CHAPTER TWENTY-FOUR: SEISMIC PETROPHYSICS 4 Seismic Inversion / Synthetic Sonics

Table of Contents
24.00: Introduction To This Chapter
24.01: Seismic Inversion and Synthetic Sonic Logs
24.02: Capturing Low Frequency Components
24.03: Displaying Seismic Inversion Traces
24.04: Case Histories: Seismic Inversion
1. Carbonate Strat Trap
2. Carbonate Reef
3. Porosity Estimation
4. Potash Mining
24.05: In Conclusion
24.06: Exercises for Chapter Twenty-Four
24.07: Bibliography for Chapter Twenty-Four

Continue to Chapter Twenty-Five

Publication History: Portions of this Chapter are based on training material prepared in 1971 by R. O. Lindseth, a pioneer in seismic inversion processing. Although these sources are more than 30 years old, the basic theory has not changed - only speed, quality, and implementation have improved dramatically.

This Chapter also formed part of Chapter Ten of Volume Two of The Log Analysis Handbook, a self published series of course notes covering geological and geophysical aspects of log analysis. First published in 1978, revised 1985, 1993. Completely revised and reorganized for this electronic edition Sep 2002.

CHAPTER TWENTY-FOUR: SEISMIC PETROPHYSICS 4 Seismic Inversion / Synthetic Sonics

24.00 Introduction To This Chapter
This Chapter continues the discussion of Seismic Petrophysics with explanations and case histories of seismic inversion, vertical seismic profiles, and amplitude versus offset studies. These are mainly the activities of geophysicists and seismic interpreters, but log data of the kinds described in Chapter Twenty-One are often used to calibrate or aid interpretation. Petrophysicists and geophysicists should both have a basic understanding of these techniques, so some brief description of these seismic techniques are included to bridge the gap between the two disciplines.

24.01 Seismic Inversion and Synthetic Sonic Logs
Wavelet processing of modern seismic field data yields results containing much more information than is found on conventionally processed data. These sections are usually called wide band or broad band sections. Yet the results may not bring joy to the average interpreter due to the noisy appearance of the data. See Figure 24.01.

FIGURE 24.01: Normal and broadband seismic data

Instead of simplifying the interpretation, the additional detail appears to mask the more obvious features on the conventional section and make the horizons more difficult to map. In fact, some of the principal markers on the conventional section practically disappear on the broad band section, while others appear to be displaced in time.

The broad band data approaches the response of the reflection coefficients and more accurately represents the acoustic impedance changes in the rock sequence. However, if the broad band data is to be used, some other means, other than the seismic wiggly trace, must be found to display it in a manner which can be adapted to routine interpretation.

One way to do this is to rearrange the reflection coefficient equation to solve for velocity, and display these velocities versus time or depth just like a sonic log. This requires the first velocity to be known, but thereafter all others can be derived by applying the formula in succession to each reflection coefficient.

The acoustic impedance from inversion of seismic data is:
_____1: AcImp2 = AcImp1 * (1 + Refl1) / (1 - Refl1)

If density is assumed based on lithology, the inversion can produce velocity instead of acoustic impedance. Inversion can be applied to both compressional and shear seismic data.

This equation suffers from progressive errors as successive layers are computed. I wrote a program to do this calculation on a TIAC in 1966 but it failed miserably - the data was too low in bandwidth and I hadn't thought of finding the low frequency component from nearby sonic logs.

The problem is reduced by filtering the results and stretching or squeezing to fit real, filtered sonic logs.

If this procedure is used to create an approximation of reflection coefficients from seismic data, and is expected to correlate to a real sonic log, some compensation must be made for the effects of density. Acoustic impedance is the product of velocity and density, so an inverted seismic trace is an acoustic impedance log rather than a sonic log. Fortunately, velocity is, to some degree, a linear function of acoustic impedance (Figure 24.02). The inverted data can be corrected accordingly.

FIGURE 24.02: Filtered sonic logs

A serious constraint to inversion is the limited bandwidth caused by filtering which may occur through the system. Both the earth (subsurface) and electronic filters reduce frequency content. A sonic log has a very broad frequency bandwidth, extending from DC to approximately 1000 Hz. Current field practice and equipment limits the low end of the seismic spectrum to about 8 to 10 Hz while the natural filter of the earth eliminates frequencies much over 100 Hz, depending upon the depth. Careful stacking and deconvolution will recover a good portion of the spectrum, often almost doubling the bandwidth of about 50 Hz on conventional data.

A sonic log can be filtered to demonstrate the loss of resolution caused by high cut filtering (Figures 24.03 and 24.04). The effect is roughly analogous to logging with a very long tool spacing, which decreases the resolution of the log by smoothing out high frequency information. A seismic trace of the same frequency will have resolution no better than the log.

FIGURE 24.03: Low frequency content of a sonic log

FIGURE 24.04: Separating low and high frequency components on a sonic log

24.02 Capturing Low Frequency Components
Of greater concern are low frequencies, which are usually lost through geophone response or band-limiting by the recording instruments.

Frequencies lost from the spectrum cannot be restored by deconvolution. Depending upon the geophones used and the seismic system response, frequencies below 5 to 10 Hz will be irrevocably lost from the spectrum. The absence of these frequencies is very serious, since they carry the basic velocity structure of the log.

In fact, a sonic log can be considered in terms of a low frequency carrier function modulated by higher frequencies. The effect is illustrated in Figure 24.04 where 6 Hz has been chosen as a crossover frequency to separate a time integrated sonic log into its low frequency and high frequency components. The sum of the two components yields the original sonic log.

The first step in generating the low frequency data is to extract reliable vertical velocity information from stacking velocities. A computer can pick a great number of sample points, which then can be statistically evaluated. The example of Figure 24.05 illustrates the results of a constant velocity analysis machine picked each 8 ms. The results are extremely erratic and apparently of little use, but application of a 7 Hz low pass filter yields a smooth continuous low frequency velocity curve. A single curve of this type probably contains residual errors, but several curves, closely spaced, can be averaged to produce more reliable results. The average velocities are then converted to interval velocities by ray path modeling.

FIGURE 24.05: Low frequency component of sonic log

With the low frequency velocity information developed, the density corrected, inverted seismic data above the crossover frequency can be summed with the velocity data below the crossover to yield the synthetic sonic, scaled in time and velocity. This log can be easily converted to scales of depth and interval transit time and then compared to real sonic logs.

This is the procedure used to obtain the synthetic sonic log, generally termed Seislog, which has been plotted together with a borehole compensated sonic log for comparison in Figure 24.44. The vertical scale is depth, and the horizontal scale is microseconds per foot, both normal parameters for sonic logs. The seismic data has been converted into the geological domain. It is expressed in terms familiar to a geologist and is directly correlative to conventional geological data.

FIGURE 24.06: Comparison of filtered sonic log and seismic inversion trace

24.03 Displaying Seismic Inversion Traces
Closely spaced Seislogs are presented in cross section format, similar to a seismic section, but on a depth scale instead of a time scale (Figure 24.07). Stratigraphic relationships are mapped on the continuous log section, under the assumption that a given horizontal lithologic unit maintains a constant velocity until the lithology changes.

FIGURE 24.07: Inverted seismic section

This assumption must be tempered by knowledge of gas zones and lithology variations defined by log analysis. Depth plots of gamma ray, density, sonic, and neutron logs, or computed lithology logs, will be a great help in understanding a Seislog section.

On Figure 24.08, a number of velocity breaks have been contoured. In normal use, the entire section is contoured. This procedure lends itself readily to automation. The contours of Figure 24.08 were machine drawn, illustrating the potential for automated stratigraphic mapping. Individual lithological units can be outlined whenever there is a small velocity contrast between adjacent units. While the Seislog velocities may not match the borehole sonic velocities exactly, the relative change in velocity from trace to trace is normally quite reliable and very sensitive to changing lithology, porosity, or fluid content.

FIGURE 24.08: Seismic inversion section with interpreted lithology based on velocity contours

Unfortunately, several closely spaced contour lines can be confusing, making it difficult to distinguish individual units. This can be remedied by the addition of color coding, which relates velocity to estimated rock type, as in Figure 24.09.

FIGURE 24.09: Contoured velocity mapping on a seismic inversion

In general, the color scheme is grouped into three major division: blue tones for the high velocities most commonly associated with carbonates; yellow and orange tones for the intermediate velocities most commonly associated with sandstones; and green tones for the lower velocities commonly associated with shales. By custom, as the velocity of sandstones and carbonates increases, the colors become darker suggesting denser material and less porosity. At the other end of the scale the darkest green colors correspond to the lowest velocity, generally shales. In practice the interpreter is given the option of varying the color scheme to fit known lithology from logs and samples.

The color code is strictly a function of velocity (transit time) and only indirectly indicates lithology. For instance, the green colors on Figure 24.09 are somewhat ambiguous. Although they represent shale in the Paleozoic section, they correspond to sandstones having the same velocity in the Cretaceous. Such ambiguities must be recognized and considered in the interpretation.

Good log analysis results, plotted to the same vertical scale as the inverted seismic section, will help calibrate lithology, porosity, and fluid changes. Raw sonic, density, and gamma ray logs overlaid on the Seislog would also be a tremendous help. It is surprising how few presentations of this type are actually made, considering that seismic inversion that is not calibrated to ground truth is merely colorful, expensive wall paper.

24.04 Case Histories: Seismic Inversion
Figure 24.10: Devonian Crossfield Strat Trap
In this example, the lightest colors in the Crossfield member at 1.4 seconds (-5200 ft) show where the porosity is highest. The darker blue near shot point 39 corresponds to tighter rock, which bounds this stratigraphic trap. Note that the correlation lines do not always follow color boundaries. The horizon at the top of the Devonian, for example, contacts variable color below the line, corresponding to changes in Devonian facies at the contact.

FIGURE 24.10: Seismic Inversion on Mississippian strat trap

Figure 24.11: Devonian Reef Trap
The example shows a conventional seismic section with a portion of a Seislog section across a Devonian reef. The Cretaceous Devonian unconformity is at 1.1 seconds and the reef top at 1.2 seconds near shotpoint 40. Drape over the reef is evident, as well as a porosity halo around the reef, caused by secondary dolomitization. Production is from the dolomite porosity.

FIGURE 24.11: Seismic inversion on a Devonian Reef

Figures 24.12 to 24.14: Reservoir Modeling
Figure 24.12 shows a schematic presentation of a seismic reservoir model based on raw logs, processed seismic data, and a transform of seismic amplitude to lithology and porosity. Such models are really seismic inversions and are discussed more fully later in this Chapter.

FIGURE 24.12: Lithology-porosity model in sand shale sequence

By combining sonic log velocity and reservoir contours based on 3-D migration of seismic, the porosity distribution of the pool can be better defined. This permits nonlinear interpolation between well control, as in Figure 24.13.

FIGURE 24.13: Velocity mapping to find porosity

The penultimate example (Figure 24.14) contrasts three modeling techniques over a porous reef. At top is a seismic inversion which created synthetic sonic logs from seismic traces. The colors represent acoustic impedance, and hence lithology or porosity variations. Sparse spike inversion, in the middle illustration, more closely resembles a blocked sonic log, making it less noisy and easier to interpret than normal inversion. Some fine detail may be lost.

FIGURE 24.14: Inversion controlled by sonic log modeling

The bottom image shows a multi trace forward model derived from interpolated sonic logs. Such models are often used to control inversion processing and interpretation. The model can be adjusted until a good fit to the inversion is found, or some inversion parameters can be adjusted until the inversion becomes more realistic. Both models can be altered under user control and viewed on a workstation.

Figures 24.15 to 24.17: Potash Mining
The final example illustrates synthetics made from sonic logs over a potash-halite-anhydrite sequence in Saskatchewan. Because the density variations between these minerals is so extreme, the synthetics would have been much more realistic if this data had been included. (Density sylvite = 1.86 gm/cc, carnallite = 1.57 gm/cc, halite = 2.03 gm/cc, anhydrite = 2.97 gm/cc, dolomite 2.87 gm/cc, limestone 2.71 gm/cc). The density contrast is larger than the velocity contrast and is an important factor in matching to real seismic.

FIGURE 24.15: Synthetic seismograms in potash beds

FIGURE 24.16: Synthetic seismograms in potash beds with mine entry edited into sonic log

FIGURE 24.17: Synthetic seismograms in potash beds compared to real seismic

This example courtesy of Boyd Geosearch, Calgary.

24.05 In Conclusion
There are many connecting links between the seismic and well logging domains. Both develop velocity, density, and lithologic relationships from their measured data. A synthetic view of seismic response can be made from well logs, as can the inverse process create a sonic log from seismic data. A clear understanding of the sources and definitions of acoustic velocity information, and the ability to communicate these differences, will go a long way toward integrating exploration and evaluation techniques.

24.06 Exercises for Chapter Twenty-Four
1. What is the basic mathematical concept behind seismic inversion and synthetic sonic logs? What other effects have to be accounted for? (10 marks)

2. How is low frequency data recovered for use in seismic inversion? (10 marks)

3. What criteria are used to interpret and colour code seismic inversion displays? What ambiguities might result from these colour codes? (10 marks)

4. Choose one of the Case Histories. Write a brief report covering the available input data, the steps taken to create the various outputs, the purpose for producing each output, and an interpretation of what these results show us. (20 marks)

24.07: Bibliography for Chapter Twenty-Four
SEISMIC INVERSION
1: Application of signal theory to well log interpretation; Lindseth,R.O.; Society of Professional Well Log Analysts, 21 p., 1966

2: The application of transforms to digital well log operations; Lindseth,R.O.; Society of Professional Well Log Analysts 10th Annual Logging Symposium, 20 p., 1969

3: Approximation of acoustic logs from seismic traces; Lindseth,R.O.; Canadian Well Logging Society Journal, V. 5, no. 1, p. 17-26, 1972

4: Sonic density logging without boreholes; Lindseth,R.O.; 5th Formation Evaluation Symposium Canadian Well Logging Society, 8 p., 1975

5: Improve stratigraphic exploration; XXX The Oil and Gas Journal, p. 183-188, 1977

6: Estimation of reflection coefficients from seismic data; Stone,D.G.; 47th Annual Meeting of Society of Exploration Geophysicists, 34 p., 1977

7: A geologic section from seismic data; Western Geophysical; Brochure, 2 p., 1978

8: Stratigraphic interpretation of seismic data; Rainon,E., Joncheray,B.; Society of Professional Well Log Analysts: The Log Analyst, p. 3-12, 1978

9: Modern seismic methods: an aid for the petroleum engineer; Ausburn,B.E., Nath,A.K., Wittick,T.R.; The Journal of Canadian Petroleum Technology, p. 1519-1530, 1978

10: Low frequency recovery in the inversion of seismograms; Galbraith,J.M., Millington,G.F.; Canadian Society of Exploration Geologists National Convention, p. 30-42, 1978

11: Velog: seismic processing for stratigraphic interpretation; Rainon,E.; Handbook, 12 p., 1979

12: G log processing; Geophysical Services inc.; Brochure, 6 p., 1980

13: Stratigraphic interpretation of seismic data; Teknica; Manual, 74 p., 1981

14: Advanced seismic techniques for delineation of petroleum reservoir; Lindseth,R.O.; The Journal of Canadian Petroleum Technology, p. 35-46, 1981

15: Seismic reservoir analysis; Ward,J.A.; Sym 3 for Unconventional Methods, 15 p., 1982

16: Use of seislog for basin evaluation and field development; Mummery,R.C.; Society of Exploration Geophysicists Seminar, 31 p., 1984

17: Suitable environments for inversion techniques: a model study; Jain,S.; Journal of Canadian Society of Exploration Geologists, v. 22, no. 1, p. 7-16, 1986

ABOUT THE AUTHOR

E. R. (Ross) Crain, P.Eng. is a Consulting Petrophysicist and a Professional Engineer with over 35 years of experience in reservoir description, petrophysical analysis, and management. He has been a specialist in the integration of well log analysis and petrophysics with geophysical, geological, engineering, and simulation phases of oil and gas exploration and exploitation, with widespread Canadian and Overseas experience.

His textbook, "Crain's Petrophysical Handbook on CD-ROM" is widely used as a reference to practical log analysis. Mr. Crain is an Honourary Member and Past President of the Canadian Well Logging Society (CWLS), a Member of Society of Petrophysicists and Well Log Analysts (SPWLA), and a Registered Professional Engineer with Alberta Professional Engineers, Geologists and Geophysicists (APEGGA)