Introduction

The Marmousi model has become synonymous with the phrase complex media. The huge amount of folding and faulting induced in this model have created a rather interesting distribution of velocity anomalies and discontinuities. Thus, the Marmousi model served as a calibration tool Audebert et al. (1994); Rekdal and Biondi (1994); Versteeg and Lailly (1991) used to test the various traveltime and migration algorithms through the years.

One of the biggest contributions of the Marmousi model is that it demonstrated the limitations of first-arrival traveltimes in imaging complex media. Specifically, Geoltrain and Brac (1993) showed that to properly image the Marmousi model we need multi-arrival traveltimes. In portions of the Marmousi model, or any other complex model, the first arrival is not necessarily the most energetic. Therefore, reflected energy from key horizons, such as the top of the reservoir, are not properly imaged by using only first arrival traveltimes.

The Marmousi data set was generated at the Institute Francais du Petrole (IFP), and used for the workshop on practical aspects of seismic data inversion at the 1990 EAEG meeting in Copenhagen, where different groups (contractors, universities, and oil companies) applied their proffered imaging tools on this data set. Detailed accounting of what transpired at the workshop is given by Versteeg and Grau (1990) and Versteeg and Lailly (1991). The original Marmousi data set was generated using a 2-D acoustic finite-difference modeling program. The Marmousi model is, however, based on the simplistic assumption that the Earth subsurface is isotropic, despite the many arguments Banik (1984); Harris et al. (1994) that suggest otherwise.

In an accompanying paper Alkhalifah (1997d), I derive an acoustic wave equation for transversely isotropic media with a vertical symmetry axis (VTI media). This equation is fourth order and, as a result, has four solutions. Two of those solutions are the P-wave solutions for incoming and outgoing waves. The other two are artifacts of the formulation that can be easily avoided by placing the receivers in an isotropic layer. This equation can be used to simulate wave propagation in VTI media using finite difference schemes.

The existence of such an acoustic wave equation allows us to generate realistic synthetic data in complex models. An example of a complex model is the ever popular Marmousi model. Although this geological model is based on a somewhat accurate expectation of the subsurface in certain Earth regions, as mentioned above, it lacks the recognition of the possible anisotropy that shales often induce in seismic waves. Unlike inelasticity, anisotropy effects seismic wave traveltimes, and in some cases, this effect is large enough to cause major traveltime differences. By ignoring anisotropy, the conventional velocity interpretation becomes biased toward typically higher velocity values in the case in which $\eta\gt$0.

Building an anisotropic Marmousi model allows us to examine the advantages as well as the drawbacks of the various methods used to calculate traveltimes in VTI media. Although the conclusions might be similar to those observed in isotropic media, these tests will give some insight into how much anisotropy might affect conventional processing.

In this paper, I outline the steps taken to build the anisotropic Marmousi model and generate synthetic seismograms using the VTI acoustic wave equation. I show snapshots of the wavefield at various times and highlight differences between the new anisotropic data set and the original isotropic one. An isotropic migration of the new anisotropic data reveals some of the drawbacks of ignoring anisotropy.