ALBERT

Notes: The primary purpose of this paper is to study the accuracy with which two single scattering approximate methods model the propagation of elastic waves in media containing complicated structure. The modelling methods we shall examine are the (Conventional) Born approximation, and the Generalized Born approximation. The first of these methods is in wide-spread use in seismology for both forward and inverse modelling in acoustic and elastic media. The Generalized Born method has been introduced more recently for forward-modelling applications in both acoustic and elastic media.A secondary aim of this paper is to attempt to better understand the relationship between the characteristics of the model, (e.g. the spatial variation of the seismic-wave impedances and velocities), and the characteristics of the recorded seismograms (e.g. fluctuations in traveltimes, amplitudes and power spectra).Previous studies of the accuracy of approximate methods have usually been of one of two types; either analytic, where the relative magnitude of the terms kept in the approximate solution and those neglected are compared, or numerical comparisons based on simple canonical models, such as point scatterers or interfaces, for which exact analytic solutions are known. Neither of these approaches yield completely satisfactory results. In this study we take advantage of recent advances in computer technology which allow us to generate finite difference results for realistic, relatively small 2-D elastic models. By realistic we mean a model which contains a degree of complexity similar to that likely to be found in the Earth. These finite difference results, which we treat as ‘exact’ solutions, may then be compared with the approximate results in both the time and frequency domains to give an indication of the accuracy of these approximations.These models are generated as realizations of Gaussian or Exponential autocorrelation functions and are specified on a rectangular grid. The models examined may be catagorized into two groups. In one, the ‘impedance’ models, the P- and S-wave velocities are kept fixed and the P- and S-wave impedances vary with position. In the other, the ‘velocity’ models, the P & S wave impedances are kept fixed but the P and S-wave velocities vary (the ratio of P to S-wave velocity is constant in every example shown). The results may be summarized by saying that in the impedance models the scattering is weak and the approximate solutions do an adequate job of modelling wave propagation. In the velocity models, however, the scattering is strong and neither of the approximate solutions model the scattering very well. The Generalized Born method, however, does significantly better than the Conventional Born approach.