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Anisotropic Marmousi model and Data set
This was generated around 1997 to provide a dataset for anisotropic migration. The synthetic data were generated by applying finite difference calculation on the anisotropic acoustic wave equation. Despite the many articles discussing the S-wave artefacts inherent in the wave equation formulation, this dataset is very clean as the source was placed in an isotropic layer and any S-waves generated through scattering are mild compared to the over whelming energy of the P-waves. It is especially good for kinematic testing of MVA procedures. Compared to what is offered out there is data can be handle via a laptop.
A detailed explanation of the dataset can be found at the following site at SEP.
Summary:
I use the acoustic wave equation for transversely isotropic media with vertical symmetry axis (VTI media), to generate synthetic VTI data for an anisotropic version of the Marmousi model. This acoustic equation, though it represents a physically impossible medium, provides an extremely accurate approximation of the widely used elastic wave equation. The anisotropic Marmousi model has the same NMO velocity as the original Marmousi model and an anisotropy $\eta$ distribution that possesses the same layering characteristics as the velocity model. Interval $\eta$ spans the range of 0 to 0.27, which are values that are commonly observed in practice. The traveltime and amplitude differences between the synthetic seismograms of this new anisotropic model and those produced by the original isotropic Marmousi data set are quite apparent.
Background:
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 used to test the various traveltime and migration algorithms through the years. 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 et al. (1990, Proceedings of 1990 EAEG Workshop).
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 that suggest otherwise. In this other paper (Alkhalifah, 1997, SEP-95), 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. It is used here to generate the anisotropic Marmousi data set.
The Model:
The original Marmousi model was built to resemble an overall continental drift geological setting. Numerous large normal faults were created as a result of this drift. The geometry of Marmousi is based somewhat on a profile through the North Quenguela through the Cuanza basin (Versteeg, 1993, Geophysics). The model contains many reflectors, steep dips, and strong velocity variations in both the lateral and the vertical direction (with a minimum velocity of 1500 m/s and a maximum of 5500 m/s). However, there is no clear evidence of the Marmousi model intended sediment or rock distribution, and this includes the distribution of shales. As a result, the same discard for sediment distribution, that went into building the sediment content of the original model, is used here. This is justified by the fact that our goal is purely imaging. Nobody seemed to care for the geological aspect of the model.
The above image (top) shows the original velocity model used by the Institute Francaise du Petrole (IFP) to generate the Marmousi synthetic data set. The image (bottom) shows an $\eta$ model that is based on the following two hypothetical assumptions:
Anisotropy increases as velocity decreases (shales have low velocity overall).
The horizontal velocity gradually increases with depth.
The second assumption means that although the NMO velocity may vary erratically, the horizontal velocity retains a relatively linear increase with depth. Although there is no settled proof that the above assumptions are accurate representation of the subsurface behavior in the presence of anisotropy, my personal experience suggests that they are at least plausible. Nevertheless, my goal is not to build a realistic geological model, but rather to obtain anisotropic data from a complex model that we can use to test existing anisotropic algorithms.
The Synthetics:
The original Marmousi data set consists of 240 shots with 96 traces per shot. The first offset is 200 m; both the shot and the receiver spacings are 25 m. The first shot is at the lateral position 3000 m, and the recording time is 2.9 s. Overall, I used the same survey geometry and settings used by IFP, the builders of the original Marmousi data set. This includes the same source and receiver locations, an identical sampling interval and recording time, and the same minimum offset.
However, I made two adjustments to the original Marmousi acquisition settings:
The peak frequency of the new, anisotropic, data is 30 Hz (5 Hz higher than the original data), which is more consistent with survey frequencies nowadays, and corresponds a causal ricker-wavelet point source.
The spread length was extended to include offsets up to 3575 m, as opposed to only 2575 m in the original data.
The second modification is important for anisotropic inversion, because a majority of the information on anisotropy inversion comes from large offsets. Although the general complexity of the Marmousi model makes it less than ideal for anisotropic inversion, parts of the model are potentially invertable, including the region under the surface location 3000 m. In addition, I implemented absorbing boundary conditions at all four boundaries of the model. Doing so eliminates the presence of surface multiples; however, other inter-bed multiples can exist.
The following is a compressed and tarred file containing the full anisotropic data set with the velocity and $\eta$ (and the $A_ijkl$) files in binary as well as SEGY formats and a postscript paper describing the data (66664 KB):
The following is a compressed and tarred file containing a subset of the anisotropic data set (with offsets up to 2575 m, similar to the original isotropic) with the velocity and $\eta$ (and the $A_ijkl$) files in binary as well as SEGY formats and a postscript paper describing the data (53780 KB):
The following is a compressed version of the postscript file describing the data (2840 KB):
Possible Applications:
One, probably obvious, application of the data set is to try out prestack isotropic migration using the original Marmousi velocity model, or using velocities obtained from prestack migration velocity analysis. Although the Marmousi model seem to be too complicated for time processing tests, portions of the model, mainly up-shallow and toward lower shot point numbers, can be well imaged using poststack schemes. Therefore, the data set can also be used to do some conventional poststack processing tests, in which we can study the impact of anisotropy.
However, the main objective of this data set is to test anisotropic algorithms, including traveltime computation, velocity analysis, and prestack imaging.
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