1. Seismic Methods Geoph 465/565 ERB 5104 Lecture 7 – Sept 16, 2015
Lee M. Liberty
Research Professor
Boise State University

2. Quiz 1
A rule of thumb is to not record signal above 70% of the Nyquist frequency. If you record a vibroseis sweep from Hz:
What integer sample rate (in milliseconds) do you need to not alias your signal?
What is the Nyquist frequency of this sample rate?
What is the bandwidth (in octaves) of this signal?
10,20,40,80,160
sample rate (ms)
Nyquist Frequency (Hz)
0.25
2000
0.5
1000 1
500 2
250 4
125 8
62.5

3. Quiz 1
If your range of recorded amplitudes is volts, what is the dynamic range of your signal?

4. Quiz 1 Source wavelet: 2, 5, 2 Reflectivity sequence: 0, 0, -1, 0, 0
Convolve
How would the cross correlated response of these two signals differ?
Source wavelet: 2, 5, 2
Reflectivity sequence: 0, 0, -1, 0, 0

5. For a velocity of 800 m/s and a dominant frequency of 100 Hz
What is the wavelength?
What is the vertical resolution according to Rayleigh criteria?
What is the lateral resolution (Fresnel zone) for a reflector at 8 m depth?

6. Seismic Unix display
suwind tmax=.15 <Highland_shot.su |suxwigb

7. Seismic Unix display
suwind tmax=.15 <Highland_shot.su |\ sugain pbal=1|suxwigb

8. Seismic Unix display
suwind tmax=.15 <Highland_shot.su |\ sugain pbal=1|\ suxwigb perc=90

9. Seismic Unix display
suwind tmax=.15 <Highland_shot.su |\ sugain pbal=1|\ suop op=neg |\ suxwigb perc=90

10. Seismic Unix display
suwind tmax=.15 <Highland_shot.su |\ sugain pbal=1|\ suop op=neg |\ suxwigb perc=90

11. Distance vs. time plot for first arrivals
V0=526 m/s
V1=1,968 m/s
Z~3 m
Surface elevation
828 m
River elevation
825 m

12. velocity and amplitude
Reflectivity
velocity and amplitude

13. Normal-incidence reflection coefficient
For normal (vertical) incidence, there is no mode conversion, and the amplitude of the reflected wave is given by:
R =
r2v2 – r1v1
r2v2 + r1v1
rv = acoustic impedance
(density x velocity)

14. Shot record showing relation between refraction/reflecti on
Reflections are asymptotic to refracted/direct arrivals
Refracted
wave
Direct
wave
Shot record showing relation between refraction/reflecti on
reflections
Surface waves

15. Angle dependence amplitude
The values for reflection coefficients are determined by the angle of incidence, and by the density (r) and wave velocities (v) for each layer.
The plot shows how the coefficients change with angle of incidence, from q=0, where the wave is traveling perpendicular to the boundary, to q=90, where the wave is parallel (grazing incidence).

16. Zoeppritz equations Ray parameter
There are 4 equations with 4 unknowns (and six independent elastic parameters)
Although they can be solved, they do not give an intuitive understanding for how the reflection amplitudes vary with the rock properties (e.g., density and velocity).
The notation used for each coefficient "RP" or "TS“ indicates whether it is a reflection or transmission coefficient, the second letter indicates whether the incident wave is P or S. The sizes of the four coefficients RP, RS, TP, and TS are related to how the energy of a P-wave is distributed when it reaches an interface.
The coefficients RS and TS can be appended with (v) or (h). This is because an S-wave can oscillate either in a plane containing a vertical line (v) or one containing a horizontal line (h). Only the former can generate or be derived from P-waves.

17. Zoeppritz equations – reflected amplitude
R(θ) = a Δα / α + b Δρ / ρ + c Δβ/β (valid for <30o angles)
where:
a = 1/(2cos2θ), = (1 + tan2θ)/2
b = [(2β2/α2) sin2θ]
c = -(4β2/α2) sin2θ
α = (α1 + α2)/2 = p-wave velocity
β = (β1 + β2)/2 = s-wave velocity
ρ = (ρ1 + ρ2)/2 = density
Δα = α2 - α1
Δβ = β2 - β1
Δρ = ρ2 - ρ1
θ = (θi + θt)/2, where θt = arcsin[(α2/α1) sinθi]
Aki, Richards and Frasier approximation: written as three terms, the first involving P-wave velocity, the second involving density, and the third involving S-wave velocity.

18. Shuey approximation – eliminates shear wave velocity estimate (often used for AVO analyses
The compressional wave reflection coefficient given by the Zoeppritz equations is simplified to the following:
The first term gives the amplitude at normal incidence, the second term characterizes at intermediate angles, and the third term describes the approach to critical angle.
Poisson's ratio s.

19. Physical properties of some rocks

20. Zoeppritz calculator http://www. crewes

21. Reflected/Refracted Waves
angular dependence
A) A compressional wave, incident upon an interface at an oblique angle, is split into four phases: P and S waves reflected back into the original medium; P and S waves refracted into other medium.
For a wave traveling from material of velocity V1 into velocity V2 material, ray paths are refracted according to Snell’s law.
i1 = angle of incidence
i2= angle of refraction

22. What happens with a velocity inversion?
angular dependence
A) A compressional wave, incident upon an interface at an oblique angle, is split into four phases: P and S waves reflected back into the original medium; P and S waves refracted into other medium.
For a wave traveling from material of velocity V1 into velocity V2 material, ray paths are refracted according to Snell’s law.
i1 = angle of incidence
i2= angle of refraction

23. Normal-incidence reflection coefficient
For normal (vertical) incidence, there is no mode conversion, and the amplitude of the reflected wave is given by:
R =
For velocity reversal, you get a negative reflection coefficient and opposite ray bending
r2v2 – r1v1
r2v2 + r1v1
rv = acoustic impedance
(density x velocity)

24. Velocity inversion

25. What happens with a fast surface layer?
Vertically oriented geophones do not optimally capture ray bending
3-c (or 2-c) recording
Larger amplitude shear waves compared to p-waves

26. Velocity modeling – next week in lab
shear wave
compressional wave

27. Seismic reflection processing

28. Common Depth Point (CDP) or Common-midpoint (CMP) method
Ideally, we would like to illuminate each point from a wide range of angles (improve lateral resolution via migration, assess physical properties at depth).
It is impractical to collect CDP data this way, so it is collected as a series of shots, then re-arranged later.
CMP gather
Shot gather

29. use vrms to flatten reflectors on the CDPs
t1,v1
t2,v2
t3,v3
t4,v4
t5,v5

30. Processing steps - Simple version
Sort (Shots to CMP domain)
Normal moveout correction (NMO)
Stack >> Brute Stack (first look at the data!)

31. Additional Processing Steps stack-migrate in time
Preprocessing
Clean up Shot Records
Amplitude recovery
Deconvolution
Sort to CMP
Velocity Analysis – iterative
Residual statics
NMO correction
Mutes
Stack (gains and filters often follow)
Migrate
Convert to depth

32. More complete processing flow
The following steps shall be included in seismic reprocessing sequence for the post stack time migration stage:
a) transcription from SEGY to industrial compliance software internal format
b) geometry assignment, 2D CDP straight or crooked line binning as required
c) trace edit – editing of bad traces
d) refraction statics analysis
e) True Amplitude Recovery using spherical divergence correction
f) application of Surface Wave Noise Attenuation filter (optional)
g) deconvolution - standard deconvolution (to be tested)
h) first interactive velocity analysis at 500m intervals
i) Residual Statics Solution – Maximum power algorithm
j) second interactive velocity analysis at 500m intervals
k) Residual Statics Correction (Second Pass) – Maximum Power
l) first mis-tie QC using industrial compliance software interpretation software
m) Common Offset DMO in TX Domain
n) final interactive velocity analysis at 200m intervals
o) Normal Moveout Correction – using final stacking velocities
p) Mute – selection and application of final top mute
q) CDP Stack
r) second mis-tie QC using industrial compliance software interpretation software
s) Finite Difference Time Migration using interval velocities function derived from smoothed final stacking velocities
t) Time Variant Bandpass filtering
u) FX Deconvolution – Random noise attenuation (optional)
v) final scaling - AGC applied

33. Seismic Methods – body waves
Surface refraction
Surface reflection
VSP
Cross well

34. Velocity Surveys: Check Shot and VSP
Source
1-Way
Time
Check Shot: geophone in hole, source at surface. Record first arrival time and calculate velocity
Advanced version is VSP (Vertical Seismic Profile) with many geophone locations and process all reflections
Reflection Recorded by VSP
Depth
Receiver in
wellbore

35. VSP ray geometries