A Numerical Ray Generation and its Application to the Computation of Synthetic Seismograms for Complex Layered Media

Abstract

Asymptotic ray theory, which represents a high frequency approximation to the solution of wave equation, is beginning to find its way into geophysical literature dealing with computation of synthetic seismograms. Because in this theory-as well as in any ray theory in general-the total wave field is decomposed into contributions attributed to the individual rays, a rational method of ray generation must be used in order to select from the infinite number of rays, which exist between the source and a receiver in any layered medium, only those with the significant amplitudes. If the medium consists of homogeneous layers separated by parallel plane interfaces the phases which travel along different paths but arrive simultaneously at each epicentral distance can be called kinematic analogues. Some of these have even the same amplitudes and will be called dynamic analogues. Given the number of layers and specifying the maximum number of path elements in a ray, number of both kinematic and dynamic analogues can be determined analytically (in case of few conversions) or with the aid of a computer (if a large number of conversions is required). Unfortunately, the concepts of kinematic and dynamic analogues cannot be used for media with curvilinear, dipping interfaces or in case of generally inhomogeneous layers. A general program, which computes codes of all possible rays for specified numbers of layers, ray paths and conversions (in case of media with curvilinear, dipping interfaces or for inhomogeneous layers) or creates the groups of kinematic and dynamic analogues (for media consisting of parallel homogeneous layers), was written and its results presented. It was shown that with the exception of the most trivial media the correct selection of all significant rays for construction of synthetic seismograms is too difficult for any human being and has to be left to a computer if serious inaccuracies are to avoided. This conclusion was inferred from synthetic seismograms computed for a twelvelayered crust model proposed by I. P. Kosminskaya (see Fig. 1) as well as from the results (see Fig. 4) obtained for a simplified three-layered model suggested for southern Alberta by E. R. Kanasewich and R. M. Clowes (Fig. 2). The first model, which consisted of homogeneous layers separated by parallel plane interfaces, also served as an example of the usefulness of splitting the rays into groups of kinematic and dynamic analogues: although more than 150 OOO refracted, reflected and head phases were examined and their contributions to the seismograms evaluated, it took less than 10 min to an IBM 360/67 computer to evaluate and select the most significant phases in the seismogram at each epicentral distance. On the basis of synthetic seismograms computed for the Alberta model the following conclusions were drawn: (1) A special attention has to be paid to the exact location of cusps on travel-time curves and to the end points of individual branches related to the same ray. As the number of these points and branches is often surprisingly high (see Fig. 3), a rather sophisticated algorithm has to be used in order to make computation reasonably efficient.