 Seismic Waves
 Vandana
and Inversion
Chopra
 Eddie Willett
 Ben Schrooten
 Shawn Borchardt
Topics



What are Seismic Waves???????
History
Types of Seismic Waves
What are Seismic Waves ???

Seismic waves are the vibrations from
earthquakes that travel through the
Earth

They are the waves of energy suddenly created by
the breaking up of rock within the earth or an
explosion .They are the energy that travels through
the earth and is recorded on seismographs
History

Seismology - the Study of Earthquakes and
Seismic Waves
 1) Dates back almost 2000 years

History Cont

Around 132 AD, Chinese scientist Chang Heng invented
the first seismoscope, an instrument that could register
the occurrence of an earthquake.

They are recorded on instruments called seismographs.
Seismographs record a zigzag trace that shows the
varying amplitude of ground oscillations beneath the
instrument. Sensitive seismographs, which greatly
magnify these ground motions, can detect strong
earthquakes from sources anywhere in the world. The
time, location and magnitude of an earthquake can be
determined from the data recorded by seismograph
stations.
Seismometers and
Seismographs





Seismometers are instruments for detecting
ground motions
Seismographs are instruments for recording
seismic waves from earthquakes.
Seismometers are based on the principal of an
“inertial mass”
Seismographs amplify, record, and display the
seismic waves
Recordings are called seismograms
Types of Seismic Waves
 Body
waves
Travel through the earth's interior
 Surface Waves
Travel along the earth's surface - similar to
ocean waves
P-Wave(Body Wave)
Primary or compressional (P) waves
a) The first kind of body wave is the P wave or primary
wave. This is the fastest kind of seismic wave.
b) The P wave can move through solid rock and fluids, like
water or the liquid layers of the earth.
c) It pushes and pulls the rock it moves through just like
sound waves push and pull the air.
d) Highest velocity (6 km/sec in the crust)
P-Wave
Secondary Wave (S Wave)

Secondary or shear (S) waves
a)The second type of body wave is the S wave or
secondary wave, which is the second wave you
feel in an earthquake.
 b) An S wave is slower than a P wave and can
only move through solid rock. (3.6 km/sec in the
crust)
 c) This wave moves rock up and down, or side-toside.
S-Wave
L-Wave

Love Waves
 The first kind of surface wave is called a
Love wave, named after A.E.H. Love, a
British mathematician who worked out the
mathematical model for this kind of wave in
1911.
 It's the fastest surface wave and moves the
ground from side-to-side.
L-Wave
Rayleigh Waves

Rayleigh Waves

The other kind of surface wave is the Rayleigh wave, named
for John William Strutt, Lord Rayleigh, who mathematically
predicted the existence of this kind of wave in 1885.
A Rayleigh wave rolls along the ground just like a wave rolls
across a lake or an ocean. Because it rolls, it moves the
ground up and down, and side-to-side in the same direction
that the wave is moving.
Most of the shaking felt from an earthquake is due to the
Rayleigh wave, which can be much larger than the other
waves.


Rayleigh Waves
Seismic Wave Equations
Outline
I’m going to briefly cover three different
Seismic wave equations
-Inhomogeneous Constant
Density 2-D Wave Equation
-First Order Wave Equation
-Acoustic Wave Equation and how it’s
derived
Inhomogeneous Constant
Density 2-D Wave Equation
The pressure wave field is ψ and the seismic source is src(t)
Media velocity, C(x,z), the sound speed with x being the
surface coordinate and z being the depth coordinate
Example of 2-D Wave
First Order Wave Equation
Again the pressure wave field is ψ, the sound speed is c
and x is the surface coordinate
Parameter α is determines the propagation direction of
the wave
This is the simplest wave propagation model
Example of First Order Wave
Developing the Acoustic Wave
Equation
Wave Equation Variables

Mass and Momentum are conserved (basis
for development of wave equation)
 Mass density is ρ
 Particle velocity is ψ
 Fluid Pressure is P
 Three spatial coordinates xi (i=1,2,3) for
domain Ω
 Stress matrix is σij (stress within the fluid)
Conservation of Mass and
Momentum
Momentum
Stress matrix
Kronecker delta function
(pseudotensor)
Mass
Some Considerations
Considering small perturbations Δ in
Particle velocity
Density
Pressure
And with Euler’s Equation with the viscosity equal to zero
And realizing P0 is constant and fb is negligible we have
Derivations
The initial medium is at rest so Euler’s Equation can be
changed to
eliminating the substantial derivatives.
Then we let the gradient of Φ be equal to the particle
velocity
giving us
Derivations cont.
Next we assume the derivatives of space and time can be
changed therefore
And removing the gradient operator on both sides gives us
Now the compressibility C and bulk modulus of K are
defined in terms of a unit volume V and ΔV
Derivations cont.
The change in the change of fluid pressure P is now
Now computing the derivative of this equation with respect
to time is
showing that the change in pressure is related to the change
in density.
Then substitutions with this equation gives us
Derivations cont.
Now using the conservation of mass equation with the
previous equation and time derivative gives us
Then using the time derivative again we get
And finally…
Derivations Concluded
We have the Acoustic Wave Equation
where
is the speed of sound in the medium
Example of Acoustic Waves
Sources

Seismic Wave Propagation Modeling and
Inversion www.math.fuberlin.de/serv/comp/tutorials/csep
 www.llnl.gov/liv_comp/meiko/apps/larsen/l
arsen3.gif
History of computing in
seismology
Reasons for Computational
methods in Seismology
 Computer development
 More memory
64k most accessible for single point
 Early 1970’s rule of thumb

 1k for 1K of computer memory
 Used more in the field
 Size shrank explosively from 1960’s – 1990’s
 Data acquisition, processing, and telemetry
 Processing speed increase
Seismic Station coverage

Worldwide coverage by a single network
of computers
 good azimuthal and fair to good depth control
for major earthquakes
 Brought about software to analyze the data on
this network
Early computer based study

Dorman & Ewing surface-wave data
inversion in 1962
 earthquake location by Bolt, 1960; Flinn,
1960; Nordquist, 1962; Eaton, 1969)
 Jerry Eaton first to include source code for
his program
 Credited with opening up software development to
others
 Computed travel times and derivatives for a
source inside multiple layers over a half space.
Developments in the 80’s
 Many
groups compiled algorithms
 Methods in Computational Physics
 the two volumes of“Computer Programs in
Earthquake Seismology”
 Other computer code algorithms were also
published in the engineering and
geophysics literature
Developments up until today
 A Working
Group on Personal
Computers in Seismicity Studies was
created in 1994
 todays personal computers are taking the
place of mainframes in this field
 This has been the trend since 1980’s
 The publication and distribution of
seismological software is a major focus
Software packages available
 Here
are a few
 CWP/SU: Seismic Unix: The Instant Seismic
Processing and Research Environment
 GeoFEM
A multi-purpose / multi-physics parallel finite
element
solver for the solid earth.
Earthquakes
Seismological
activity as of
4/4/2002
11:21 AM
Software
 Seismic Waves: A program for
the
visualization of wave propagation
 By Antonello Trova
 http://www.dicea.unifi.it/gfis/didattica.html
References and more info















http://www.iris.washington.edu/DOCS/off_software.htm
http://orfeus.knmi.nl/other.services/software.links.shtml
http://www.dicea.unifi.it/gfis/didattica.html
http://www-gpi.physik.uni-karlsruhe.de/pub/martin/MPS/
http://wwwrses.anu.edu.au/seismology/ar98/swp.html
http://www.nea.fr/abs/html/ests1300.html
http://www.cwp.mines.edu/software.html
http://www.iris.washington.edu/seismic/60_2040_1_8.html
http://www.es.ucsc.edu/~smf/research.html
http://nisee.berkeley.edu/
http://www.seismo.unr.edu/ftp/pub/louie/class/100/seismic-waves.html
http://mvhs1.mbhs.edu/mvhsproj/Earthquake/eq.html
http://www.riken.go.jp/lab-www/CHIKAKU/index-e.html(found it interesting, but cannot read
Japanese)
http://www.cs.arizona.edu/japan/www/atip/public/atip.reports.99/atip99.043.html
http://www.engr.usask.ca/~macphed/finite/fe_resources/node162.html
Seismic Wave Projects
And Visualizations
Talking Team #2
Why are seismic waves important?
Some things seismic waves are good for include
 Mapping the Interior of the Earth
 Monitoring the Compliance of the Comprehensive Test Ban Treaty
 Detection of Contaminated Aquifers
 Finding Prospective Oil and Natural Gas Locations
An Example of a Wave Interacting With a Boundary
http://www.mines.edu/fs_home/tboyd/GP311/MODULES/SEIS/NOTES/Lmovie.html
 We Collect Information from the waves as they are reflected back to us and as they propagate to the other ends of the medium.
 What would happen if there was only 1 medium?
The P and S wave velocities of various earth materials are shown below.
Material
P wave Velocity (m/s)
S wave Velocity (m/s)
Air
332
Water
1400-1500
Petroleum
1300-1400
Steel
6100
3500
Concrete
3600
2000
Granite
5500-5900
2800-3000
Basalt
6400
3200
Sandstone
1400-4300
700-2800
Limestone
5900-6100
2800-3000
Sand (Unsaturated)
200-1000
80-400
Sand (Saturated)
800-2200
320-880
Clay
1000-2500
400-1000
Glacial Till (Saturated)
1500-2500
600-1000
Visualizations Done With Seismic Wave Data in Supercomputing
3-D Seismic Wave Propagation on a Global and Regional
Scale: Earthquakes, Fault Zones, Volcanoes
Information and Images Source: Prof. Dr. Heiner Igel
Institute of Geophysics, Ludwig-Maximilians-University, Germany
Whats the purpose of the accurate simulation of seismic wave propagation through
realistic 3-D Earth Models?
 Further understanding of the dynamic behavior of our planet
 Deterministic earthquake fore-casting, assessing risks for various zones (i.e. San Francisco Bay
Area)
 Understanding active volcanic areas for risk assessment
Goals of the project:
1. Parallelization and implementation of algorithms for numerical wave propagation on the Hitachi
SR8000-F1
2. Verification of the codes and analysis of their efficiency
3. First applications to realistic problems
Before moving into 3-D the base numerical solutions had to be compared to analytical solutions for simple (layered) model geometries.
The System used for Simulation
 Hitachi SR-8000 F1
 Typical Speed 750Mflops per node
 Internode Transfer Speed 1GB/s
Technical Methods
 Numerical solutions to the elastic wave equations in Cartesian and spherical coordinates.
 Time dependent partial differential equations are solved numerically using high-order finite difference
methods
 Space-dependent fields are defined on a 3-D grid and the time extrapolation is carried out using a Taylor
expansion
 Space derivatives are calculated by explicit high-order finite-difference schemes that do not necessitate
the use of matrix inversion techniques
Languages Used
 Fortran 90 coupled with the Message Passing Interface (MPI)
Performance
The parallel performance was tested with a code where all I/O was – as in production runs – carried out. An FD algorithm was run for 10 time steps
on varying number of nodes.
Experiments Implemented
Volcano topography in 3-D seismic wave propagation
1. The seismic signature of pyroclastic flows
2. Seismic sources inside magma chambers and volcanic dykes
3.
Scattering vs. topographic effects as observed on Merapi
Site effects of the Cologne Basin
-In this project the first 3D calculation for the area in Germany with the highest seismic risk – the Cologne
Basin – were carried out. The simulations show remarkably good agreement with observed data as far as the
amplitudes for the ground motion is concerned which tells us that we are on the right way to be able to
predict the possible ground motion amplification due to 3D structure for this (and other) areas.
The seismic signature of subduction zones
- Subduction zones contain the largest earthquakes on Earth. Knowledge of there structural details not only is important for hazard assessment but
also to understand the dynamics of subduction and mantle convection. In this project a 3D algorithm in spherical coordinates was implemented
and earthquakes in subduction zones simulated. We were able to simulate particular wave effects observed in nature which – in the future – can be
used to further constrain the structure of subduction zones.
Fault zone wave propagation
- Fault zones (FZ) are though to consist of a highly localized
damage zone with low seismic velocity and high attenuation. The structure of FZs at depth has important implications for the size of (future)
earthquakes and the dynamic behaviour of the rupture. Only recently it was observed that right above FZs a particular wave type (guided waves)
can be observed which may allow imaging FZs at depth. Numerical simulations play an important role in developing imaging schemes and assess
their reliability.
Future of this Project
a. Wave Propagation in a heterogeneous spherical Earth (DFG, 2000-2002)
b. The seismic signature of plumes (DFG, 2001-2003)
c. The simulation and interpretation of rotational motions after earthquakes (BMBF, 2002-2005)
d. Numerical wave propagation in seismically active regions (KONWIHR, initially until 2002, may be further
extended).
e. International Quality Network: Georisk (www.iqn-georisk.de) funded by the DAAD, 2001-2003. Will
allow students, post-docs, professors from other countries to visit our Institute and take part in research
projects. In combination with our simulation algorithms this may allow us to combine the numerical aspects
with data from regions at risk. Involved countries: USA, Indonesia, China, New Zealand, Japan. The core of
this network is a research group (1 post-doc, 3 PhD students) residing in Munich working of risk and hazard
related problems in seismology and volcanology.
REGIONAL OBSERVATIONS OF MINING BLASTS BY THE GSETT-3 SEISMIC
MONITORING SYSTEM
Brian W. Stump and D. Craig Pearson
EES-3, MS-C335
Los Alamos, NM 87545
Background:
The cessation of testing of any nuclear explosive devices in all environments is the goal of the Comprehensive Test Ban Treaty. In order to assure
compliance with such a treaty, an international monitoring system has been proposed. This system will include seismic, infrasound, hydroacoustic
and radionucleide monitors located throughout the world. The goal of this system is the detection of any nuclear test.
The monitoring technologies that are included in the treaty are designed to detect a nuclear explosion in any environment and include seismic (50
primary and 120 auxiliary stations), infrasonic (60 stations), hydroacoustic (6 hydrophone and 5 T-phase) and radionuclide (80 stations) sensors
distributed throughout the world (CD/NTB/WP.330/Rev.2, 14 August 1996). These sensors and the accompanying data would then become a part
of the International Monitoring System (IMS) with the collation, analysis and dispersal of the resulting data and data products by an International
Data Center (IDC).
Purpose of this Project:
Mining explosions generate both ground motion and acoustic energy that have some characteristics similar to small nuclear explosions, thus the
proposed monitoring system may detect, locate and characterize some mining explosions.
In order to gain practical experience with the seismic component of worldwide monitoring, a series of empirical tests in the gathering, exchange
and analysis of seismic data have been conducted under the auspices of the Conference on Disarmament in Geneva.
These tests have been titled the Group of Scientific Experts Technical Tests (GSETT) with the most extensive and recent test,
GSETT-3.
An example of a set of seismic stations that could be used for international monitoring of a CTBT. Primary stations are represented as circles and
Auxiliary stations are represented as triangles.
Teleseismic Events and Regional Events
Seismic waves that travel hundreds to over a thousand kilometers are classified as regional seismograms because they travel primarily in the
earth's crust. Events that are only observed regionally are generally smaller than those observed teleseismically since the amplitude of the seismic
disturbance decays as it propagates. The right part of Figure 2 illustrates the regional GSETT-2 triggers at Lajitas. It is interesting
to note that these smaller regional events occur primarily Monday through Friday and during working hours,
suggesting that they are man made. This data suggests that a number of these regional signals may be
associated with mining operations, in this case near surface coal extraction in Northern Mexico.
GSETT-3 included a greater number of seismic stations, continuous transmission of data and more detailed analysis of the data than GSETT-2.
This experiment and the resulting data products allow further insight into the numbers and types of mining explosions that might be detected by
regional seismic
stations.
The fifteen months of activity represented in Figure 3 suggests that in an active mining region such as the Powder River Basin, as many as several
events per month might be expected.
Event location is very important in the assessment of the seismic data. Utilization of the arrival times of multiple seismic phases at a single
seismic station, relative arrival times at an array of closely spaced seismometers, and observations at multiple stations are used to determine the
origin of the events in space and time as well as some assessment of error in the estimates.
Figure 4: GSETT-3 events located in the Southern Powder River Basin compared to SPOT imagery and known locations of the events in coal
mines in the region.
 5 Active mines outlined in Green Boxes
 Ellipses show GSETT-3 Detections
 Detections in many cases will associate with a region and not a specific mine with the GSETT-3
Conclusions of the Project:
Large scale mining explosions, with the detonation of a large amount of explosives simultaneously, are
observed at regional (100-2000km) and occasionally teleseismic (2000-10000 km) distances with seismic
sensors.
As a result of the CTBT verification system, the largest of these events will have to be associated with standard mining operations to avoid the
conclusion that the signal was created by a small nuclear explosion.
There is a need to implement techniques designed to reduce seismic amplitudes to reduce problems with the
CTBT detection system.
Improved understanding of blasting practices and their effects on regional seismograms provides the
opportunity for improved monitoring of a CTBT. Similarly, blasting practices designed to maximize
explosive efficiency while minimizing ground motion within the mine are exactly those practices best for
reducing both the size and ambiguity of regional seismic signals.
Sources:
Wave Pictures and Movie Source
http://www.mines.edu/fs_home/tboyd/GP311/MODULES/SEIS/NOTES/Lmovie.html
The GSETT3 Project
http://www.geology.smu.edu/~dpa-www/papers/pdf/gsett3.pdf
The 3D Seismic Wave Propagation Simulation Project
http://www.lrz-muenchen.de/projekte/hlrb-projects/reports/h019z_r1.pdf
Addition Reading Recommended on mine blasting detection, monitoring of seismic waves caused by Blasting.
Black Thunder mine research with Los Alamos National Labs
http://www.geology.smu.edu/~dpa-www/papers/pdf/blackt.pdf
THE END