and interpretation. → it removes both dipole and non-dipole contributions, leaving only local anomalies. An Introduction to Applied and Environmental Geophysics by John M. Reynolds Magnetic Instruments Magnetic Instruments Magnetometers used specifically in geophysical exploration can be classified into three groups: 1. torsion (and balance): still in use at 75% of geomagnetic observatories, particularly for the measurement of declination. 2. fluxgate 3. resonance An Introduction to Applied and Environmental Geophysics by John M. Reynolds Fluxgate Magnetometer Origin & Purpose • Developed during World War II for submarine detection. • Later adapted for geophysical exploration & archaeological prospection. Principle of Operation • Two parallel ferromagnetic cores wound with primary & secondary coils. • Primary coils: driven by alternating current (50–1000 Hz). • In absence of external field → induced voltages in secondary coils cancel (zero output). • In presence of external magnetic field → one core saturates earlier, producing phase shift → non-zero voltage output. • Output amplitude ∝ strength of external field component. Advantages • Measures specific magnetic components aligned with sensor cores. • Insensitive to steep field gradients (better than resonance devices). • Provides continuous output → excellent for airborne surveys. • Can achieve ±1 nT accuracy with good insulation & orientation control. Limitations • Portable ground models may suffer from temperature effects → lower resolution (±10–20 nT). https://archaeologicalsurveys.wordpress.com/2009/05/07/working-with-the-grad601-2/ An Introduction to Applied and Environmental Geophysics by John M. Reynolds https://www.imperial.ac.uk/space-and-atmospheric-physics/research/areas/space-magnetometer-laboratory/space-instrumentation-research/magnetometers/fluxgate-magnetometers/how-a-fluxgate-works/ Resonance Magnetometers Proton Free-Precession Magnetometer (Proton Magnetometer) Principle • Sensor: Bottle of proton-rich liquid (e.g., water, kerosene) wrapped in coil. • Protons: Each has magnetic moment (M) + angular momentum (like tiny spinning tops). • In Earth’s field (F) → most align parallel, some antiparallel → net magnetisation forms. Operation • Polarisation: Apply strong magnetic field (~50–100× Earth’s) at right angles. • Switch off field: Protons precess (spin) around Earth’s field at Larmor frequency (fp). • Induced signal: Precession produces alternating voltage in coil. • Decay time: Signal lasts 2–3 seconds → enough to measure fp. • Precision: ±0.1 nT (requires frequency measured to ±0.004 Hz). Limitations • Accuracy reduced in strong field gradients: • e.g., gradient of 500 nT/m → ~75 nT difference across 15 cm sensor bottle. • Precision: ~1 nT at 400 nT/m, ~0.5 nT at 200 nT/m. • Measurement rate is slow (not continuous). An Introduction to Applied and Environmental Geophysics by John M. Reynolds Gradiometers Principle • Measure difference in total magnetic field strength between two identical magnetometers. • Sensors separated by 0.5–1.5 m (ground instruments). • Gradient expressed in nT/m, applied at mid-point between sensors. Advantages • No diurnal correction needed – both sensors equally affected by daily field variations. • Suppress long-wavelength noise → enhances shallow/local anomalies. • High-resolution → excellent for detailed mineral exploration. Instrument Types • Fluxgate gradiometers: • Continuous reading, good for automatic data logging. • Widely used in archaeological prospection and near-surface work. • Resonance-type gradiometers: • Higher sensitivity, used in detailed surveys. • Modern caesium vapour gradiometers: • Sensitivity: 0.05 nT. • Fast sampling: 10 readings/sec. • Can integrate with differential GPS for simultaneous position + field logging. https://previous.terradat.co.uk/survey-methods/magnetics/ Magnetometer vs Gradiometer Magnetometer What it measures: • The absolute magnetic field strength (flux density, 𝐵) at a single point. • Usually gives the total field intensity in nanotesla (nT). Use in surveys: • Records Earth’s field + geological/archaeological anomalies. • Needs a base station magnetometer for diurnal correction (since it measures absolute values). • To map regional and deep features, we need the absolute magnetic field (total intensity) over wide areas. Magnetometer = single sensor → measures the absolute magnetic field. Gradiometer What it measures: • The difference in magnetic field between two points separated by a fixed distance. • Usually arranged vertically (one sensor above the other). • Measures the field gradient (nT/m). Use in surveys: • Cancels out the Earth’s large background field (and diurnal variations) automatically, because both sensors see the same big field. • Highlights local anomalies caused by near-surface features. • Ideal for archaeological prospection (walls, ditches, kilns), but not for large-scale geology. • Gradiometers enhance shallow, local anomalies but suppress the broad background. Gradiometer = two sensors → measures the difference in field, cancelling background and enhancing local anomalies. Magnetic Survey and Corrections Magnetic Surveys • • • Magnetic surveys generally involve measuring the total magnetic field in the area, and then subtracting the earth’s normal or expected magnetic field. The difference obtained can be positive, meaning the magnetic field is higher than expected, or negative, where the field is lower than expected. These are called positive/negative anomalies which are due to different objects in earth’s crust (ranging from WW2 bombs, metal pipes to geologic features) Ground surveys • Typically for geological surveys, consists of magnetic survey lines spaced every 20-40m apart and oriented perpendicular to the geological strike of formations • In detailed geological surveys, line spacing may be as close as 1-2m • In engineering and environmental surveys, line spacing will ideally be smaller than the size of the target object. • Magnetic materials in the wearing apparel of the observer, like keys, wrist watches can interfere with the instrument. Airborne surveys • Most aeromagnetic surveys are flown at a height between 70~200m, but much lower altitudes (30~35m) are also done for increased resolution. • Flight paths should intersect for allow for reoccupation of stations and allow for diurnal corrections Base Stations in Ground Magnetic Surveys Purpose: • Monitor diurnal variations of the Earth’s magnetic field. • Provide reference data for correcting survey measurements. Site Selection Criteria: • Must be located away from suspected magnetic targets (e.g., ore bodies, buried metal). • Should avoid cultural noise sources (power lines, vehicles, fences). • Chosen where the magnetic gradient is flat to avoid spurious readings. Practical Considerations: • Base station must be easy to access, relocate, and re-occupy throughout the survey. • Typically records continuous or regular time-series data. • Corrections are later applied to survey results → improving accuracy and reliability. Magnetic Surveying - Noise Sources of Noise in Magnetic Data • All raw datasets contain unwanted signals in addition to subsurface anomalies. • Noise can come from: • Personal items: keys, knives, some wristwatches. • Field equipment: geological hammers near proton magnetometers. • Cultural features: cars, metal sheds, power lines, buried pipes, railways. • Geological background: mafic rock walls, igneous intrusions. Good Practice in the Field • Keep all magnetic objects away from the sensor. • Maintain a safe distance from cultural noise sources. • Always inspect surroundings before recording. Next Step • After minimizing noise → apply corrections Corrections - Diurnal Variation • Earth’s magnetic field changes daily due to ionospheric currents. • Base station readings record this drift → used to correct survey data. • Example: If field ↑ 10 nT at point A → subtract 10 nT from A. • If field ↓ 19 nT at point B → add 19 nT to B. • Gradiometers: No correction needed (both sensors equally affected). • Airborne/Marine surveys: Use tie-lines & intersections instead of base stations. An Introduction to Applied and Environmental Geophysics by John M. Reynolds For example, at point A in Figure 3.25, the ambient field has increased by 10 nT and thus the value measured at A should be reduced by 10 nT. Similarly, at B, the ambient field has fallen by 19 nT and so the value at B should be increased by 19 nT. Corrections – Terrain Corrections • • • • Terrain corrections in magnetics are rare but critical in rugged areas with magnetic rocks. Without correction → anomalies may reflect topography, not geology. Terrain can distort magnetic measurements if the ground itself is magnetic. Corrections are more complex than in gravity surveys. When Corrections Are Needed • Low-susceptibility rocks (e.g., sedimentary): • Minimal distortion → terrain correction usually unnecessary. • High-susceptibility rocks (e.g., igneous, metamorphic): • Distort the Earth’s magnetic field. • Terrain correction factor must be applied. • Corrections: Complex, computationally heavy. • Alternative: Upward continuation (process data to a higher reference plane). Data Reduction In order to produce a magnetic anomaly map of a region, the data have to be corrected to take into account the effects of latitude and longitude. Why Reduce Data? • To isolate magnetic anomalies caused by subsurface geology. • Must remove effects of Earth’s main magnetic field (varies with latitude & longitude). Latitude & Longitude Effects • Earth’s magnetic field strength: • 25,000 nT at magnetic equator & 69,000 nT at poles. • Increase in magnitude with latitude needs to be taken into account Latitude & Longitude Correction 1. Basic correction using IGRF • At any survey location, data can be corrected by: δF = Fobs − Fth • Fobs = measured field value • Fth = theoretical field value from the International Geomagnetic Reference Field (IGRF). • This method works well near geomagnetic observatories where the IGRF is accurate. • But in many regions, the IGRF is too crude. 2. Local correction using gradients • In many places, IGRF may be too crude → Instead, a local correction is applied. • The correction is assumed to vary linearly across the survey area. • Regional latitudinal (ϕ) and longitudinal (θ) gradients are determined and tied to a base value (F0) at a reference point (e.g., southeast corner of survey). • Gradients are expressed in nT/km: • δF/δϕ → northward gradient • δF/δθ → westward gradient • Example (UK): • 2.13 nT/km north • 0.26 nT/km west Latitude & Longitude Correction 3. Calculating anomalies The anomalous value of the total field (δF) can be calculated arithmetically (Box 3.7). 4. Statistical method (residual field) • Another approach is to statistically determine the trend of the regional field. • This isolates the higher-frequency anomalies, similar to gravity residuals. • Then: δF = Fobs − Fregional • The result is a residual field δF (Figure 3.28A). 5. Small survey areas (< 500 × 500 m) Figure 3.28B • For very small-scale surveys (archaeology, engineering, mineral prospecting), using regional gradients is not practical. • Instead, use a local base station (Fb) away from suspected sources. • Correction is done by: δF = Fobs − Fb • Fobs = diurnally corrected observed value • Fb = base station value An Introduction to Applied and Environmental Geophysics by John M. Reynolds Qualitative Interpretation Qualitative Interpretation Display of Magnetic Data • Profiles (line plots) or maps (contour/color maps). • Different interpretation approaches depending on display. Complications in Magnetic Interpretation • Dipolar Nature of Earth’s Field • Anomalies may appear as: • Positive peak only • Negative peak only • Doublet (positive + negative) • Remanent Magnetisation • Presence, intensity, and direction (Jr) often unknown. • Can distort anomaly shape and polarity. Non-Uniqueness Problem • Multiple geophysical models can explain the same anomaly. • Use other geophysical methods (e.g., gravity, seismic) + geological data. • Caution: Geological “facts” may also be interpretations → don’t accept uncritically. Qualitative Interpretation Magnetic Anomalies: Vector Summation • Total anomaly = Earth’s field (F) + induced magnetisation (Ji) + remanent magnetisation (Jr). • Northern Hemisphere: • Negative anomaly to the north • Positive anomaly to the south • (Opposite in Southern Hemisphere). Depth & Amplitude Clues • Short wavelength anomaly → shallow source. • Long wavelength anomaly → deeper source. • Equal amplitudes at different depths → deeper body must have stronger magnetisation. Displaying Corrected Data An Introduction to Applied and Environmental Geophysics by John M. Reynolds Profiles The simplest way to interpret magnetic profiles is by identifying zones with different magnetic behaviour: • Magnetically quiet zones → little variation → associated with rocks of low susceptibility. • Magnetically noisy zones → strong variation → indicate the presence of magnetic sources in the subsurface. Key clues: • The amplitude (positive or negative) of anomalies. • The local magnetic gradients. • Both help infer subsurface conditions. From profiles, we can: • Identify zones with magnetic sources. • Infer possible dip direction of targets. • Estimate relative intensities of magnetisation. Then: • Carry out more detailed fieldwork to collect additional data. • Or apply quantitative interpretation methods Profiles –example 1 • Profile shows both noisy and quiet segments. • Noisy segments → linked to metalliferous mineralisation. • The negative anomaly on the northern side of a doublet indicates: • Little remanent magnetisation (Jr). • Anomaly is mainly due to induced magnetisation (Ji). An Introduction to Applied and Environmental Geophysics by John M. Reynolds Profiles –example 2 • Profile across a beach section over three vertical dolerite dykes. • Dyke A and Dyke B → large positive anomalies. • Dyke C → broader low anomaly. • All dykes have similar geochemistry and petrology → hence similar susceptibilities. • Difference in magnetic response is explained by a magnetic reversal: • Dyke C intruded during a reversed polarity phase. • Dykes A and B intruded during a normal polarity phase. • Context: In the British Tertiary Igneous Province, doleritic intrusions lasted ~10 million years, spanning a magnetic reversal (Dagley et al., 1978). • Thus, magnetic profiles can distinguish between dykes from different intrusion phases—something not possible by rock description alone An Introduction to Applied and Environmental Geophysics by John M. Reynolds Maps • When magnetic data are collected on a grid (without spatial aliasing), they can be displayed as: • Contoured maps • 3D isometric projections • Image-processed displays • Even basic interpretation of these displays can quickly provide valuable geological information. • Key advantage of airborne surveys → they can reveal geology in areas covered by water. An Introduction to Applied and Environmental Geophysics by John M. Reynolds Pattern analysis of the same area (Figure 3.34B) compares well with Flinn’s geological interpretation (Figure 3.35) Main observations: 1.Magnetic lows (Band A): 1. Psammites and migmatised psammites injected by pegmatite. 2.Magnetic lows (Band B): 1. Gneissified semipelites and psammites intruded by granites and pegmatites. 3.Short-wavelength, high-amplitude magnetic highs (east of Band A): 1. Caused by pelitic schist and gneiss. 4.Structural features: 1. Truncation of NE–SW contours → associated with the Whalsay Sound Fault. 2. Lunning Sound Fault and Nesting Fault → separate zones of different magnetic character, aligned with aeromagnetic contours. 5.Localised positive anomalies (h, i, j): 1. Found along the thrust beneath the Quarff Nappe. 2. Attributed to phyllites containing ~4% hematite. 3. Hematite alone cannot explain the anomaly → additional contribution from remanent magnetisation. 6.Large-amplitude anomaly (k, SE corner): 1. Caused by a large buried intrusive (also detected in gravity data). 2. Other similar anomalies occur under the sea. 3. Exact rock type unknown because they have not been sampled. Basic Magnetic Anomaly Patterns Why Look at Anomaly Patterns? • Magnetic maps often show recognisable shapes → give clues about subsurface geology. • Interpretation starts by identifying patterns of anomalies. Key Magnetic Anomaly Patterns • Circular features • Roughly equal extent in all directions. • granitic intrusions, basic intrusions, ore bodies. • Long, narrow features • Elongated anomalies, often linear. • dykes, shear zones, folded strata, long ore bodies. • Dislocations • Anomaly shifted or offset. • faults or tectonic breaks. • Sheets • Broad, irregular high-intensity areas. • basalt flows, gabbro intrusions, greenstone belts. • Quiet zones • Low variation, little relief, no distinct pattern. • quartzite, limestone, monzonite (but exceptions exist if mineralised) Quantitative Interpretation Quantitative Interpretation • The goal is to determine: • Depth of a magnetic body. • Shape and size of the body. • Details of its magnetisation. Two main approaches • Direct method • Field data are interpreted directly to produce a physical model of the source. • Inverse method • A range of models is generated. • From these, synthetic magnetic anomalies are calculated. • These are then statistically fitted to the observed data. Practical limitations • The level of detail depends on: • The quality of the data. • The amount of data available. • The methods used (manual techniques or computer software). Magnetic anomalies from different geometric forms General principles • Magnetic data can be interpreted in terms of geometric forms approximating subsurface magnetised bodies. • 2D profiles → simple shapes like spheres or dipping sheets. • 3D models → more complex, used for irregular bodies 1) Common geometric models • Sphere – uniformly magnetised (Fig. 3.36). • Total field anomaly plus horizontal and vertical components. • Amplitude of this anomaly depends on the magnetisation strength and the depth An Introduction to Applied and Environmental Geophysics by John M. Reynolds Magnetic anomalies from different geometric forms 1) Common geometric models • Vertical dykes of different thicknesses (Fig. 3.37): • 50 m thick → wide anomaly, large amplitude (830 nT). • 5 m thick → narrow anomaly, small amplitude (135 nT). • Anomaly shape depends on strike: • East–west strike → positive–negative doublet (negative to the north*). • North–south strike → single symmetric positive peak. • Magnetised slabs (e.g., 70 m thick, 400 m long, 30 m deep): • North–south strike → symmetric M-shaped anomaly (Fig. 3.37B). • East–west strike → positive–negative inflection (negative to north*). * In the Northern Hemisphere, anomalies show negative to the north, positive to the south, because the Earth’s magnetic field dips northward. An Introduction to Applied and Environmental Geophysics by John M. Reynolds Magnetic anomalies from different geometric forms 2) Depth effects • As depth increases: • Anomaly amplitude decreases. • Anomaly becomes wider. 3) Dip effects 4) Low-susceptibility semicylinders 5) Latitude effects 6) Remanent magnetisation effects An Introduction to Applied and Environmental Geophysics by John M. Reynolds Simple Depth Determinations – Half Width Method Crude estimates from anomaly shape • For simple bodies (sphere or horizontal cylinder): • The width of the main anomaly peak at half its maximum value (δFmax/2) ≈ depth to the centre of the body. • For dipping sheets or prisms: • The gradient method is preferred to estimate the depth to the top of the body. • Rule of thumb: • Measure the linear extent (d) of the central straight portion of the main peak. • Depth ≈ d (±20%). An Introduction to Applied and Environmental Geophysics by John M. Reynolds Simple Depth Determinations – Half Slope Method Peters’ Half-Slope Method • Graphical method for estimating depth: • Draw a tangent (Line 1) at the point of maximum slope. • Construct a second line (Line 2) with half the slope of Line 1. • Draw two more lines parallel to Line 2 (Lines 3 and 4), tangential to the anomaly. • The horizontal distance (d) between Lines 3 and 4 ≈ depth to the body. An Introduction to Applied and Environmental Geophysics by John M. Reynolds Simple Depth Determinations Parasnis’ method for dipping dykes • For asymmetric anomalies over a dipping dyke of known latitude, dip, and strike: • Use both anomaly shape and amplitude. • Example: • δFmax = 771 nT, δFmin = −230 nT. • Sum = 541 nT → the point where anomaly amplitude = 541 nT gives the centre of the top edge of the dyke. • More complex cases (thick dipping sheets, other bodies) require advanced formulas. • Today, computer methods are normally used instead of manual calculations. An Introduction to Applied and Environmental Geophysics by John M. Reynolds Reduction to the Pole (RTP) Problem with Magnetic Data • Magnetic anomaly shape and amplitude depend on magnetic latitude. • Makes direct interpretation of TMI (Total Magnetic Intensity) maps difficult. Reduction to the Pole (RTP) • RTP = mathematical process to remove latitude effects. • Produces anomaly map as if survey was at the magnetic pole. How RTP Works • Assumes anomalies are due to induced magnetisation only. • Implemented in the frequency domain. • Problem: As inclination → 0° (magnetic equator) & π/2 (a north–south feature), the operator L(θ) → ∞. Issues with RTP • RTP amplifies noise in TMI data, especially at low latitudes. • Problems with: • Remanent magnetisation in rocks. • High-frequency anomalies (small wavelength ≈ grid cell size). • Causes “ringing” (artificial noise) during processing. An Introduction to Applied and Environmental Geophysics by John M. Reynolds Total magnetic field intensity profiles over a vertically-dipping dyke for striking (left) east–west and (right) north–south with magnetic inclinations ranging from 90◦ to 0◦. FromMacLeod et al. (1993). Surface Imaging Introduction to Applied Geophysics 지반구조영상화 Applied Seismology - Introduction and Principles Types of Geophysical Methods: Seismic https://www.researchgate.net/figure/Ground-vibrationinduced-by-blasting_fig1_346517507 https://www.researchgate.net/figure/Schematicrepresentation-of-a-vertical-seismic-reflectionexperiment_fig13_280835886 Crucial geophysical technique for imaging subsurface structure. It uses artificially generated or natural seismic waves to image and analyse subsurface structures based on differences in wave velocity and reflection. Applications • Oil & gas exploration • Environmental & engineering studies • Geological research • Creates detailed images of Earth’s interior using seismic waves Principle of Seismic Method • Uses artificially generated seismic waves • Sources: Heavy weight drops, explosives, vibrational sources • Waves travel through subsurface → recorded by geophones/accelerometers How It Works • Seismic waves travel at different velocities through different rocks • Variations in speed reveal: Composition, Density, Geometry of layers • Recorded data → processed to build seismic images Geophysical Methods https://shiawaves.com/english/news/world/america/chile/13 2032-7-5-magnitude-earthquake-hits-south-of-chiletsunami-threat-subsides/ https://www.pacgeo.biz/s-seismic/ Two types of methods • Passive • Method that detects naturally occurring fields or signals generated by the Earth itself • = Detect natural variations in Earth’s field • Examples: Earth’s gravitational field, Earth’s magnetic field, Natural seismic events (earthquakes) etc. Seismic wave generation Passive - Earthquake • Active • Method that generate their own signals and measures how the Earth responds to them (requires artificial energy sources) • = Transmit artificial signals into the ground ⭢ Signals modified by subsurface materials ⭢ measured and interpreted • Examples: Radar antennas (GPR), Hammers or weight drop (shallow seismic), Electro current generators etc. Active - Weight drop https://opentextbc.ca/physicalgeology2ed/chapter/9-1-understanding-earth-through-seismology/ Basic Principle of Seismology • Imagine clapping your hands in a cave. • Clap in a cave → echo • You make a sound → it travels through the air, hits the cave wall, and bounces back. • The time delay of the echo tells you how far away the wall is. • Seismology works the same way: • You create a signal at a known time (like an explosion, hammer strike, or vibroseis truck). • That signal travels as seismic waves into the ground. • When the waves hit boundaries between different underground layers, part of the energy reflects back and part refracts (bends and continues deeper). • We record the returning signals at the surface using sensors (geophones). • By measuring how long the waves take to return, we figure out the depth and properties of subsurface layers. Seismic Methods Seismic Methods Today Two main methods: 1. Refraction Seismology – Good for: • Finding bedrock depth • Engineering site investigations • Shallow subsurface studies 2. Reflection Seismology – Good for: • Oil & gas exploration (deep structures) • Shallow investigations (<200 m, especially <50 m) after 1980s thanks to better high-frequency sources and computers. Applications of Seismology • Hydrocarbon exploration (main driver). • Engineering & construction: depth to bedrock, site suitability. • Environmental & hazard studies. • Forensics: aircraft crash analysis (e.g., Lockerbie disaster, 1989). • Rescue operations: locating trapped miners. An Introduction to Applied and Environmental Geophysics by John M. Reynolds Seismic Waves Stress and Strain • Stress is the internal force per unit area within a body resisting an external load. • Strain is the resulting deformation or change in shape relative to the original dimensions. https://www.geeksforgeeks.org/physics/stress-and-strain/ Stress and Strain Stress • Definition: Stress = Force ÷ Area (F/A) Example: If you press your finger on a table, the pressure you apply per square centimeter is the stress. • Stress comes in two main forms: • Normal stress: Acts perpendicular (right angle) to the surface. => Like pushing down on a table. • Shear stress: Acts parallel to the surface. => Like sliding one card over another in a deck. Strain • Definition: Strain = Change in size ÷ Original size. • If a rod 1 m long is stretched by 1 cm → strain = 0.01 ÷ 1 = 0.01 (dimensionless). • Think of strain as “how much the material deforms”. => Stress is the cause; strain is the effect. Hooke’s Law • stress and strain are linearly dependent and the body behaves elastically until the yield point is reached. • (stress and strain are proportional: double the stress → double the strain) Yield point: The limit where elastic behavior ends. Beyond this point: • Material behaves plastically (ductilely) → permanent deformation. • Eventually, with more stress, the material fractures. • Example: Bending a plastic ruler too far => first elastic, then plastic, then it snaps. Elastic Moduli (Material Properties) • Materials have constants that describe how they deform: • Young’s modulus (E): Resistance to stretching. • Shear modulus (G): Resistance to shearing. • Bulk modulus (K): Resistance to compression (change in volume). • These moduli define how stress relates to strain in different situations. An Introduction to Applied and Environmental Geophysics by John M. Reynolds Elastic Moduli The stress/strain relationship for any material is defined by various elastic moduli. An Introduction to Applied and Environmental Geophysics by John M. Reynolds Types of Seismic Waves Seismic waves • = consist of tiny packets of elastic strain energy • travel away from any seismic source at speeds determined by the elastic moduli and the densities of the media through which they pass 1) Body wave • those that pass through the bulk of a medium • Ex) P-wave, S-wave 2) Surface wave • those confined to the interfaces between media with contrasting elastic properties, particularly the ground surface • Ex) Rayleigh wave, Love wave Body Waves • When seismic waves travel through the Earth (not along the surface), we call them body waves. • There are two main kinds: • P-waves (Primary Waves) • faster, push–pull motion, travel through solids + liquids + gases. • S-waves (Secondary Waves) • slower, side-to-side or up–down motion, travel only through solids. An Introduction to Applied and Environmental Geophysics by John M. Reynolds Body Waves: P-Waves (Primary Waves) • Also called compressional waves, longitudinal waves, or push waves. • How they move: • Particles move back and forth in the same direction as the wave is travelling. • Like a slinky toy when you push and pull it. • • • • They create zones of compression (particles squeezed together) and dilatation (particles spread apart). P-waves are the fastest seismic waves → arrive first at detectors. Travel through solids, liquids, and gases. Analogy: Just like sound waves in air. 𝑉𝑝 = 𝑘+ 4𝜇 3 𝜌 k bulk modulus, μ shear modulus, ρ density of the medium https://www.jamesspring.com/news/invention-of-the-slinky/ Body Waves: S-Waves (Secondary Waves) • Also called shear waves or transverse waves. • How they move: • Particles move at right angles (perpendicular) to the wave direction. • side-to-side motion (perpendicular to direction of travel). • Like shaking a rope up and down while the wave moves horizontally. • They involve shear strain (sliding motion). • S-waves are slower than P-waves → arrive second. • Cannot travel through liquids or gases (because fluids can’t resist shear). 𝑉𝑠 = 𝜇 𝜌 μ shear modulus, ρ density of the medium Body Waves: S-Waves (Secondary Waves) Polarisation of S-Waves • If the motion is confined to one plane, we call them polarised: • SV (Shear-Vertical): Particles move up and down. • SH (Shear-Horizontal): Particles move side to side. • This detail is very useful in exploration seismology because different polarisation directions can tell us about fractures, layering, and anisotropy in the subsurface. Surface Waves Definition: • Waves that stay near the Earth’s surface (do not go deep like Pand S-waves). • They are slower than body waves but often have larger amplitudes, which makes them very noticeable in earthquake records. Two main types: • Rayleigh waves • rolling, elliptical motion. • Love waves • side-to-side horizontal motion. • They are dispersive, so they help study Earth’s structure. • In exploration seismology, Rayleigh waves = ground roll (noise), so we work hard to minimise them. An Introduction to Applied and Environmental Geophysics by John M. Reynolds Surface Waves: Rayleigh Waves • Travel along the surface. • Particle motion: • In a retrograde ellipse (rolling backwards like ocean waves). • Motion is in a vertical plane → particles move up, down, and back as the wave passes. • Since they involve shear strain, they only travel in solids. • Analogy: Imagine a cork floating on the surface of water → it goes up, back, down, forward in a looping path. In Exploration Seismology • Rayleigh waves appear as ground roll: • Large amplitude • Low frequency • Mask useful reflections in seismic records → treated as noise. • How to deal with them: • Survey design (geometry, source–receiver spacing) can reduce them. • Filtering during data processing removes ground roll. Surface Waves: Love Waves • Only occur if there is a low S-wave velocity layer on top of a higher S-wave velocity layer (a kind of “soft over hard” situation). • Particle motion: • Side-to-side, horizontal motion. • Perpendicular to wave travel direction, but parallel to the surface. • These are polarised shear waves (SH type). • Analogy: Like shaking a rug sideways across the floor. Earthquakes? The surface waves (Love and Rayleigh waves) are usually the most destructive in earthquakes. Why surface waves are the most dangerous • Amplitude • Surface waves have the largest ground displacements. • Their energy is concentrated near the surface, so shaking is stronger where people and buildings are. • Duration • They last longer than body waves. • Prolonged shaking increases structural fatigue and collapse risk. • Motion type • Love waves move the ground side-to-side → very damaging for building foundations, railways, pipelines. • Rayleigh waves create an elliptical rolling motion (like ocean waves) → cause both vertical and horizontal shaking, destabilizing structures. https://www.britannica.com/science/earthquake-geology https://www.cdc.gov/earthquakes/about/index.html Dispersion (Key Feature of Surface Waves) • Dispersion = different frequencies travel at different speeds. • Result: The wave “changes shape” as it moves. • Why important? • By studying dispersion patterns, seismologists can figure out the velocity structure of Earth’s crust and upper mantle (lithosphere + asthenosphere). • Contrast: Body waves (P & S) are non-dispersive → all frequencies travel at the same velocity in a uniform medium. Wave Velocity • In a given material, all frequencies of a body wave travel at the same velocity (this is called nondispersive behavior). • Velocity depends on: • Elastic moduli (how stiff the material is) → how stiff the rock is (resistance to deformation). • Density (how heavy the material is) → how heavy or compact the rock is. • General rule: higher density and stiffer rocks = faster seismic waves. • If the rock properties are consistent, the wave travels smoothly without distortion. Poisson’s ration (σ) • tells us how compressible vs. rigid a material is • in geophysics it’s a key link between seismic velocities and rock/fluid properties. • the ratio Vp/Vs is defined in terms of Poisson’s ratio • Maximum value for Poisson’s ration = 0.5 𝑉𝑝 = 𝑉𝑠 1−𝜎 1 2−𝜎 𝑉𝑝 = 𝑘+ 𝜌 4𝜇 3 𝑉𝑠 = 𝜇 𝜌 k bulk modulus μ shear modulus (μ=0 for fluids) ρ density of the medium Measuring Velocities – Why They Differ • Seismic velocity depends on rock stiffness, density, fluid content, and structure. • Measurements in the lab and field may differ because of cracks, fluids, and sample conditions. • Velocities also vary with direction (anisotropy). • Understanding these effects is crucial for interpreting seismic data correctly, especially in areas with complex geology or varying water conditions. An Introduction to Applied and Environmental Geophysics by John M. Reynolds Terminologies: Waveform Wavelength() Wavenumber(k ) Period(T) Frequency( f ) f = 1 T V= k= 2 = 2 f distance = = f time T V ph = k (Phase velocity) Terminologies Wavefront surface of equal phase (e.g., all points that have the wave at the same time). Ray imaginary line that shows the direction of energy propagation of a seismic wave at any point. It is always perpendicular to the wavefront. Raypath the actual trajectory the ray follows through the Earth, including all bends and reflections (line that show the direction that the seismic wave is propagating). Entire route the ray takes through the subsurface. Wavefront is an imaginary surface that connects all points in a medium where a wave has the same phase at a given time Incident ray An incident ray is the incoming seismic (or any wave) ray that strikes a boundary or interface between two different media. (If no E loss: A0=A1+A2) https://scienceready.com.au/pages/properties-of-waves-of-transverse-waves?srsltid=AfmBOoot65_xD8L9z1sqEH5GJCcvCaduOSHrjgDBwZNmChhmllQRFXrA https://testbook.com/physics/wavefront https://www.researchgate.net/publication/343167964_Imaging_of_2D_Seismic_Data_Using_Time_Migration_of_Ajeel_Oilfield_Central_of_Iraq https://pburnley.faculty.unlv.edu/GEOL452_652/seismology/notes/SeismicNotes06RayPath.html Terminologies Property Refraction Reflection Diffraction Scattering Result Wave bends Wave bounces back Wave spreads around edge Wave energy dispersed in many directions Energy path Into new medium Back to original medium Around obstacle In all random directions Critical refraction Critical refraction occurs when a seismic wave hits a boundary between two layers at the critical angle, such that the refracted wave travels along the boundary between them rather than continuing downward. This happens when the lower layer has a higher velocity than the upper layer. Head wave A head wave is a refracted seismic wave that travels along the boundary between two layers when it hits at the critical angle (𝑉2 > 𝑉1 ) An Introduction to Applied and Environmental Geophysics by John M. Reynolds Elasticity & Plasticity Elasticity the property of a material that deforms reversibly under stress Plasticity the propensity of a material to undergo permanent deformation under stress Hooke’s law Huygen’s Principle Every point on a wavefront can be considered to be a secondary source of spherical waves. An Introduction to Applied and Environmental Geophysics by John M. Reynolds Fermat’s Principle • also known as the principle of stationary time • It states that: • the wave path between any two fixed points is the path that can be traveled in the least time • The ray follows a minimal time path. • Snell's law can be derived from Fermat's principle Snell’s Law i = r sin i VP1 = sin t VP 2 sin 𝜃𝑖 = sin 𝜃r Short Exercise: Derive Snell’s Law - reflection 𝐿(𝑥) = L(A0) + L OB = d v=t O t = t ( x) = sin 𝜃𝑖 = sin 𝜃r 𝑥 2 + 𝑎2 + (𝑑′ − 𝑥)2 + 𝑎2 L( x) VP1 𝑥 2 + 𝑎2 (𝑑′ − 𝑥)2 + 𝑎2 t 𝑥 = + Vp1 Vp1 dt x d '− x = − =0 2 2 2 2 dx VP1 x + a VP1 (d '− x) + a L(A0) = sin i = 𝑥 2 + 𝑎2 x a +x 2 2 L OB = sin r = (𝑑′ − 𝑥)2 + 𝑎2 d '− x (d '− x) 2 + a 2 𝑥 𝑉𝑃1 𝑥 2 + 𝑎2 sin 𝜃𝑖 sin 𝜃r = Vp1 Vp1 = 𝑑′ − 𝑥 𝑉𝑃1 (𝑑′ − 𝑥)2 + 𝑎2 sin 𝜃𝑖 = sin 𝜃r Short Exercise: Derive Snell’s Law - refraction 𝐿(𝑥) = L(A0) + L OC = d v=t O t = t ( x) = Vp1 sin 𝜃𝑖 = sin 𝜃t Vp2 𝑥 2 + 𝑎2 + (𝑑 − 𝑥)2 + b 2 L( x) VP1 𝑥 2 + 𝑎2 (𝑑 − 𝑥)2 + b 2 t 𝑥 = + Vp1 Vp2 𝑑𝑡 𝑥 𝑑−𝑥 = − =0 𝑑𝑥 𝑉𝑃1 𝑥 2 + 𝑎2 𝑉𝑃2 (𝑑 − 𝑥)2 + b 2 L A0 = sin i = 𝑥 2 + 𝑎2 x a2 + x2 L OC = sin t = (𝑑 − 𝑥)2 + b 2 d−x (d − x)2 + b 2 𝑥 𝑉𝑃1 𝑥 2 + 𝑎2 sin 𝜃𝑖 sin 𝜃t = Vp1 Vp2 = 𝑑−𝑥 𝑉𝑃2 (𝑑 − 𝑥)2 + b 2 Vp1 sin 𝜃𝑖 = sin 𝜃t Vp2 Snell’s Laws & Critical Refraction sin 𝜃𝑖 𝑉1 = sin 𝜃𝑡 𝑉2 In case of critical refraction sin 𝜃𝑖𝑐 𝑉1 = sin 90˚ 𝑉2 𝑉1 sin 𝜃𝑖𝑐 = 𝑉2 𝜃𝑖𝑐 = critical angle 𝜃𝑖𝑐 = sin −1 𝑉1 𝑉2 An Introduction to Applied and Environmental Geophysics by John M. Reynolds Loss of Seismic Energy • As seismic waves travel, their amplitude (strength) decreases. • This is called attenuation or loss of amplitude. • There are three main causes: • Spherical divergence • Energy spreads out as the wavefront expands (like ripples spreading out on water) • Intrinsic attenuation (absorption) • Energy converted to heat due to internal friction in rocks. • Scattering • Occurs when waves encounter heterogeneities (fractures, layers, voids) • Energy is redirected in different directions. Seismic Sources Type Land Marine Etc Impact Hammer, Thumper(weight dropper) Impulsive Dynamite, Dinoseis(Propane -oxygen gas gun), Air-gun Air-gun, Gas-gun, Sparker, Maxipulse Flexotir, Detonating cord, Water gun, Steam gun Flexichoc Finger, Boomer, Sparker Vibration Vibroseis Mini-Sosie Hydrapulse Marine Vibroseis Piezoelectric vibrator • Impact sources • Produce seismic waves by a sudden mechanical impact. • Impulsive sources • Produce a short, high-energy pulse (used for deeper exploration). • Vibratory sources • Generate continuous vibrations over a range of frequencies An Introduction to Applied and Environmental Geophysics by John M. Reynolds https://www.researchgate.net/publication/255210352_LANDSTREAMERGIMBALED_GEOPHONE_ACQUISITION_OF_HIGH_RESOLUTION_SEISMIC_REFLECTION_DATA_NORTH_OF_THE_200_AREAS_HANFORD_SITE https://www.usgs.gov/media/images/may-26-2023-vibroseis-hilina-pali-road-kilauea Seismic Sources Air-gun Mini-Sosie Sparker Vibroseis Marine Vibroseis Seismic Detection/Receivers • Sensors to detect the returned signals. • Two main types: 1. Geophones – used on land • Measure: ground particle velocity (ideal for seismic reflection/refraction) • Accelerometer: measure acceleration (ideal for strong motion, earthquake, engineering monitoring) 2. Hydrophones – used in water • Respond to pressure, not motion. • Typically attached along long cables called streamers towed behind a survey vessel. An Introduction to Applied and Environmental Geophysics by John M. Reynolds https://cheming.ec/sismografo-x824s-mae/ https://www.usgs.gov/media/images/seismic-survey https://ulstein.com/news/tows-largest-man-made-moving-object https://fishsafe.org/en/offshore-structures/seismic-surveys/ Geophone Seismic Receivers Geophone Hydrophone Seismic Refraction & Reflection When geophysicists say “seismic data” they almost always mean seismic reflection data. Why? • Because reflection surveying produces large, high-density, continuous datasets, • and these are the ones that require: • Advanced signal processing (filtering, deconvolution, stacking, migration, etc.) • Large-scale imaging of subsurface layers and structures (hydrocarbon traps, faults, stratigraphy). Refraction data are used mainly for: • Shallow subsurface structure (engineering, groundwater, near-surface corrections). • Layer velocities and depths, not reflection images. Surface Imaging Introduction to Applied Geophysics 지반구조영상화 Seismic Refraction Seismic Refraction Basic Principle • The seismic refraction method is based on Snell’s Law. • When a seismic wave (P-wave or S-wave) hits a boundary between layers of different velocities, → the wave bends (refracts) as it enters the new medium. What Causes Refraction? • Change in seismic velocity between two layers. • Velocity increases with: • Rock density • Elastic properties (modulus) • Compaction or lithification What We Can Learn from Refraction • Layer velocities (from slopes of t–x lines). • Depths to interfaces (from intercept times). • Lateral variations in rock properties (e.g., weathered layer, bedrock). Typical Applications • Mapping depth to bedrock. • Detecting water table or weathered zones. • Engineering site investigations. • Groundwater or foundation studies. Snell’s Laws & Critical Refraction • Seismic sources radiate waves in all directions • Some ray must hit interface at exactly the critical angle, ic • This critically oriented ray will then travel along the interface between the two layers Snell’s Law: sin 𝑖 𝑉1 = sin 𝑟 𝑉2 In case of critical refraction: sin 𝑖𝑐 𝑉1 = sin 90˚ 𝑉2 sin 𝑖𝑐 = 𝑉1 𝑉2 𝑖𝑐 = critical angle 𝑉1 𝑉1 −1 𝑖𝑐 = arcsin = sin ( ) 𝑉2 𝑉2 Potential Paths in a Refraction Survey • When doing a seismic refraction survey, a recorded ray can come from three mains paths • The direct ray • The reflected ray • The refracted ray • Because these rays travel different distances and at different speeds, they arrive at different times. • The direct ray and refracted ray arrive in different order depending on distance from source and the velocity structure. Source Direct ray ic ic Layer 1, V1 Layer 2, V2 Receiver Refracted ray The Time-Distance (t-x) Diagram Refracted rays are not visible in the first few parts of t-x diagram. Think about: • What would a fast velocity look like on this plot? Slope = rise over run (y/x) =t/d Inverse of d/t = velocity Slope =1/v Steeper the slope = slower! Gentler the slope = faster! • Why is direct ray a straight line? Linear because it is travelling in constant velocity, v1 • Why is refracted ray straight line? Refracted ray travels along the boundary between the two layers • Why does refracted ray not start at origin? Refracted ray have to travel through the first layer first. • Why does reflected ray start at the origin? Reflect downward and bounce back Distance = location/position of geophones The direct ray arrival time: • Simply a linear function of the seismic velocity and the shot point to the receiver distance 𝑡𝑑𝑖𝑟𝑒𝑐𝑡 = Source Layer 1, V1 Layer 2, V2 𝑥 𝑉1 Time (t) The Direct Ray Distance (x) Direct ray Receiver The reflected ray arrival time: • Is never a first arrival • Plots as a curved path on t-x diagram • Asymptotic with direct ray • Y-intercept (time) gives thickness Source Layer 1, V1 Layer 2, V2 Time (t) The Reflected Ray Gives information about the thickness of the first layer Distance (x) Receiver The refracted ray arrival time • Plots as a linear path on t-x diagram • Parts travels in upper layer (constant) • Parts travel in lower layer (function of x) • Only arrives after critical distance (first arrival only after cross over distance) Time (t) The Refracted Ray Critical distance Cross over distance Distance (x) Source A refracted ray travels along a subsurface boundary where the lower layer has a higher velocity. Potentially the fastest. That’s why refracted wave eventually overtakes the direct wave. Receiver Critical distance No refracted rays ic ic ic Layer 1, V1 Layer 2, V2 Refracted ray First Arrivals? Why Do We Focus on First Arrivals? • After the first arrival, many waves (reflections, multiples, surface waves) arrive and overlap. • These later waves become mixed and complex, making them hard to interpret. • Therefore, in seismic refraction we mainly uses the first arrivals. First arrival • Direct ray – (after cross over distance)- Refracted ray Cross over distance Critical distance Time (t) What Are “First Arrivals”? • The first arrival is the earliest seismic wave to reach a receiver. • It represents the shortest travel-time path through the subsurface. • Recorded as the first visible signal on a seismogram. Distance (x) Direct Waves Do Not Always Arrive First. 1. At short distances (near the source) • The direct wave travels straight through the upper, slower layer. • The head wave (refracted wave) must travel down to the deeper layer, along it, and then back up — a longer path. • So, at short offsets, the direct wave arrives first, because even though it’s slower, it travels the shortest distance. 2. At greater distances (farther from the source) • The head wave travels partly through the faster lower layer (V₂). • Even though it has a longer path, its much higher velocity makes up for that extra distance. • Beyond a certain point — called the crossover distance — the head wave’s total travel time becomes shorter than the direct wave’s. Near the source: • Direct wave = first arrival • Head wave = later arrival Beyond crossover distance: • Head wave = first arrival • Direct wave = later arrival Making a t-x diagram Y-intercept to find thickness, h1 Step 1 Pick first arrivals =first breaks in the plot Seismic section V2 =1/slope V1 =1/slope Step 2 Plot it on a graph, And we can interpolate the velocity and thickness of the layers Travel-Time Calculation So far we have been looking at two-layer case. Short Exercise Derive that, z TSA = TBG = V1 cos𝜃12 d sin 𝜃i = 2z 1 12 x + x−2ztan𝜃12 2z x 2ztan𝜃12 = + - V V2 V1 cos𝜃12 V2 2 2z = V + V cos𝜃 2 y=mx+c y=(1/V2)x+t1 1 12 x 2ztan𝜃12 x 1 tan𝜃12 = + 2z( ) V2 V2 V1 cos𝜃12 V2 1 = V + 2z(V cos𝜃 2 1 12 - tan𝜃12 x 1 ) = + 2z V2 V2 V1 cos𝜃12 − 𝑉1 𝑉2 t=v V2 = V1 sin 𝜃i sin 𝜃i 𝑉1 = sin 𝜃i 𝑉2 sin𝜃 tan𝜃 = cos𝜃 sin𝜃 2 + cos𝜃 2 = 1 TSG=TSA+TAB+TBG TSG= V cos𝜃 d v=t x − 2ztan𝜃12 TAB = V2 tan𝜃12 V1 sin 𝜃12 sin𝜃 x 1 = V + 2z(V cos𝜃 2 TSG=TSA+TAB+TBG 1 12 − sin 𝜃12 tan𝜃12 x 1 ) = + 2z( V1 V2 V1 cos𝜃12 sin𝜃12 2 − V cos𝜃 1 12 = x 1 + 2z V2 V1 cos𝜃12 = x 2zcos𝜃12 1 + x +t1 = V2 V1 V2 = x 1−sin𝜃12 2 + 2z V cos𝜃 V2 1 12 t1 = 2zcos𝜃12 V1 − = sin 𝜃12 cos𝜃12 12 V1 ) x cos𝜃12 2 + 2z V cos𝜃 V2 1 12 Three-layer case Crossover Distance Surface Imaging Introduction to Applied Geophysics 지반구조영상화 Seismic Reflection Seismic Reflection • Most widely used geophysical technique since the 1930s. • Main uses: • Oil and gas exploration • Crustal structure research (deep studies) • Typical depth of penetration: up to several kilometres. Shallow Seismic Reflection (Since 1980s) • Increasingly used in engineering and environmental studies. • Typical depth: <200 m. • Applications include: • Mapping Quaternary deposits and buried valleys. • Locating shallow faults or aquifers. • Coal exploration, foundation and tunnel planning. • Offshore wind farm site investigations. General Principle Why do you get a reflection or an echo? • Because the densities and sound velocities of air and rock are very different More specifically, the P-wave velocity (compressional wave) 𝑉𝑝 = 4𝜇 𝑘+ 3 𝜌 k bulk modulus, μ shear modulus, ρ density of the medium P-wave velocity is • Proportional to the stiffness & Inversely proportional to the density • However, dense rocks tend to have high seismic velocities. • This is because as the density of a rock increases, its stiffness (or elastic modulus) also increases, often at a faster, nonlinear rate. • As a result, the influence of density on velocity becomes secondary, and the increase in stiffness dominates, leading to higher overall velocities. • Therefore, the most important parameter of the wave velocity is the stiffness. Body Waves and Surface Waves 1) Body wave • P-waves (Primary or Compressional): particles move back and forth in the direction of travel. • S-waves (Secondary or Shear): particles move sideways (perpendicular) to the direction of travel. 2) Surface wave • Travel along the ground surface • Rayleigh wave, Love wave P-waves are the primary wave type used in seismic surveys Ground roll → in exploration and applied geophysics, treated as noise. • P-waves are the primary wave type used for both reflection and refraction methods. • Why? • Travel easily through solids and fluids • Strong reflections at layer boundaries • Travel fastest easiest to pick “first arrivals” • But that doesn’t mean we don’t we S-waves at all… • S-waves are just usually not the main focus in standard surveys. Acoustic Impedance & Reflection Coefficient Acoustic impedance tells you how much resistance a material gives to the passage of a sound or seismic wave. Acoustic impedance (Z) is the product of a material’s density (ρ) and the velocity (v) of sound (or seismic wave) through it: ρ = density of the rock (kg/m³) 𝑍 = ρ𝑣 v = seismic velocity (m/s) • High impedance → wave travels fast or material is dense (e.g., limestone, basalt) • Low impedance → wave travels slower or is less dense (e.g., sand, water, clay) → Reflection occurs when there is a contrast in impedance between two layers. Why It’s Important in Seismic Reflection • Reflections occur whenever a wave passes from one layer to another with a different acoustic impedance. • The reflection coefficient (R) between two layers is: 𝐴1 𝑍2 − 𝑍1 𝑉2 ρ2 − 𝑉1 ρ1 𝑅= = = 𝐴0 𝑍2 + 𝑍1 𝑉2 ρ2 + 𝑉1 ρ1 𝑅 ≤ ±1 If no loss of energy along any raypath 𝐴0 = 𝐴1 + 𝐴2 Acoustic Impedance & Reflection Coefficient cave In cave or valley = air & rock • Air & rock have very large acoustic impedance, R ≈ 0.999 • seismic velocity of air <<< seismic velocity of rock • Almost all of the sound is reflected back at you = echo In real earth (subsurface) = rock & rock • In Geophysics we look at the boundaries between different type of rocks. • Acoustic impedance is not much different (similar) • Low R ≈ 0.01 • Thus, at most interfaces, 99% of the energy is transmitted, and only 1% is reflected. • This means that your recording system has to be able to detect very faint signals coming back from the subsurface. • For very weak signals we try to increase the signal-to-noise ratio (S/N ratio or SNR) valley What Are We Measuring? • In seismic reflection, we are measuring the time that we made the sound and the time that we recorded the echo. • The time difference is a function of the velocity of sound in the air and twice the distance between us and the wall because the sound has to go from us to the wall and come back again. • In seismic reflection profiling, the source of the sound (an explosion etc.) and receiver (geophones) are offset from each other, but we process them as if they were in the same place. source time travel ← time travel → Key Points About Seismic Reflection Profiling 1. Measure time, not depth 2. The time recorded is round trip / two-way time d 3. To get the depth, we must know the velocity of the rocks v = 𝑑 = 𝑣𝑡 t • Velocities of rocks in the crust range between about 2.5km/s~6.8km/s • Most sedimentary rocks have velocities ≤ 6km/s • These are P-waves velocities Seismic Reflection Profiles ≠ Geological Cross-Sections • Seismic reflection profiles resemble geological cross-sections, but they are not! • They are distorted because rock velocities vary laterally and vertically. Image right • Top: Depth section showing the true thickness of the geology • Bottom: Equivalent time section. Raw data, the first output you can create from seismic survey. Using this, we can convert this into depth section. Artifacts • 6km horizontal boundary (blue) is not shown as a straight horizontal line in time section. Why? • In high velocity material have shorter twoway travel time than the section where there is lower seismic velocities Artifacts: false or misleading features Common Mid-Point (CMP) Actual Reflected Seismic Energies • In Geophysics we look at the boundaries between different type of rocks. • Acoustic impedance is not much different (similar) → Low R ≈ 0.01 • This means that your recording system has to be able to detect very faint signals coming back from the subsurface. • For very weak signals we try to increase the signal-to-noise ratio (S/N ratio or SNR) • If you measure something many times (repeating), the signal in which we are interested should add together constructively. • The signal (the reflection from the true geological interface) • → occurs at the same time and phase each time. • → so when you add or stack the traces: the signal reinforces (constructive interference). • Whereas the random noise should add together destructively. • The noise, on the other hand, • → is random in time and amplitude, • → so when you stack many traces: some positive and some negative noise values cancel each other out (destructive interference). Common Midpoint Reflection Geometry • Source (S) and geophones along a survey line. • Reflections occur at points halfway between S and receiver. • Spacing of reflection points = ½ of geophone spacing. • Total subsurface coverage = ½ of total spread length. Common Midpoint (CMP) • Same subsurface point can be reflected from multiple shot–receiver pairs. • That point = Common Midpoint (CMP). • Notice, that there are twice as many CMPs as there are stations on the ground each receivers (geophones) has a corresponding midpoint between the receivers, another midpoint which will be reflected to corresponding geophone midpoints = reflectors move out Explanation: “Notice, that there are twice as many CMPs as there are stations (geophones) on the ground” 𝑥 • If only 1 shot is made 5 geophones & 5 midpoints Reflection points = common midpoints 1 𝑥 2 • Move the source and make another shot You now have another set of 5 geophones & 5 midpoints reflection point Spacing of reflection points = ½ of geophone spacing new midpoints are shifted by half the receiver spacing compared to the previous shot. • Repeat this until you make a full measurement now you have 9 common midpoints (≈2x number of geophones) Reflection points of first shot Reflection points of 2nd shot Reflection points of 3rd shot Reflection points of 4th shot 5 rays through this midpoint Reflection points of final shot 1 2 3 4 5 6 7 8 9 2 rays through this midpoint Data Redundancy redundancy = repeating.. • In a complete survey, the number of traces through each midpoint will be equal to one half the total number of active stations at any time. Example: 48 receivers -> each midpoint to receive 24 readings = 24 fold (=seismic data) = each depth point was sampled 24 times • This will increase S/N ratio (higher quality data) • Modern seismic reflection surveys use at least 96 (sometimes as many as 1024 channels), so that the number of traces through any one CMP will be at least 48. Data Processing Preprocessing Seismic Data Processing There are three principal stages in seismic data processing: • Deconvolution • Deconvolution assumes a stationary, vertically incident, minimum-phase source wavelet and reflectivity series containing all frequencies, and which is noise-free. • Stacking • Hyperbolic move-out is assumed for stacking. • Migration • Migration is based on a zero-offset (primaries only) wavefield assumption. rebember a step Preprocessing → Convolution/Deconvolution → Velocity Analysis & Stacking → Filtering → Migration 1) Preprocessing 1. Demultiplexing • Field data are often recorded in a “multiplexed” format = mixed traces from multiple channels. • Demultiplexing separates (sort) data into individual seismic traces for each receiver and shot. 2. Editing • Involves checking data quality and removing bad traces or noisy channels (fix & delete). • Ensures only reliable data are used in processing. 3. Gain Recovery (Amplitude Compensation) • As waves travel, amplitude decreases due to: Spherical spreading, Absorption, and Scattering. • Amplifies late (weak) arrivals so reflections from deeper layers remain visible. 4. Static Correction • Corrects for time delays caused by variations in elevation or nearsurface velocity. • Purpose is to align reflections to what they’d look like if all sources and receivers were at the same elevation and surface velocity. • Elevation statics → correct for topography. • Weathering statics → correct for slow near-surface (lowvelocity) layer. Multiplexed: data from multiple channels or sensors are combined and transmitted in sequence through a single communication line very rapidly one after another, so they appear to be sent “at the same time.” Ex) Imagine a teacher calling attendance: “Student 1 — here. Student 2 — here. Student 3 — here.” All answers go through one microphone line (one channel), but each student’s voice is recorded separately in quick succession. 1) Preprocessing 5. Source–Receiver Geometry • Defines where each shot and receiver was located in the field. • Establishes offsets and common midpoints (CMPs). • Correct geometry is critical for: Velocity analysis, Stacking, Migration. 6. Feathering Correction • Occurs when streamers drift sideways due to ocean currents. • Adjusts geometry to true receiver positions using navigation data. 7. Weathered Layer Correction • The weathered layer = low-velocity, unconsolidated near-surface material. • Causes time delays and distortion in first arrivals. • Corrected by: • Measuring near-surface velocity. • Applying static time shifts to remove its effect. 2) Convolution/Deconvolution The Big Idea • When we record a seismic trace, it’s not a pure reflection of the subsurface. • it’s a mix of: • the source wavelet (the pulse we generated) • the reflectivity of the subsurface (real geology) • and some noise • The recorded trace is basically: Recorded Trace = Source Wavelet ∗ Reflectivity + Noise “∗” means convolution • Thus, Convolution is the process of the seismic source wavelet interacting with the Earth's reflectivity series. • Deconvolution is the mathematical process of undoing the convolution = removing the effect of the source wavelet to recover the reflectivity series. https://www.mdpi.com/1404510 convolution 3) Velocity Analysis & Stacking • The most critical parameter in seismic survey = seismic velocity • Seismic velocity is the factor which is used to convert from the time domain (the seismogram) to the depth domain (geological cross-section). • To improve the signal-to-noise ratio and emphasise the coherent signals we need to stack traces collected in a common midpoint (CMP) • However, it is important to estimate the ‘correct’ stacking velocity. Gathering Traces Through a Common Midpoint Station 1 Station 3 Station 2 Station near to the source/midpoint CDP = common depth point = CMP (common midpoint) NMO =Normal moveout correction Station far from the source/midpoint Location of the stations (geophones) Midpoint A • At midpoint (reflection point) A, there are 3 ray path (red, blue, green) reflecting. • Each ray path is recorded by three different stations. • However, the further away the station, the longer it takes for the ray to travel ↑distance = ↑travel time → shown in (a) • Each station has a different two-way travel time • We cannot stack these data directly • Correction / processing needed (NMO correction) to make it look like (b) Showing reflection at one reflection point (CMP) at different stations NMO: Correction For Offset From The Source • The first step in data processing is to gather all seismic traces for each Common Midpoint (CMP). • We can’t add them directly, since each trace has a different travel path and time. • We apply Normal Moveout (NMO) correction using a set of velocities to align reflections. • This correction makes all signals from the same reflector line up across traces. • The travel time 𝑡𝑥 depends on the horizontal offset 𝑥 and the NMO velocity. 2 𝑥 𝑡𝑥2 = 𝑡0 + 2 𝑉 2𝑧 𝑤ℎ𝑒𝑟𝑒, 𝑡0 = 𝑉 ∆𝑇 = 𝑡𝑥 − 𝑡𝑜 = 𝑥2 𝑥2 𝑡0 + 2 − 𝑡0 ≈ 𝑉 2𝑉 2 𝑡0 V= seismic velocity z=a depth to a reflector ∆𝑇= normal moveout correction 𝑥22 − 𝑥12 𝑡2 − 𝑡1 ≈ 2𝑉 2 𝑡0 4) Filtering Why We Need Filtering • When you record a seismic trace, it contains: • Signal → real reflections (usually 10–100 Hz range) • Noise → surface waves, ground roll, cultural noise, and instrument noise (often <10 Hz or >120 Hz) • Filtering helps you keep only the frequencies where reflections dominate and remove those where noise dominates. • Ex) Low-pass filter: keeps low frequencies, removes high frequencies (reduces high-frequency noise) • After filtering → cleaner section, improved signal-to-noise ratio (SNR) In the Frequency Domain • A seismic trace can be decomposed into its frequency content using the Fourier transform. • Filtering = multiplying the seismic spectrum by a filter function 𝐻 𝑓 𝑆𝑓𝑖𝑙𝑡𝑒𝑟𝑒𝑑 𝑓 = 𝑆 𝑓 × 𝐻 𝑓 • 𝑆 𝑓 :original spectrum • 𝐻 𝑓 :filter transfer function (e.g., passes 10–100 Hz) • The result keeps the desired frequencies, suppresses the rest. Filtering: selectively allowing certain frequency components of the seismic signal to pass through while removing others (usually noise). 5) Migration • CMP processing makes it seem like the source and receiver are at the common midpoint. • All CMPs are shown as if they lie directly below the surface, however this is valid only for flat layers. • In dipping layers, the true reflection point is shifted away, causing distortion. • Dipping reflections appear farther down (deeper) the slope and look less steep (gentler) than they really are. • This distortion increases with higher velocity and greater dip angles. Figure. A dipping reflector in the subsurface will not appear in its proper position on a seismic reflection profile because all CMPs are assumed to be vertically beneath their corresponding station at the surface. Migration is a process that corrects this artifact. 5) Migration • The purpose of the migration process is to place a given seismic event in its correct position on the time section • Migration corrects the distortion from dipping layers, • but needs accurate velocity data • assumes all reflections lie in the same vertical plane. • A migrated section often shows curved “migration smiles” at the bottom or edges. • If smiles appear inside the main area, it means the data was overmigrated. • Migration also removes diffractions. Same portion of a seismic section: unmigrated (top) and overmigrated (right). slow velocity Diffractions • In seismic reflection, we assume most energy comes from continuous, flat reflectors. But when the wave hits a small, isolated or sharply curved feature (a fault tip, a small cavity or boulder, the edge of a layer or lens, the top of a buried object), the wave energy spreads out (scatters) in all directions • That scattered energy produces diffraction waves. Diffraction = helps us to identify dipping/vertical features • Their shape depends on velocity: higher velocity makes them broader (wide) and more open. • At great depths, diffractions can look like gentle reflections and be hard to tell apart. • A good migration removes all diffractions, so diffraction should be corrected first (diffraction ⭢ migration). • It’s useful to compare both migrated and unmigrated profiles for interpretation. https://research.csiro.au/msci/projects/mining/seismic-diffraction-imaging/ fast velocity Diffraction hyperbolae Surface Imaging Introduction to Applied Geophysics 지반구조영상화 Electrical Resistivity Introduction • Electrical resistivity methods are widely used to • find groundwater and monitor pollution • locate cavities, faults, permafrost, and old mine shafts in engineering surveys • map buried walls and foundations • There are wide range of electrical methods, and this course will focus only on the use of direct current (or very low frequency alternating current) methods. • Resistivity is a key physical property measured by many techniques, including EM induction. Direct current is electricity that flows in a single, constant direction with a constant polarity (positive → negative). ex) water flowing through a pipe in only one direction without changing. https://www.genspark.ai/spark/data-processing-methodologies-for-geophysical-profiles/9fac9271-5c70-4524-af95-876cba4205ab https://geologyscience.com/geology-branches/geophysics/electrical-resistivity-surveys/ https://www.usgs.gov/media/videos/usgs-scenario-evaluator-electrical-resistivity-survey-design-tool Direct Current (DC) Direct current is electricity that flows in a single, constant direction with a constant polarity (positive → negative) ex) water flowing through a pipe in only one direction without changing. Why is Direct Current (DC) used? • It spreads radially and steadily • It gives a stable potential field • Easier to measure ground resistance • No inductive (EM) effects that AC would generate Alternating Current (AC) • Flows back and forth • Creates magnetic induction • Not used for ERT • Used in EM methods (EM31, MT, GPR) https://startpac.com/blog/direct-current/ https://taraenergy.com/blog/power-electrical-grids-need-to-know/ https://kids.britannica.com/students/article/battery/273129 battery Power grids Rocks and Materials are Electrically Charged • Rocks consists of atoms, which can be viewed as electrically charged particles. • (A positively charged nucleus surrounded by negatively charged electrons) • Usually, the positive and negative particles are in balance and cancels each other. • However, certain chemical and physical processes could disrupt this balance, and the bodies could reveal themselves by an electrical charge. • This creates natural or induced electrical charges used in self-potential and induced-potential methods. • Nevertheless, most of the geoelectrical methods are based on the flow of current rather than on the potentials. https://letstalkscience.ca/educational-resources/backgrounders/introduction-static-electricity https://grade8science.com/5-1-1how-do-rocks-form/ Potential Difference ⭢ Flow of Current • Electric current is the flow of charged particles (electrons or ions). • By convention, current is considered to flow from positive (source) to negative (sink) even though electrons move the opposite way. • The electrical current (I) • measured in amperes (A) • the amount of charge passing a point per second • caused by a potential difference V (the amount of imbalance) measured in volts (V) • Most materials (including rocks) carry more current when the voltage increases. https://byjus.com/physics/electric-current/ convention: a usual or accepted way of behaving Potential Difference (V) and Current (I) Potential difference = Voltage • The relationship between potential difference (V) and current (I) depends on the material. • The ratio between potential difference and current is described by resistance R of the material. • This relation is called the Ohm’s Law: 𝑉 𝑅= 𝐼 R= Resistance measured in Ohms (Ω) • Resistance depends on • the material’s electrical properties (the ability to conduct the current) • the size of the media (diameter of the material) 𝐿 𝑅∝ 𝐴 𝑅= 𝜌𝐿 𝐴 • Resistivity (ρ): 𝜌= 𝑅𝐴 (𝛺𝑚) 𝐿 𝜌= 𝑉𝐴 (𝛺𝑚) 𝐼𝐿 R= Resistance L= Length A= Area ρ=Resistivity https://www.careers360.com/physics/difference-between-resistance-and-resistivity-topic-pge https://www.rhopointcomponents.com/faqs/calculating-resistance-ohms-law/ Terminologies Resistance (R) • How strongly an object as a whole opposes the flow of electric current. • Resistance depends on the material, length of the object, and its cross-sectional area. Resistivity (ρ ) • A material property that describes how strongly the material itself resists current flow. • Resistivity is independent of size. It only depends on the physical characteristics of the material. Current (I) • The amount of electric charge flowing per unit time. Voltage (V or ΔV) • The difference in electrical potential between two points. Conductivity (σ) • How easily electric current flows through a material. https://www.careers360.com/physics/difference-between-resistance-and-resistivity-topic-pge https://www.researchgate.net/publication/322116711_Design_of_the_Propulsion_System_For_an_Electric_Formula_Car True Resistivity vs. Apparent Resistivity True Resistivity (ρ) • The actual resistivity of the subsurface material. • What we want to know from the survey. • Difficult to measure directly because underground layers are heterogeneous. Apparent Resistivity (ρₐ) • The resistivity calculated from the measured current (I) and voltage (ΔV) for a given electrode geometry. • Not the real resistivity. • It is a “blended” value representing all materials influencing the current path. • Average of the multiple layers…. Conductivity (σ): How • Apparent resistivity is the overall resistivity of multiple layers easily electric current • The reciprocal of resistivity is the conductivity (σ): flows through a material. 1 𝜎 = (𝑆/𝑚) 𝜌 https://www.rhopointcomponents.com/faqs/calculating-resistance-ohms-law/ Conductivity σ unit: Siemens per meter (S/m) Resistivity of Rocks and Minerals Insulator: any of various substances that block or retard the flow of electrical or thermal currents. Plastic, wood, glass and rubber are good electrical insulators. • Most minerals forming rocks are insulators (↑resistivity & ↓conductivity) • However, the structure of rocks containing pores, cracks and joints filled with water, ore veins, clay minerals, etc. makes the rocks more or less conductive. • Although the pure water is also a good insulator, the water in rocks is almost never pure, but contains dissolved salts coming from weathered rocks. • These salts split into charged ions that can move through the water and create electric current = ionic conduction. • Therefore: Resistivity of rocks are very sensitive to water content. Ionic conduction • is the movement of charged ions (not electrons) through pore water in the ground. • In most soils and sediments, current flows mainly through water in the pores, not through the solid mineral grains. • is the main reason for rocks to be conductive We want the ground to have neither extreme conductivity nor extreme insulation. We want clear resistivity contrasts to identify subsurface features. Resistivity of Rocks • Geological resistivity varies hugely • Igneous rocks are most resistive (↑resistivity, ↓conductivity) • Sedimentary rocks are most conductive (↓ resistivity) due to pore water • Metamorphic rocks are in between • Older rocks are usually more resistive (↑resistivity, ↓conductivity) because compaction reduces porosity • In sediments, pore-water resistivity is the key factor (Archie’s Law). • Groundwater can range from very conductive (saline, 0.05 Ωm) to very resistive (>1000 Ωm). • Mixed rocks show resistivity based on proportions: • More clay = lower resistivity (can trap water easily) • Dry clay = high resistivity (non-conductive) • Modern surveys aim to find true resistivity, which reflects real geology. • Apparent resistivity = measured resistance × geometric factor (depends on electrode layout) An Introduction to Applied and Environmental Geophysics by John M. Reynolds How Resistivity Survey Works Electrical Resistivity Survey Measures how strongly subsurface materials resist electric current. Principle • Method: • inject current → measure resulting voltages • Based on voltage differences around electrodes in a conductive medium • Voltage distribution depends on resistivity (Ω·m) & conductivity (1/ρ) • Detects lateral & vertical changes in subsurface materials https://www.researchgate.net/publication/364378228_Spatial_appraisal_of_aquifer_characterization_through_hydrogeophysical_investigations_in_central_part_of_Bari_Doab_Punjab_Pakistan?_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6Il9kaXJlY3QiLCJwYWdlIjoiX2RpcmVjdCJ9fQ Current flow Resistivity Survey equipotential • To get an idea of what is measured with resistivity methods, we should first look at how the electricity flows through the rocks. • The current is injected into ground by a pair of electrodes (metal sticks pushed into the ground). • The potential difference between the electrodes causes current to flow. • The current flows between the electrodes using the easiest path, which is the path with lowest resistance. • As current spreads, it moves downward and outward from the electrodes. • As the resistance decreases with increasing diameter of pathway (i.e., increased current), the current paths spreads. 𝜌𝐿 𝑅 = 𝐴 …? An Introduction to Applied and Environmental Geophysics by John M. Reynolds Increasing Electrode Separation Increases Depth of Penetration • The highest concentration of the current is near the surface. Smaller pathway • In uniform ground only about 30% of the current penetrates deeper than the separation length of the current electrodes. • Separation length x 30% ≈ penetration depth • This also implies that the depth of penetration of the current and a volume of rock sampled depends on the distance between the current electrodes • The further the electrodes are placed, the deeper is the penetration, however, a larger volume of rock is sampled and hence the survey is less detailed. penetration depth: depth that can be measured using the geophysical method https://pburnley.faculty.unlv.edu/GEOL452_652/resistivity/notes/ResistivityNotes12Depth.html Bigger diameter for pathway (thicker pathway) Potential Difference is Also Measured • For resistivity survey: • current (I) is injected through the electrodes = current is a known quantity • potential difference (Voltage) is also measured by another pair of electrodes (potential electrodes) with a voltmeter connected to them. • The potential difference measured between the potential electrodes is usually denoted ΔV. • It measures the voltage at that point. • The voltage applied to the current electrodes generally depends on the separation of electrodes and resistivities of the subsurface, but usually is between 100–300 V for the near-surface surveys. • The current is, however, usually less than one ampere and the potential difference read is in millivolts. 𝑉 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑅 = 𝐼 𝑅𝐴 (𝛺𝑚) Resistivity 𝜌 = 𝐿 known (Ohm’s Law) Cross section area (A) and length (L) of the current flow are related to the spacing of the current electrodes (=electrode spacing) But actually, apparent resistivity… https://wiki.seg.org/wiki/Electric_resistivity_methods Currents Can Also Refract • Currents can also undergo refraction. • When you have a current which meets a layer with a higher resistivity, your current will follow the steeper path = steeper dip 𝜌2 < 𝜌1 , 𝜃2 > 𝜃1 𝜌2 > 𝜌1 , 𝜃2 < 𝜃1 • Conductive surface = shallow penetration • Contact resistance: If the electrode is located on a part of the ground which is too resistive (nonconductive, ex. very dry desert) = current would not penetrate to the subsurface =cause the current to penetrate deeper into the ground Looking into the earth: an introduction to geological geophysics. By Mussett, Alan E., and M. Aftab Khan. Modes There are two basic modes of resistivity survey: sounding & profiling Sounding (vertical profile) • Measuring at a single point • Repeating measurements on one place with increasing distance of current electrodes (change depth) • Measures different depth levels and a vertical profile of a subsurface could be derived • Depth of penetration increases with distance of current electrodes • The depth of penetration ≈ ¼ distance between the current electrodes xxxxxx • Ex. to locate conductive aquifers (similar to a borehole, but cannot replace boreholes) Profiling (lateral profile) • Use same electrode distances (same depth) for all measurements, but the whole array moves along the profile. • You can get apparent resistivity of different position on the ground. • Ex. Locate something on a large area, e.g. aquifer Can combine profiling and sounding! Electrode Configuration Commonly Used Electrode Arrays Four electrodes (2 potential electrodes, 2 current electrodes) are necessary, however, their positioning substantially influence the results and could be the factor determining whether the survey is successful or not. Wenner array • All the distances between the electrodes are equal Schlumberger array • The distance between the potential electrodes is much smaller than the distance between the potential and current electrodes. • The most common configuration is to put the measuring dipole in the centre of the array Dipole-dipole array • The measuring dipole is remote from the current electrodes An Introduction to Applied and Environmental Geophysics by John M. Reynolds Potential electrodes P1, P2 or M, N Current electrodes C1, C2 or A, B Array Geometry Correction Factors 𝑉 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑅 = 𝐼 𝑅𝐴 (𝛺𝑚) Resistivity 𝜌 = 𝐿 known (Ohm’s Law) Cross section area (A) and length (L) of the current flow are related to the spacing of the current electrodes (=electrode spacing) But actually, apparent resistivity… we don’t really know the A&L of pathway.. Instead, we use geometric correction factor Geometric factor (κ) • Geometric constat of the array • Depends on the spacing between the electrodes 𝜌 = 𝜅𝑅 apparent resistivity…! Groups of Electrode Arrays • The most common electrode arrays are: • Wenner • Schlumberger • Dipole-dipole • These can be divided into three basic groups: • Potential • Gradient • Dipole arrays An Introduction to Applied and Environmental Geophysics by John M. Reynolds Groups of Electrode Arrays: Potential Arrays Potential Arrays (Wenner Array) • Measure the electric potential difference between two potential electrodes to estimate subsurface resistivity. • Key Principle: • Wider spacing between potential electrodes → larger voltage (ΔV) measured. • Larger ΔV improves signal-to-noise ratio, especially in difficult survey environments. • When Potential Arrays Are Useful: • Areas with poor grounding (dry, rocky, compacted surfaces). • High-noise settings where small voltage changes are hard to detect. • Situations requiring stable, reliable voltage readings despite environmental challenges. • Ex. Wenner Array • Simplest configuration: equal spacing between all electrodes (C1–P1–P2– C2). • Produces strong, clear potential differences due to larger P1–P2 spacing. • High current improves penetration and measurement quality. • Field-friendly and widely used for teaching, calibration, and general surveys. An Introduction to Applied and Environmental Geophysics by John M. Reynolds Resistivity and Induced Polarization By Andrew Binley and Lee Slater Groups of Electrode Arrays: Gradient Array Gradient Array (Schlumberger Array) • Measures the potential difference between two very closely spaced electrodes. • Electrode spacing is made as small as possible (approaching 0-distance in theory). • With extremely small spacing, the measurement approximates the first derivative of the potential field. • Effect: • Produces sharper detection of resistivity changes, especially at boundaries of anomalous bodies. • Highly sensitive to contacts, layer interfaces, and geological edges. • Example – Schlumberger Array: • Potential electrodes (P1–P2) placed very close together. • Current electrodes (C1–C2) placed widely apart to generate a broad current field. • Excellent for locating sharp boundaries or lateral resistivity contrasts. • Disadvantages: • Very small P-spacing → very small voltage differences, making readings more affected by noise. • Lower signal strength than potential arrays such as Wenner. • Comparison with Wenner: • Wenner: large ΔV, good in noisy/poor grounding conditions, but less sensitive to boundaries. • Gradient/Schlumberger: high boundary sensitivity, but poor noise performance due to tiny ΔV. An Introduction to Applied and Environmental Geophysics by John M. Reynolds Resistivity and Induced Polarization By Andrew Binley and Lee Slater First derivative of the potential field • Measuring how the electric potential changes with distance • Equivalent to measuring the gradient • Sensitive to boundaries and edges Groups of Electrode Arrays: Diploe Array Diploe Array (Dipole-dipole Array) • General Characteristics • One of the most sensitive electrode configurations for resolving lateral changes in resistivity. • High sensitivity → strong delineation of subsurface structures. • Also most affected by noise due to very low measured voltages. • Imaging Behaviour • Produces clear resistivity contrasts but often generates complex images (e.g., side lobes, artefacts). • In complex geology, resistivity curves may become overcomplicated, making interpretation difficult. • Depth & Electrode Geometry • Approximate depth of investigation ≈ ¼ of the distance between the centres of the two dipoles. • Maximum recommended dipole separation = 5–6 times the internal dipole electrode spacing. • Larger separations → voltages become too small, noise dominates, measurement error increases. • For deeper penetration, increase the internal dipole electrode spacing, not only the dipole separation. An Introduction to Applied and Environmental Geophysics by John M. Reynolds Resistivity and Induced Polarization By Andrew Binley and Lee Slater • • Advantages • Very sensitive to lateral resistivity variations. • Useful for mapping faults, cavities, utilities, and sharp boundaries. Disadvantages • Small potential difference → high noise • Complex artefacts in data, especially in geologically heterogeneous areas. Apparent resistivity curves over a thick dyke a) Wenner array • Most simple image b) Dipole-dipole array • dashed line: reverse array, solid line: forward array • Superimpose it so that they can determine the midpoint of the object. c) Schlumberger array • Can observe sharp boundaries Low resistivity body Introduction to Applied Geophysics by M. Tvrdý and Stanislav Mares High resistivity body Low resistivity body Dipole-diploe Forward and Reverse Array Forward Array • In a dipole–dipole resistivity survey, you have: • A current dipole (C1–C2) • A potential dipole (P1–P2) • The array direction matters. You can set it up in two opposite orientations: Forward and Reverse Forward Array (normal orientation) • Current electrodes → Potential electrodes Reverse array (opposite orientation) • You flip the positions of the dipoles: • Potential electrodes → Current electrodes • You keep the same spacing, same dipole length, same n-factor, but reverse the order in which the dipoles are arranged along the line. Resistivity and Induced Polarization By Andrew Binley and Lee Slater Reverse Array Why do we do forward + reverse? • Because dipole–dipole data is not symmetric. • The array is directional: the current field and potential field are not the same when reversed. • So the subsurface response in the forward direction may look slightly different from the reverse direction, especially when: • the target is not centered • the geology is asymmetric • there is noise on one side • the ground conditions differ left vs right • By comparing forward and reverse, you can: • Reduce directional bias • Improve positioning accuracy • Detect asymmetry in resistivity bodies • Estimate the true midpoint of anomalies • Increase data reliability Low resistivity body High resistivity body Low resistivity body Apparent Resistivity Profiles With Different Arrays An Introduction to Applied and Environmental Geophysics by John M. Reynolds Vertical Electrical Sounding Vertical Electrical Sounding (VES) • There are two basic modes of deployment of electrode arrays: • Depth sounding: vertical electrical sounding (VES) • Horizontal profile (lateral variation of resistivity): • constant separation traversing (CST) • electrical resistivity tomography (ERT) Vertical Electrical Sounding • The sounding benefits from the fact that the depth of the penetration increases with a distance of current electrodes. • Hence repeated measurements on one place with increasing distance of current electrodes measures different depth levels and a vertical profile of a subsurface could be derived (similar to a borehole). • The depth of penetration depends on the resistivity values of rocks encountered • rough estimate: ¼ × current electrode spacing • Usually used for hydrological application: locating aquifers, finding depth of the bedrock etc. • The most common electrode array for the VES measurements is the Schlumberger array. https://www.researchgate.net/publication/335320747_Using_Vertical_Electrical_Soundings_to_Characterize_Seawater_Intrusions_in_the_Southern_Area_of_Romanian_Black_Sea_Coastline Vertical Electrical Sounding (VES) Electrode array for the VES measurements = Schlumberger array. • The reason is that for changing the depth only the current electrodes need to be moved • Hence, to measure the VES point, the electrodes are positioned at the desired point and the current and voltage values for the first current electrode separation (depth level) are measured. • The resistivity is computed and plotted into the log-log graph (Fig. 4.9). • Then the current electrodes are moved to the next etc. • When the measured potential becomes too low, it is necessary to increase the distance between the potential electrodes. • In this case it is necessary to measure several points with both potential dipole separations to be able to connect both sets of measurements • Finally, when all the desired points are measured the resistivity curve is checked for smoothness. • Any outliers are most likely errors and should be measured once more. Looking into the earth: an introduction to geological geophysics. By Mussett, Alan E., and M. Aftab Khan. Move the current electrode away from each other, so the signal can penetrate deeper. VES Chart • Plotting Method • VES results are displayed on a log–log graph (log AB/2 vs. log apparent resistivity). • Logarithmic scaling compresses large numerical ranges, allowing both small and large values to be shown clearly on one plot. • Why Log Scale? • Electrode spacings increase geometrically, not linearly. • Resistivity values may vary by orders of magnitude, requiring a scale that preserves visibility of all data. • Depth vs. Resolution • As spacing increases → we investigate greater depths. • Resolution becomes coarser at depth, so constant spacing is unnecessary. • Wider spacing intervals are acceptable (and typical) at deeper levels. https://www.agiusa.com/vertical-electrical-sounding-ves x-axis= AB/2 = spacing of the current electrode/2 y-axis= apparent resistivity = average resistivity of all the layers being penetrated ERT Electrical Resistivity Tomography Electrical Resistivity Tomography (ERT) • There are two basic modes of deployment of electrode arrays: • Depth sounding: vertical electrical sounding (VES) • Horizontal profile (lateral variation of resistivity): • constant separation traversing (CST) • electrical resistivity tomography (ERT) • VES =1D survey, ERT = 2D survey Electrical Resistivity Tomography • A 2D or 3D geophysical imaging method that maps subsurface resistivity variations by injecting current and measuring potential differences across many electrode combinations. How It Works • A long line of electrodes (typically 24–96+) is placed on the ground. • A computer-controlled system automatically selects electrode pairs to: • Inject current (C1–C2) • Measure voltage (P1–P2) • This dense dataset provides many overlapping measurements, allowing detailed imaging. https://www.epa.gov/environmental-geophysics/electrical-resistivity https://geologyscience.com/geology-branches/geophysics/electrical-resistivity-surveys/ Electrical Resistivity Tomography (ERT) Unlike VES, ERT can use various electrode configurations: Array Type Key Characteristics Wenner • • • • • High signal strength (good SNR) Very stable, smooth data Good vertical (layer) detection Less sensitive to lateral changes Electrodes equally spaced (a–a–a) • • • Stratigraphy (layering) Groundwater table detection Simple, horizontally layered geology Schlumberger • • • • Similar to Wenner but with wider current electrode spacing Greater depth penetration Good vertical resolution Less sensitive to noise • • • Deep sounding within 2D ERT Layered or semi-layered geology Sites where deeper penetration is required Dipole–Dipole • • • • Very sensitive to lateral changes High resolution for vertical/narrow structures Excellent for faults and archaeology Lower signal strength (noisy at depth) • • • • • Fault detection Walls, ditches, foundations (archaeology) Karst cavities/voids Contaminant plumes Steep/dipping structures An Introduction to Applied and Environmental Geophysics by John M. Reynolds Best For Electrical Resistivity Tomography (ERT) What ERT Reveals • Layer boundaries, faults, cavities, archaeological features, groundwater levels, bedrock depth, contamination plumes, etc. • Good for mapping both vertical and lateral changes in the subsurface. Advantages • High-resolution imaging • Deep penetration (depending on array and spacing) • Works well in complex geology • Flexible configurations (Wenner, Schlumberger, Dipole–Dipole, Mixed arrays) Limitations • Requires good electrode contact • Time-consuming in the field • Sensitive to cultural noise and surface conditions • Inversion results are non-unique → need geological constraints (A) Example of the measurement sequence for building up a resistivity pseudo-section. (B) Example of a measured apparent resistivity pseudo-section. An Introduction to Applied and Environmental Geophysics by John M. Reynolds How It Works.. • You do NOT need to move the electrodes to change electrode arrays! • Because modern ERI/ERT instruments control everything. • Electrode spacing: depends on the target and survey type. Survey Type Typical Electrode Spacing (a) Archaeology 0.5 m – 1 m – 2 m Engineering/Environmental 2m–5m Hydrogeology / Faults • Depth of investigation: Deep geological surveys Maximum depth ≈ 20%–25% of total line length Depth ≈ 3 to 5 times the electrode spacing (depending on array) More spacing → deeper penetration Ex. 1 m spacing → ~3–5 m depth • Resolution (ability to detect small features) • Small spacing = high resolution • Large spacing = low resolution https://www.researchgate.net/publication/378674139_Numerical_Simulation_of_Geophysical_Models_to_Detect_Mining_Tailings'_Leachates_within_Tailing_Storage_Facilities 5 m – 10 m 10 m – 20 m – 50 m https://www.sciencedirect.com/science/article/abs/pii/S1367912021002182 https://www.researchgate.net/publication/338504656_Pseudo-3D-electrical_resistivity_tomography_imaging_of_subsurface_structure_of_a_sinkhole-A_case_study_in_Greene_County_Missouri?_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6Il9kaXJlY3QiLCJwYWdlIjoiX2RpcmVjdCJ9fQ Inversion Apparent Resistivity to Resistivity Inversion Inversion in geophysics is the mathematical process of taking measured data (seismic, resistivity, gravity, magnetics, GPR, etc.) and estimating the subsurface properties that produced that data. In short: Forward problem: Earth model → Predict data Inverse problem (inversion): Data → Estimate earth model Why do we need inversion? • Because geophysical instruments do not measure geology directly. • For example: • Seismic measures travel times and reflections, not velocity or rock type • Resistivity surveys measure voltage, not true resistivity • Gravity surveys measure gravity variations, not density • Magnetics measure anomalies, not magnetic susceptibility • So we need mathematics to convert measured signals into actual subsurface properties. Apparent Resistivity to Resistivity • We use inversion to: • convert measured apparent resistivities to true resistivities • convert current electrode separations into depth of interfaces • Nowadays, inversion process is carried out on the computer • In the past, a set of master curves was used for inversion (no need to understand the curve… ☺) Looking into the earth: an introduction to geological geophysics. By Mussett, Alan E., and M. Aftab Khan. Inversion: Problem With Thin Layers Thin Layers Lack Unique Inversion Solutions • Thin subsurface layers often produce non-unique interpretations during inversion. • This limitation is known as the principle of equivalence. High-Resistivity Thin Layer • For a thin layer with much higher resistivity than surrounding layers: • Layers with the same t × ρ (thickness × resistivity) produce nearly identical responses. • Therefore, many combinations of thickness and resistivity fit the same data. Low-Resistivity Thin Layer • For a thin layer that is much more conductive than surrounding layers: • Layers with the same t / ρ (thickness ÷ resistivity) look indistinguishable in the data. Thick layer with low resistivity & thin layer with high resistivity => same in inversion process (no unique solution for this) Looking into the earth: an introduction to geological geophysics. By Mussett, Alan E., and M. Aftab Khan. Computer Inversion • The black curve represents the observed data measured in the field. • The blue step‐shaped line shows the interpretation model: • Each step = a subsurface layer with assigned resistivity. • This is the model proposed by the inversion algorithm (or starting model chosen by the interpreter). • From the blue model, the software calculates what the apparent resistivity curve should look like. • This predicted curve is shown in red. • If the red (calculated) curve matches the black (measured) curve closely, → the model is mathematically consistent with the data. • If they differ significantly, the model must be adjusted until the mismatch (error) is minimized. Inversion Concept • • There is no simple formula that turns apparent resistivity into true resistivity. True resistivity is obtained by iterative inversion, where a computer keeps adjusting a subsurface model until its calculated apparent resistivities match the measured ones. 1. What we actually measure • In the field we measure: the apparent resistivity 2. Build a starting earth model • For inversion, the software: • Divides the subsurface into cells/blocks (1D layers, 2D mesh, or 3D mesh). • Assigns an initial resistivity to each cell (e.g. all 100 Ω·m, or based on a guess). • So we start with a guess model of true resistivity. 3. Forward modelling from that model • From that guess model, the program does forward modelling: • Solve Poisson’s equation for current flow in the earth • Compute the predicted potentials at the potential electrodes • Convert those to predicted apparent resistivities 𝜌𝑎,calc for each measurement • Now we can compare: • Field data: 𝜌𝑎,obs • Model prediction: 𝜌𝑎,calc Inversion Concept 4. Compare data and model (misfit) • The software calculates a misfit (difference between observed and calculated data), usually something like: 5. Adjust resistivity values to reduce misfit • Now comes the inversion step: • The algorithm adjusts the resistivity of the cells. • It tries to find changes in the model that make 𝜌𝑎,calc closer to 𝜌𝑎,obs . • This is done using maths like least-squares , gradient methods, Gauss–Newton or similar • AND it includes regularization (smoothing, damping) so that: • the model is not too noisy • we avoid crazy, unrealistic resistivity jumps 6. Iterate until a good fit • The program repeats the cycle: • Model → Forward modelling → Compare with data → Update model → … over and over • until: • misfit is small enough, or • improvements become negligible 7. The final model of cell resistivities is what we call: “True resistivity” model (or at least our best estimate of it)
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