Seismic Reflection

Seismic Reflection Method

Top: Monument unveiled in 1971 at Belle Isle (Oklahoma City) on 50th anniversary of first seismic reflection survey by J. C. Karcher. Middle: Two early reflection records from Belle Isle, 1921. Bottom: Karcher's interpretation of same.

uses reflected energy from interfaces between subsurface layers to determine their configuration
reflections recorded as two-way (down and back up) travel times, not depths
fraction of incident energy reflected from interface called reflection coefficient
dependent on acoustic impedance contrast across interface

Polarity of reflected wave depends on sign of reflection coefficient (unchanged polarity means compression remains compression, dilatation remains dilatation)

Hypothetical Rock Properties
Rock	V_P, km/s	r, kg/m³	V x r
Granite	5.0	2700	13,500
Basalt	5.5	3000	16,500
Limestone	6.0	2300	13,800
Sandstone	4.2	2500	10,500
Shale	2.5	2300	5,750

For these hypothetical values, limestone-granite contact will be poor reflector

Simple Zero-offset Reflection Survey

zero offset (distance between source and receiver)
single layer on half-space

reflections produce a time-section approximating interface (that even geologists can understand)
travel time:
2 problems:
- what is V? [We measure t. If we knew V, we could find d - convert time section to depth section.]
- energy source is expensive in time and money
solution to both problems: use geophones at different offsets

Seismic Reflection Survey with Offset, Single-fold Coverage

record traces from several geophones spaced away from source (shot)
display traces side-by-side, so distance between traces proportional to geophone spacing
display increasing time downward (time approx. proportional depth)

Note that subsurface reflection points have half the spacing of geophones. To get complete "single-fold "coverage of the subsurface, can shoot from either end of geophone spread:

One can also use a "split-spread" arrangement, here with shot at point B, then move half the geophones forward and shoot at C:

The next two figures show recording-truck signal check for 36-channel split-spread layout:

The travel time for the primary reflection (first layer) where geophone offset = x, thickness d, velocity V

this is a hyperbola, as we saw earlier:

for multiple geophones, seismic traces look like:

for deeper layers, the hyperbola is "flatter:"

direct ray is straight line, per rate equation
reflections from 1st and 2nd reflectors are not flat; reflections are hyperbolas
because of normal moveout (NMO): reflection time increases with x, nonlinearly
normal move-out (NMO): the difference in reflection travel-times from a horizontal reflecting surface due to variations in the source-geophone distance
can correct for this using NMO correction, so reflections are flat
because deeper reflectors produce flatter parabolas, NMO is less:

from before, we have:
so the NMO is just t - t₀, where t₀ is simply 2d/V
but we don't know d or V
however,
so, plot t² vs. x²:
measure slope to get V
intercept gives d

Multiple Layers

foregoing assumed a straight-line path from source to reflector to receiver
with multiple layers with different velocities, this clearly does not hold (actual path compared with straight-line assumption):

however, if depths are large compared to total geophone spread, error can be small

Green Method

assuming straight-line paths, one can still just use a x²-t² plot to estimate velocities and depths
however, there is a more accurate method:

The Dix Equation

uses special velocity called V_RMS
_{still assumes nearly vertical incidence/straight line
raypaths}
given n horizontal beds, and Dt is the one-way vertical travel-time through bed i, Dix equation states:

use x²-t² plot to determine RMS velocities to each layer
then can get interval layer velocities and thicknesses
replace velocity terms by V_RMS

it can be shown that Dix's equation can be solved for the individual interval velocities
in fact, the following is sometimes referred to as Dix's equation:

thicknesses can then be easily determined:

Velocity Scans

Signal Summing; Stacking

As seismic energy moves away from the source, there is a decrease in signal strength as the energy spreads out.
This causes energy to decrease by E = E₀/(2pr²).
Since energy is proportional to the square of the amplitude, the signal amplitude drops off like 1/r.
In addition, since rocks are not truly elastic (anelastic), some energy is lost to heat with every cycle, leading to an exponential loss of energy.
Higher frequencies go though more cycles to a given depth (shorter wavelength), so high frequency energy is lost with depth
Taking both of these effects into consideration, we have:

reflections from significant depth have amplitudes that may be well below the noise level
summing and stacking adds (coherent) signals and (random) noise
improves signal-to-noise ratio (S/N, or S/(S+N))
- summing n times increases signal by n
- summing n times increases noise by square root of n
Example:
- reshoot a line 36 times
- signal increases by 36
- noise increases by 6 (square root)
- S/N improves by 36/6 = 6
different means of improving S/N:

geophone groups

"Geophones are rarely used singly. Normally several (as many as 20 or more) are electrically connected to each other in a group in such a way that the outputs of the individual phones are effectively summed. The information from each group must be transmitted via cables to the recording truck. In modern land recording with 48, 96, or more group recordings, the cables are long and heavy and often add noise to the recording, especially in the presence of powerlines or water." - Dobrin and Savit, Introduction to Geophysical Prospecting, 4th ed.

"geophone" is actually a group of geophones "tied together" in a geophone group
signals in parallel, fed into one channel of system
signal usually has small incident angle, reaches all geophones together (coherent)
surface noise sweeps across geophones, tends to cancel

multiple shots

dynamite in hole
vibroseis trucks: multiple trucks, all in sync; shake several times
multiple hammer blows, shotgun blasts, etc.

multi-fold coverage

Example: 4 geophones (channels); move shot and geophones one geophone spacing and reshoot:

note that subsurface reflection points twice as closely spaced as geophones
had we moved shot (array) 2 geophone spacings, only get single-fold coverage
try this with different numbers of geophones and shot spacings to find a simple formula to calculate fold-coverage

Rock Velocities

P, S velocities of various rocks (See Sydney Clark's GSA Memoir for much more)
velocity vs. density
velocity vs. density, part 2
velocity vs. rock age for sandstones and shales

Data Collection

Source

Geophones

Geophones (~ $100 each) have a typical natural frequency of 10 Hz
Response is relative good over a range from about 2 Hz to 100 Hz

Recording Digitally

Analog signal from phones (continuous voltage vs. time)
sampled (typically every 2 msec) by an A-to-D (A/D) converter
originally integer recording
- example: 16-bit recording;
- 2¹⁶ = 65,536, or -32767 to +32768
- dynamic range of about 4.5 orders of magnitude
- poor resolution at low amplitudes
floating pointing recording
- single precision, 4 bytes, 6 digits of resolution, dynamic range 10^+/-32

Processing Steps

At one time, greatest computing power was owned by government (mostly DOD)
Petroleum companies ranked second
most seismic reflection processing is computer intensive, but requires intelligent "operator" input at many steps in the process

AGC: automatic gain control

early-arriving reflections may be orders of magnitude larger in amplitude than later ones
AGC looks at average amplitude in a sliding time window and boosts (or attenuates) amplitude to a constant value over that window
AGC causes loss of true amplitude information
modern floating-point recording allows full amplitude information to be retained
retaining "relative, true amplitude" done with linear or quadratic increase of gain with time:

Filtering

remove or attenuate certain frequencies to reduce noise and improve S/N
notch filter common at 60 Hz
filtering often done with FFT
filters must be "ramped" to avoid ringing (Gibbs phemonemon)

Statics Removal

refraction statics - requires reversed profile
up-hole shooting

vertical velocity distribution near the surface determined by shooting up the hole" (Geophysical Services, Inc.):

automatic statics

Migration

Synthetic Seismograms

Directions Seismic Reflection is Heading

Percentage of seismic activity involving various techniques. (Data from SEG annual Geophysical Activity Reports, pre-1981 data are for U.S. activity, post-1980 for worldwide activity, 3-D data from Dutt, 1992, adjusted according to judgment expressed in Goodfellow, 1991.)