Presented at the 1995 Annual SEG International Meeting, Houston,
A study is initiated comparing the responses of elastic and acoustic wavefield propagation in subsalt simulations. The intent of this study is to examine the pitfalls of using acoustic methods for modeling and imaging subsalt environments. A comparison is included which demonstrates the difference in energy distribution and amplitude response between elastic and acoustic simulations for a single shot over a complex salt structure.
Subsalt exploration continues to be a topic of significant economic importance to the energy industry. One measure of its importance can be seen in the current effort, spearheaded by the joint SEG/EAEG Modeling Committee, to use numerical modeling to generate 3D prestack seismic data. One of the two data sets being produced in this effort uses a model which represents a typical Gulf Coast salt structure (Aminzadeh, et al., 1994a, 1994b, 1995). This project has already involved tremendous contributions of effort by a significant cross- section of researchers from oil companies, geophysical contracting companies, and academia. In addition to the financial support that has been contributed by the employers of these people, several US national labs are contributing a combined total of thousands of hours of processing time on their supercomputers for the purpose of generating these data.
The SEG/EAEG 3-D modeling project will provide scores of researchers with synthetic seismic data for studying imaging algorithms, acquisition configurations, and wave propagation in a complex structural setting. However, this data does not realistically mimic real-world exploration seismic data. It would not be computationally feasible to consider comprehensive 3-D modeling of an elastic wavefield through a model of the size required for this project. As a result, the SEG/EAEG project is modeling the propagation of an acoustic wavefield.
For practical seismic analysis, most subsalt modeling and imaging projects apply acoustic approximations; this includes work in which the authors of this paper have been involved (e.g., Kessinger, 1993). Likewise, the algorithm which is being used in the SEG/EAEG modeling project is also an acoustic approximation. Therefore it is quite relevant to investigate how the acoustic assumption effects the modeling and imaging of subsalt reflections.
As seismic energy propagates through an idealized media composed of homogeneous units, it experiences a splitting of propagation modes whenever it passes from one unit into another at any non-normal angle of incidence. Along the coast of the Gulf of Mexico, the rugose nature of salt surfaces and the severe contrasts in material properties between salt and surrounding sediment deposits amplifies the elastic nature of seismic wave propagation.
In the elastic Earth, the loss of P-wave energy to converted modes at interfaces may be quite significant. In particular, energy conversion at the interface of a salt body may be a significant factor in seismic propagation through these structures. In a recent publication, Purnell (1992) used physical modeling to study seismic propagation through a high velocity layer. He demonstrated that the magnitude of the converted S-wave energy created at the top interface is angle dependent and may be as great as or greater than the magnitude of the unconverted P-wave energy. In subsequent imaging of his data, Purnell showed that a superior image of reflectors beneath a high velocity layer may sometimes be obtained by using acoustic imaging algorithms to focus the converted S-wave energy rather than the unconverted P-wave energy.
In an acoustic wavefield, on the other hand, energy propagates only in the P-wave mode; as a result, energy incident on an interface may be split into a transmitted wave and a reflected wave, but both components will be P-wave energy, and the amplitudes will not be in agreement with the elastic case.
Although Purnell did not specifically address seismic propagation through salt bodies, his work may have important relevance to subsalt imaging research. Purnell's work indicates that a significant factor in reducing the penetration of unconverted P-wave energy may be its conversion to S-wave energy at the top of salt. For researchers working with the SEG/EAEG data, and for subsalt researchers in general, an understanding of this phenomena may be crucial.
We have available a number of wavefield modeling programs which we are applying in this study, including 2-D and 3-D acoustic and elastic modeling software. These programs are optimized for vector supercomputer use, and are presently installed on an NEC SX-3 supercomputer. The algorithms use the Fourier pseudo spectral method for computing the derivatives necessary for wavefield modeling (Kosloff and Kessler, 1990).
The comparison included here was produced using 2D acoustic and elastic modeling algorithms. The model for this experiment and its physical properties are shown in Figure 1. The asterisk in the figure indicates the location of the shot for both the acoustic and elastic experiments. A spatial grid of 20 meters was used, and a pressure source was simulated for the elastic modeling.
Figure 2 and Figure 3 are plots of the acoustic and elastic results, respectively. Only the vertical displacement component is shown from the elastic experiment. As can be easily seen, a significantly greater number of reflections are present in the elastic results, particularly after the direct P-wave reflection from the top of salt. In order to easily compare reflection events, a one second AGC has been applied to both gathers. Relative amplitude displays of the gathers reveal significant differences in the amplitudes of direct P-wave returns in the two gathers.
In future work we propose to use a 2-D cross section from the SEG/EAEG geologic model to produce equivalent 2-D synthetic data sets using acoustic and elastic modeling routines. Migration of this data will provide a comparison of imaging differences inherent to acoustic and elastic data. With this exercise we hope to demonstrate how the "noise" associated with elastic wave propagation affects not only the final image, but also the imaging process.
We also hope to use 3-D elastic modeling to compute synthetic seismograms for several shots using the SEG/EAEG model. After computation of the elastic results, we plan to compare our synthetic seismograms to the acoustic seismograms produced as part of the SEG/EAEG project. This comparison will enable us to quantify the reduction of P-wave energy caused by converted waves and other elastic media effects. Furthermore, we will be able to identify where converted energy interferes with unconverted energy in the elastic case.
Aminzadeh, F., et al., 1994, Progress report from the SEG/EAEG 3-D modeling committee: The Leading Edge, 13, no. 2, 110-112.
Aminzadeh, F., et al., 1994, Progress report from the SEG/EAEG 3-D modeling committee: The Leading Edge, 13, no. 9, 949-952.
Aminzadeh, F., et al., 1995, 3-D modeling project: 3rd report: The Leading Edge, 14, no. 2, 125-128.
Kessinger, W., 1993, Subsalt imaging by iterative 3D depth migration: Expanded Abstracts, 63rd Annual SEG Exposition and International Meeting.
Kosloff, D., and Kessler, D., 1990, Seismic numerical modeling in oceanographic and geophysical tomography: Elsevier Science Publishers, 251-312.
Lewis, G.G., Yong, K.T., Finn, C.J., and Schneider, Jr., W. A., 1994, Analysis of subsalt reflections at a Gulf of Mexico salt sheet through 3-D depth migration and 3-D seismic modeling: The Leading Edge, 13, no. 8, 873-878.
Purnell, Guy, 1992, Imaging beneath a high-velocity layer using converted waves: Geophysics, 57, no. 11, 1444-1452.
Figure 1: Model used in acoustic and elastic modeling.
Figure 2: Acoustic shot gather.
Figure 3: Elastic shot gather.
