Synthetic seismogram

A synthetic seismogram is the result of forward modelling the seismic response of an input earth model, which is defined in terms of 1D, 2D or 3D variations in physical properties. In hydrocarbon exploration this is used to provide a 'tie' between changes in rock properties in a borehole and seismic reflection data at the same location. It can also be used either to test possible interpretation models for 2D and 3D seismic data or to model the response of the predicted geology as an aid to planning a seismic reflection survey. In the processing of wide-angle reflection and refraction (WARR) data, synthetic seismograms are used to further constrain the results of seismic tomography.[1] In earthquake seismology, synthetic seismograms are used either to match the predicted effects of a particular earthquake source fault model with observed seismometer records or to help constrain the Earth's velocity structure.[2] Synthetic seismograms are generated using specialized geophysical software.

## Contents

* 1 1D synthetics
* 2 1.5D seismic modelling
* 3 2D synthetic seismic modeling
* 4 3D synthetic seismic modelling
* 5 WARR data modelling
* 6 Earthquake modelling
* 6.1 Source modelling
* 6.2 Velocity modelling
* 7 References

## 1D synthetics

Seismic reflection data are initially only available in the time domain. In order that the geology encountered in a borehole can be tied to the seismic data, a 1D synthetic seismogram is generated. This is important in identifying the origin of seismic reflections seen on the seismic data. Density and velocity data are routinely measured down the borehole using wireline logging tools. These logs provide data with a sampling interval much smaller than the vertical resolution of the seismic data. The logs are therefore often averaged over intervals to produce what is known as a 'blocked-log'.[3] This information is then used to calculate the variation in acoustic impedance down the well bore using the Zoeppritz equations.[4] This acoustic impedance log is combined with the velocity data to generate a reflection coefficient series in time. This series is convolved with a seismic wavelet to produce the synthetic seismogram. The input seismic wavelet is chosen to match as closely as possible to that produced during the original seismic acquisition, paying particular attention to phase and frequency content.

## 1.5D seismic modelling

The convolutional 1D modelling produces seismograms containing approximations of primary reflections only. For more accurate modelling involving multiple reflections, head waves, guided waves and surface waves, as well as transmission effects and geometrical spreading, full waveform modelling is required. For 1D elastic models the most accurate approach to full waveform modelling is known as the reflectivity method.[5] This method is based on the integral transform approach, whereby the wave field (cylindrical or spherical wave) is represented by a sum (integral) of time-harmonic plane waves.[6] The reflection and transmission coefficients for individual plane waves propagating in a stack of layers can be computed analytically using a variety of methods, such as matrix propagator,[7][8][9][10][11] global matrix[12] or invariant embedding.[13] This group of methods is called 1.5D because the earth is represented by a 1D model (flat layers), while wave propagation is considered either in 2D (cylindrical waves) or 3D (spherical waves).

## 2D synthetic seismic modeling

A similar approach can be used to examine the seismic response of a 2D geological cross-section. This can be used to look at such things as the resolution of thin beds or the different responses of various fluids, e.g. oil, gas or brine in a potential reservoir sand.[14] It may also be used to test out different geometries of structures such as salt diapirs, to see which gives the best match to the original seismic data. A cross-section is built with density and seismic velocities assigned to each of the individual layers. These can be either constant within a layer or varying in a systematic fashion across the model both horizontally and vertically. The software program then runs a synthetic acquisition across the model to produce a set of 'shot gathers' that can be processed as if they were real seismic data to produce a synthetic 2D seismic section. The synthetic record is generated using either a ray-tracing algorithm or some form of full waveform modelling, depending on the purpose of the modelling. Ray-tracing is quick and sufficient for testing the illumination of the structure,[15] but full waveform modelling will be necessary to accurately model the amplitude response.[16]

## 3D synthetic seismic modelling

The approach can be further expanded to model the response of a 3D geological model. This is used to reduce the uncertainty in interpretation by modelling the response of the 3D model to a synthetic seismic acquisition that matches as closely as possible to that actually used in acquiring the data that has been interpreted.[17] The synthetic seismic data is then processed using the same sequence as that used for the original data. This method can be used to model both 2D and 3D seismic data that has been acquired over the area of the geological model. During the planning of a seismic survey, 3D modelling can be used to test the effect of variation in seismic acquisition parameters, such as the shooting direction or the maximum offset between source and receiver, on the imaging of a particular geological structure.[18][19]

## WARR data modelling

Wide Aperture Reflection and Refraction (WARR) models' initial processing is normally carried out using a tomographic approach in which the time of observed first arrivals is matched by varying the velocity structure of the subsurface. The model can be further refined using forward modelling to generate synthetic seismograms for individual shot gathers.[1]

## Earthquake modelling

### Source modelling

In areas that have a well understood velocity structure it is possible to use synthetic seismograms to test out the estimated source parameters of an earthquake. Parameters such as the fault plane, slip vector and rupture velocity can be varied to produce synthetic seismic responses at individual seismometers for comparison with the observed seismograms.[20]

### Velocity modelling

For seismic events of known type and location, it is possible to obtain detailed information about the Earth's structure, at various scales, by modelling the teleseismic response of the event.[2]

## References

1. ↑ 1.0 1.1 Makris, J., Egloff, F. & Rihm, R. 1999. WARRP (Wide Aperture Reflection and Refraction Profiling): The principle of successful data acquisition where conventional seismic fails, SEG 1999 Expanded Abstracts
2. ↑ 2.0 2.1 Helmberger, D.V. 1974, Understanding Seismograms by Constructing Numerical Models, Engineering and Science, 38, 26–29.
3. ↑ Goldberg, D., Wilkens, R.H. & Moos, D. 1987. Seismic modeling of diagenetic effects in Cenozoic marine sediments at Deep Sea Drilling Project sites 612 and 613, DSDP Initial report on Leg 95, 23
4. ↑ OBartels, T., Krastel, S., and Spiess, V., 2007. Correlation of high-resolution seismic data with ODP Leg 208 borehole measurements. In Kroon, D., Zachos, J.C., and Richter, C. (Eds.), Proc. ODP, Sci. Results, 208: College Station, TX (Ocean Drilling Program), 1–27
5. ↑ Fuchs, K., and G. Muller, 1971, Computation of synthetic seismograms with the reflectivity method and comparison with observations, Geophys. J. R. Astron. Soc, 23, 417.
6. ↑ Aki, K. and Richards, R.G., Quantitative Seismology, Theory and Methods, Vol. I, W. H. Freeman, 1980.
7. ↑ Thomson, W.T., 1950, Transmission of elastic waves through a stratified solid material, Journal of Applied Physics, 21, 89–93.
8. ↑ Haskell, N. A., The dispersion of surface waves in multilayered media, , Bulletin of the Seismological Society of America, 43, 17–34,1953.
9. ↑ Dunkin, I.W., 1965, Computation of model solutions in layered elastic media at high frequencies, Bulletin of the Seismological Society of America, 55, 335–358.
10. ↑ Thrower, E.N., The computation of the dispersion of elastic waves in layered media, Journal of Sound and Vibration, 2, 210–226.
11. ↑ Molotkov L.A., 1984, Matrix method in the theory of wave propagation in layered elastic and fluid media, Nauka (in Russian).
12. ↑ Schmidt, H and Tango., 1986, Efficient global matrix approach to the computation of synthetic seismograms, Geophysical Journal of the Royal Astronomic Society, 84, pp 331–359.
13. ↑ Kennett, B. L. N., 1985, Seismic wave propagation in stratified media, Cambridge University Press.
14. ↑ Hodgetts, D. & Howell, J.A. 2000. Synthetic seismic modelling of a large-scale geological cross-section from the Book Cliffs, Utah, USA, Petroleum Geoscience, 6, 221–229.
15. ↑ Graham, S., Lawton, D. & Spratt, D. 2005. Sub-thrust imaging:modelling example from the Cusiana oilfield, Llanos Basin, Colombia, CSEG National Convention, Abstract.
16. ↑ Li, Y., Downton, J. & Xu, Y. 2004. AVO Modeling in Seismic Processingand Interpretation II. Methodologies, CSEG Recorder, January, 38–44.
17. ↑ Gawith, D.E. & Gutteridge, P.A. 1996. Seismic validation of reservoir simulation using a shared earth model, Petroleum Geoscience, 2, 97–103.
18. ↑ Gjøystdal, H., Iversen, E., Lecomte, I., Kaschwich, T., Drottning, Å. and Mispel, J. 2007. Improved applicability of ray tracing in seismic acquisition, imaging, and interpretation, Geophysics, 72, 261–271.
19. ↑ Ray, A., Pfau, G. & CHen, R. 2004. Importance of ray-trace modeling in the discovery of Thunder Horse North Field, Gulf of Mexico, The Leading Edge, 23, 68–70.
20. ↑ Cotton, F. & Campillo, M. 1994. Application of seismogram synthesis to the study of earthquake source from strong motion records, Annali di Geofisica, 37, 1539–1564.

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