1. Seismic Methods Geoph 465/565 ERB 5104 Lecture 5 – Sept 9, 2015
Lee M. Liberty
Research Professor
Boise State University

2. PSWIGB - PostScript WIGgle-trace plot of f(x1,x2) via Bitmap Best for many traces. Use PSWIGP (Polygon version) for few traces. pswigb n1= [optional parameters] <binaryfile >postscriptfile Required Parameters: n1 number of samples in 1st (fast) dimension Optional Parameters: d1=1.0 sampling interval in 1st dimension f1=0.0 first sample in 1st dimension n2=all number of samples in 2nd (slow) dimension d2=1.0 sampling interval in 2nd dimension f2=0.0 first sample in 2nd dimension x2=f2,f2+d2,... array of sampled values in 2nd dimension bias=0.0 data value corresponding to location along axis 2 perc=100.0 percentile for determining clip clip=(perc percentile) data values < bias+clip and > bias-clip are clipped xcur=1.0 wiggle excursion in traces corresponding to clip wt=1 =0 for no wiggle-trace; =1 for wiggle-trace va=1 =0 for no variable-area; =1 for variable-area fill =2 for variable area, solid/grey fill SHADING: 2<= va <=5 va=2 lightgrey, va=5 black nbpi=72 number of bits per inch at which to rasterize verbose=1 =1 for info printed on stderr (0 for no info) xbox=1.5 offset in inches of left side of axes box ybox=1.5 offset in inches of bottom side of axes box wbox=6.0 width in inches of axes box hbox=8.0 height in inches of axes box x1beg=x1min value at which axis 1 begins x1end=x1max value at which axis 1 ends d1num=0.0 numbered tic interval on axis 1 (0.0 for automatic) f1num=x1min first numbered tic on axis 1 (used if d1num not 0.0) n1tic=1 number of tics per numbered tic on axis 1
Seismic Methods Lab 1

3. SUMUTE - MUTE above (or below) a user-defined polygonal curve with the distance along the curve specified by key header word sumute <stdin >stdout xmute= tmute= [optional parameters] Required parameters: xmute= array of position values as specified by the `key' parameter tmute= array of corresponding time values (sec), in case of air wave muting, correspond to air blast duration ... or input via files: nmute= number of x,t values defining mute xfile= file containing position values as specified by the `key' parameter tfile= file containing corresponding time values (sec) ... or via header: hmute= key header word specifying mute time Optional parameters: key=offset Key header word specifying trace offset =tracl use trace number instead ntaper=0 number of points to taper before hard mute (sine squared taper) mode=0 mute ABOVE the polygonal curve =1 to zero BELOW the polygonal curve =2 to mute below AND above a straight line. In this case xmute,tmute describe the total time length of the muted zone as a function of xmute the slope of the line is given by the velocity linvel= =3 to mute below AND above a constant velocity hyperbola as in mode=2 xmute,tmute describe the total time length of the mute zone as a function of xmute, the velocity is given by the value of linvel= =4 to mute below AND above a user defined polygonal line given by xmute, tmute pairs. The widths in time of the muted zone are given by the twindow vector linvel=330 constant velocity for linear or hyperbolic mute

4. Mid-term presentations: topics in seismology
Oct – 2 or 3 per day
15-minute oral presentation
Include: history of topic, theory, approach to addressing/solving topic, relevance to industry/society
Topic?
Andrew: seismic monitoring of volcanoes
Tate: glacial monitoring using seismology
Aiada: seismoelectric
Travis: fat ray path/WET inversions
Marlon: nuclear seismology
Will: ETS
Dmitri

5. Friday quiz Know these concepts – definitions and use
Nyquist frequency fmax=1/(2dt)
Convolution (deconvolution)
Correlation (cross correlation, autocorrelation)
Bandwidth - frequency range contained in a source wavelet or seismic trace
Resolution – vertical (Rayleigh criterion) and horizontal (Fresnel zone)
Dynamic range: amplitude (A) or power (P) ratio (in dB):

6. Convolution and Correlation
Correlation is a measure of similarity between two signals
(t) = ∫ f(t) g(t-t)dt
Convolution is a measure of effect of one signal on the other (output response on input signal).
h(t) = ∫ f(t) g(t-t)dt
In practice, correlation is done the same way as convolution in the time domain, except that the wavelet is not reversed before the multiplication process.
If the filter is symmetric, then convolution and correlation produce the same result

7. Filtering in the time domain - convolution
h(t) = f(t) * g(t) = ∫ f(t) g(t-t)dt
Given two arrays:
1. Reverse moving array
2. Multiply and add
3. Shift
4. repeat step 2 2
time
* = -1

8. Convolution Source wavelet: 2, 4, 3
Reflectivity sequence: 0, 0, 1, 0, 0, 0, 0

9. Vibroseis
Vibroseis sources use cross-correlation to synthesize a short, zero- phase wavelet from a long source sweep.

10. Autocorrelation
Correlation between a function and itself is called an autocorrelation.
The autocorrelation of a function gives the zero-phase wavelet, scaled to the total energy in the trace.
Autocorrelation is used to retrieve the zero- phase wavelet from a seismic trace.

11. Fresnel zone
a reflection coming back to the surface from a point in the subsurface is actually being reflected from an area with the dimension of the First Fresnel Zone.
The dimensions of the Fresnel Zone can be calculated for a plane reflector in the constant velocity case, allowing for two-way travel time.

12. Lateral Resolution
What is the minimum horizontal distance between two subsurface features such that we can tell them apart seismically?
Neidell & Poggiaglioimi, 1977
AAPG©1977 reprinted with permission of the AAPG whose permission is required for further use.

14. Resolution
Wavelength (l), velocity (v) and frequency (f) l = v/f f = v/l
fresnel zone 
Depth  d=(v*t)/2 where t=two-way travel time
Fresnel zone~
For example: v=1,500 m/s, f=100 Hz(dominant)
l = v/f = 15 m; vertical resolution =3.75 m
Fresnel zone lateral resolution ~47 ms (75 m depth)
Fresnel zone lateral resolution ~15 ms (7.5 m depth)

15. Direct/Reflection/Refraction arrivals and travel times

16. Direct Wave
The travel time to each geophone for the direct wave in the first layer is:

17. 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

18. The Reflected Ray v1 v2 is never a first arrival
Plots as a (hyperbolic) curved path on t-x diagram
Asymptotic with direct ray
Time (t)
Distance (x)
Receiver
Shot Point v1
Layer 1 v2
Layer 2

19. The Refracted Ray “Critical Distance” No Refracted Rays  v1 v2
The Refracted Ray Arrival Time:
Plots as a linear path on t-x diagram (assuming v2>v1)
Part travels in upper layer (constant)
Part travels in lower layer (function of x)
Only arrives after critical distance
Is first arrival only after cross over distance
Travels long enough in the faster layer
Time (t)
Distance (x)
critical
distance
cross over
distance
“Critical Distance”
No Refracted Rays  ic ic ic ic v1
Layer 1
Layer 2 v2

20. Refracted wave
The ray path and the travel time for the refracted wave for a 2-layer model can be derived as B C
trefract=x/v2+ti

21. Refraction seismology
A refraction refers to the wave energy that travels below the upper interface at the velocity of the lower layer.
The refraction travels horizontally along the lower interface, then travel back toward the earth’s surface.
The refracted wave can only be received after the critical distance xcrit beyond the critical angle icrit .

22. Snell’s Law & Critical Refraction
Seismic sources radiate waves in all directions
Some rays hit an interface at exactly the critical angle, ic
This critically oriented ray will then travel along the interface between the two layers
If more oblique than critical, all wave energy is reflected

23. The Time-Distance (t-x) Diagram
Intercept time - tint
Critical distance - xcrit
Cross over distance - xcross

24. Minimum distance where refractions are generated

25. Cross over distance
At the crossover distance xcross the travel times to the point are the same for the direct wave and the refracted wave, so we have

27. Intercept time
Y-intercept of refracted arrival

28. Single layer calculation

29. Summary: Direct/Reflection/Refraction Travel times
Travel times for the direct, reflected, and refracted waves for a 2-layer model

30. 3 layer refraction problem

31. 3-layer problem

32. Dipping Planar Interfaces
When a refractor dips, the slope of the traveltime curve does not represent the "true" layer velocity:
shooting updip, i.e. geophones are on updip side of shot, apparent refractor velocity is higher
shooting downdip apparent velocity is lower
To determine both the layer velocity and the interface dip, forward and reverse refraction profiles must be acquired.

33. Dipping Layer V1 h1  Letting j = 2h1 we can alternatively write 
Here, j is
distance
from the
shotpoint
to an image
point h1 
Letting j = 2h1
we can alternatively write 

35. Complex velocity models
Time-distance plots are used to provide a best fit between observed and modeled results

36. Undulating Interfaces
Undulating interfaces produce non-linear t-x diagrams
There are multiple approaches to address this
delay times & plus minus method

37. Reciprocal method
Used to map an undulating interface that separates two materials of contrasting seismic velocity beneath an undulating surface;

38. Detecting Offsets
Offsets are detected as discontinuities in the t-x diagram
Offset because the interface is deeper and D’E’ receives no refracted rays.

39. Diving waves

40. Refraction Tomography

41. Caveats of Refraction
Only works if each successive layer has increasing velocity
Cannot detect a low velocity layer
May not detect thin layers
Requires multiple (survey) lines
Make certain interfaces are horizontal
Determine actual dip direction not just apparent dip

42. The Low Velocity Layer
If a layer has a lower velocity than the one above…
There can be no critical refraction
The refracted rays are bent towards the normal
There will be no refracted segment on the t-x diagram
The t-x diagram to the right will be interpreted as
Two layers
Depth to layer 3 and Thickness of layer1 will be exaggerated

43. The Hidden Layer
Recall that the refracted ray eventually overtakes the direct ray (cross over distance).
The second refracted ray may overtake the direct ray first if:
The second layer is thin
The third layer has a much faster velocity

44. Geophone Spacing / Resolution
Often near surface layers have very low velocities
E.g. soil, subsoil, weathered top layers of rock
These layers are likely of little interest
But due to low velocities, time spent in them may be significant
To correctly interpret data these layers must be detected
Decrease geophone spacing near source

45. Fan Shooting
Discontinuous targets can be mapped using radial transects: called “Fan Shooting”
A form of seismic tomography

46. Refraction Tomography
Complex solution to complex geologic problems