Program notes and results: Ray synthetic seismogram programs for P-SV wave propagation in isotropic, anisotropic and viscoelastic plane layered media
P. F. Daley
When processing seismic data modelling programs can be useful tools provided that they are fast, reasonably accurate, and require minimal user interaction in the form of data preparation. Also, the results should be in a form that makes their display as uncomplicated as possible and in a form that allows for a straightforward interpretation of events of interest. The general program type that is often used for this purpose is a plane parallel layered model for the coupled PSV wave propagation amplitude versus offset (AVO) analysis of a geological structure. Although far from realistic, this class of programs provides a basic means of obtaining at least a general trend of the seismic response of a specified subsurface geology and as a consequence an indication of how accurately a data processor may be interpreting field data.
A determining factor in the usefulness of these programs is that their run time be in the range of seconds or at the most minutes for models with a large number of layers and many offsets. This allows a user to compute synthetics for a series of models in an attempt to iterate to the optimal solution of the problem being considered in a time efficient manner. Past experience has shown that this and the ease of use determine whether or not the software is used as an interpretation or modelling tool.
Programs also exist for more complicated geological structures in both two and three dimensions. This, however, introduces the not insignificant process of model building, which is almost a science in itself. Efficient use of these program types requires one or more persons dedicated solely to the tasks of building models, model databases and computing the synthetics, as the complexity of the model translates into a comparable complexity in the synthetic program with respect to data input as well as run time and turn around time. This takes control of the modelling aspect away from the primary user who, again from past experience, will not be inclined to use this service.
The three programs described below are of the first type described above, each with a mild increase in the degree of difficulty related to the input. They all assume a plane parallel layered geometry with both source and receivers on the surface and progress from isotropic layers (isoavo), to transversely isotropic layers with the axis of anisotropy aligned with the plane interfaces (tiavo), to viscoelastic layers with frequency dependent P and SV quality factors, Q() , and hence frequency dependent complex valued velocities (visavo). The principal output from these three programs consist of two files containing the synthetic traces for the vertical and horizontal, generally complex, amplitude components of particle displacement written in SEGY format.
A very select subset of rays is used in the computations allowing for a large number of layers to be considered. Models with large number of layers usually consist of P-wave, Swave and density logs together with the depth indication of these parameters. A blocked model is probably preferable but this task can be time consuming. The use of logs extends the range of applicability for the use of asymptotic ray theory (ART), used in all of the above programs, to its limits, (Hron and Kanasewich., 1971; Cerveny and Ravindra, 1970; Cerveny et al., 1976; Cerveny, 2001).
The programs described here are a preliminary subset of a more complete set. Other members include the vertical seismic profile (VSP) versions of the abovementioned programs. These are all in some state of flux at present, the most tested being tivsp, a program to produce synthetic traces resulting from surface sources and down hole receivers for a plane layered transversely isotropic medium