Seismometers
• Inertia of a mass
• Record velocity or
acceleration
• 1-component versus 3components
• Timing is very
important (GPS)
• Noise
Seismometers and seismograms
• Broadband seismometers
have force-feedback
electronics that apply a force
proportional to the
displacement of the inertial
mass to prevent it from
moving significantly
• Accelerometers can record
(acceleration due to) very
large ground motions
without clipping
V = f "#
$
V=
#
T
Seismograms
• Typically: P, then S, then surface waves
• Seismograms recorded by a 3-component
seismograph at Nana:
• S wave arrives significantly after the Pwave because S-wave velocity in rocks
is lower than P wave velocity.
• Additional arrivals between the P and
the S wave are P and S waves that have
traveled more complicated paths (such
as the pP and PP phases and P-to-S
converted phases) from the earthquake
location to the seismograph.
• Surface waves arrive after the S waves
because surface wave velocities in rocks
are lower than the shear wave velocity.
• Surface waves extend over a long time
interval because surface wave
propagation is dispersive (the velocity
of propagation is dependent on the
frequency of the wave).
• Dispersive character can easily be seen
in the Rayleigh wave on the vertical (Z)
component seismogram in that the
earliest Rayleigh wave energy has a
longer period (lower frequency) than the
later arriving waves
http://www.eas.purdue.edu/~braile/edumod/waves/WaveDemo.htm
Broadband recordings
a) Full waveform
b) Low pass filtered at 0.03 Hz
c) High pass filtered at 0.5 Hz
d) Zoom on local event
Exploration seismology
• Use the propagation of seismic wave to infer the
geometry of geological structures at depth, such
as:
–
–
–
–
Top of the water table?
Geometry of a salt diapir?
Depth of the Moho?
Etc…
• The techniques involve:
– Refraction / reflection of seismic waves
– Active sources
Wave propagation
– Snell-Descartes law:
sini sin r
=
V1
V2
– If V2>V1 (usual case in the Earth), then
r>i
!
y
ra
ed
ct
i
fle
ay
tr
Reflection: iincident = ireflection
Refraction:
en
•
•
cid
– Some of the energy is reflected back in
medium 1 = reflection
– Some of the energy goes trough the
interface into medium 2 = refraction
In
When a wavefront hits the interface
between 2 medias with different
physical properties (⇒ different
seismic velocities)
re
•
i
velocity 1
interface
refr
velocity 2
(v2 > v1)
r
acte
d ra
y
Wave propagation
reflected by the surface
direct wave
reflected by the
velocity discontinuity
refracted by the
velocity discontinuity
One layer (V=6 km/s) over a half-space (V=8 km/s)
Reflected and refracted waves (or rays)
• Seismic source at O
• Homogeneous and uniformly thick layer with
velocity V1 on top of layer V2 (V2 >V1).
• Let’s consider seismic rays with increasing
incidence angle i:
sin(r) = (V2/V1) x sin(i) with V1=4.0 km/s V2=5.7 km/s
90
80
70
refraction angle (r)
Wave
propagation
60
50
40
30
20
10
critical angle i0=53.13o
0
0
10
20
30
40
50
60
70
80
90
incident angle (i)
– Between O and C:
• Simple reflection and refraction
• r increases as i increases (because V2 >V1)
O
– At C and after:
• i is such that r = π/2
• i0 = critical angle of incidence
• Refracted ray travels at 90o from normal to interface
=> parallel to interface (but in lower layer) = critically
refracted rays
• Refracted rays accompanied by reflections upward
with angle i0 = head wave
• Still reflections = supercritical reflections (or wideangle reflections)
subcritical reflection
critical
distance
supercritical reflection
reflected
rays
V1
incident
rays
V2
“head waves”
ic
io
C
refracted rays
critically refracted ray
Wave propagation
direct wave
reflected by the
velocity discontinuity
head wave
refracted by the
velocity discontinuity
One layer (V=6 km/s) over a half-space (V=8 km/s)
Reflected and refracted waves (or rays)
Critical reflection and head wave
Wave propagation, the movie…
A
B
depth
source
One layer over a half-space - Draw a seismogram at A and B!
http://appliedgeophysics.berkeley.edu:7057/seismic/index.html
Refraction
O
x
ray
act
ic
refr
t=
h1
ic
ed
• Homogeneous medium of uniform velocity V1 over
medium V2: travel time of direct, refracted and reflected
rays?
• t as a function of distance x along the profile = t-x curve
x
• Direct ray:
D’
direct ray
S
V1
V1
V2
⇒ t-x curve: straight line, slope 1/V1
C
D
• Refracted ray (head wave):
SC CD DD"
!
t=
+
+
=2
V1
with
V2
direct arrivals
slope = 1/V1
CD = x # 2h1 tanic
$ t =2
since
V1
travel time t
h1
CD
+
V1 cosic
V2
h1
x 2h1 tanic
+
#
V1 cosic V2
V2
V1
= sinic
V2
refracted rays
slope = 1/V2
tint
2
2
x 2h1 cosic
x 2h1 V2 # V1
x
$t=
+
=
+
=
+ t int
V2
V1
V2
V1V2
V2
!
⇒ t-x curve: straight line, slope 1/V2
⇒ Intercept time tint=> h1
O
critical
distance
cross-over
distance
x
Reflection
source
x
D
t =2
V
(t=
•
•
D=
" x %2
h +$ '
#2&
lec
ted
h
ref
D
2
2
reflector
2
2
" x%
2h
x
x
h2 + $ ' =
1+
= t o 1+
2
#2&
V
4h
4h 2
travel time t
t-x curve:
–
–
!
2
V
and
receiver
direct ray
ray
Horizontal reflector
Homogeneous medium of uniform velocity V
Two-way travel time the source and receiver:
At x=0, vertical reflection: t = to= 2h / V
When x increases, normal move out
For reflected arrivals, the t-x equation can also be written:
t2
x2
"
=1
2
2
to
4h
reflection
hyperbola
to = 2h/V
•
•
•
x
O
direct arrivals
slope = 1/V1
⇒ Hyperbola, asymptotic to direct arrivals
O
!
x
Reflection / Refraction
O
subcritical reflection
reflected
rays
V1
incident
rays
V2
“head waves”
ic
io
C
critically refracted ray
refracted rays
source
depth
critical
distance
supercritical reflection
A
B
Reflection / Refraction
•
•
•
•
Ground motion recorded from a
seismic wave propagating through a
layer over a halfspace ⇒ 2 arrivals,
~100 ms and ~150 ms.
What are these arrivals actually?
Direct wave, reflected? Refracted?
Head wave? ⇒ difficult to know with
one record only
Usually ground motion is recorded at
a number of different receivers and
plotted as a function of time and
distance from the source
Questions:
– How many waves?
– What are they?
A shot record
Reflection / Refraction
•
Using a simple one layer over half-space
model, we can compute the theoretical
arrival times of the various seismic waves
should be and overlay them on top of the
shot record
Solution:
–
First arrival at short offsets:
•
•
–
First arrival at larger offsets (>275 m):
•
•
–
0
Refracted arrival = head wave
Small amplitudes and a constant move-out
(smaller value than the move-out of the
direct arrival).
0
100
Last arrival recorded at all offsets:
•
•
•
Direct arrival
Constant move-out over all offsets.
Reflected arrival.
It does not have a constant move-out at all
offsets
Plots of times of arrivals of the various
waves versus offset from the source =
travel-time curves (often shown without
overlaying them on shot records)
critical
distance
200
Distance (m)
direct
refracted
Time (ms)
•
200
300
reflected
Reflection / Refraction
• Seismic Refraction: the
signal returns to the
surface by refraction at
subsurface interfaces, and
is recorded at distances
much greater than depth of
investigation.
source
seismic
reflection
seismic
refraction
In both cases:
• Seismic Reflection: the
seismic signal is reflected
back to the surface at layer
interfaces, and is recorded
at distances less than depth
of investigation.
– Objective: recover the geometry of a geological
structure
– Artificial seismic signal produced at a known
place = source
– Seismic waves are reflected/refracted by
interfaces at depth
– Receivers = seismometers at the surface (=
geophones) record the arrival of waves
– Usually performed along profiles across
geological structures
Refraction seismology
•
Objectives of a refraction survey:
– Build a t-x graph using several source-receiver
distances
– Locate the direct arrivals and estimate V1
– Locate the refracted arrivals and estimate V2
•
Equipment:
– Source (hammer, explosive)
– Geophones at various distances from the source
– Recording device
Cherry Lane P-wave
Cherry Lane S-wave
Refraction seismology
• Things can get
much more
complicated with
several layers,
dipping layers, etc
=> use of ray
tracing to infer the
structure
http://appliedgeophysics.berkeley.edu:7057/seismic/raytracing/index.html
Refraction seismology
Actual common point source record (S-waves here) and velocity structure
inferred from several similar observations
(pubs.usgs.gov/of/2003/ ofr-03-218/ofr-03-218.html)
Refraction seismology
Crustal-scale refraction seismology in the southern Andes
(http://www.scielo.cl/scielo.php?pid=S0716-02082003000100006&script=sci_arttext&tlng=en)
-x
Reflection seismology
0
x
S
• One horizontal reflector:
h
t2
x2
"
=1
2
2
t o 4h
• In seismic reflection, the lay out is such
that x << d, therefore:
( !
" x %2+
t = t o *1+ $ ' ) # 2h & ,
12
(
( 1 " x %2
+
= t o *1+ $ ' + ...- . t o *1+
*)
) 2 # 2h &
,
2+
1" x % $
'
2 # Vt o & -,
to
x2
/ 0t n = t 1 t o =
2V 2 t o
x
/V =
2t o0t n
•
!
Δtn
Δtn = normal move-out (=NMO)
– to, x, and Δtn measured from the t-x curve
– V can be calculated
x
O
t
Reflection
seismology
On land or at sea:
• Source: hammer,
shaker trucks,
dynamite, air- or
water gun
• Sensors: geophones
or hydrophones
• Cables
Seismic
reflection at sea
• Multichannel streamer
• 49 liter airgun
Single-channel / multichannel
•
Example at sea:
– Streamer (series of hydrophones) towed
behind ship
– Streamer composed of 6 traces
•
Shot scenario:
– Shot 1, reflection at P recorded by trace 1
– Shot 2:
• Reflection at P recorded by trace 3
• Reflection at P’ recorded by trace 2
– Shot 3:
• Reflection at P recorded by trace 5
• Reflection at P’ recorded by trace 4
– Etc…
•
•
P = common depth point (= CDP)
P is sampled 3 times (traces 1, 3, 5)
– If we know V, we can correct for the move-out
– Once the move-out is corrected, we can add the
3 traces = stacking ⇒ random noise cancels,
signal enhanced
Multichannel reflection
A seismic reflection profile is created by plotting side-by-side each
stacked trace from the CMP gathers along a seismic profile.
Before NMO
correction
After NMO
correction
CDP “gathers”: seismic arrivals appear
approximately hyperbolic with their
apex at zero offset
Stacking enhances primary reflections and
suppresses random noise and unaligned
coherent arrivals such as multiples
Dipping reflectors
• Pulse sent by source P:
– Reflects from A (shortest
path)
– Plotted on a distance-time
cross-section as if coming
from A’
• Distortion, the interface
appears:
– Shallower
– Less steep
• Unmigrated cross-section
Dipping reflectors
• More complex geometries
• On unmigrated crosssections:
– Synclines: “bow-tie” figure
– Anticlines: broader than
actual
– Depth, dip, geometry of
reflectors is misrepresented
• Migration: numerical
process that corrects for
reflections on nonhorizontal interfaces
Migration
•
•
Migration moves
reflections on a stacked
seismic section to their true
subsurface position
Under migration:
– A diffraction becomes a
point
– A point becomes a semicircle.
– A bowtie becomes a
syncline
– An anticline becomes a
narrower, steeper
anticline
unmigrated
migrated
3D seismic
surveying
•
•
•
•
In 2-D surveys, shots and receivers
lie along the same surface line.
3-D surveys can be acquired with
shots fired along a line orthogonal to
the recording spread, so midpoints
are equally distributed
CMP gathers comprise shot-receiver
pairs with different azimuths, but
NMO and stacking is carried as in 2D
Final result of a 3-D survey is a data
cube that provides a continuous
image of a subsurface volume.
Other issues in reflection
• Diffraction points (ex. tip of faults)
• Multiples:
– Multiple reflections from the sea surface, or from inside
layers
– “Singing”: in shallow water, resonance of multiples
creates an harmonic
• The source: must be chose according to the
purpose of the experiment
– Penetration: low-frequency source
– Resolution: high-frequency source
What have we learned?
• One can use seismic waves generated artificially to image
deep structures:
– Seismic reflection:
• Receiver and source close
• Arrivals describe hyperbolas
– Seismic refraction:
• Receiver and source far apart
• Arrivals describe straight lines
• Data collection, processing (increase SNR and remove
artifacts), interpretation
• Applications: oil exploration, sequence stratigraphy, etc.