Practical synthetic seismograms for laterally varying media calculated by asymptotic ray theory

Abstract

A fast, efficient algorithm based on asymptotic ray theory has been developed for the calculation of synthetic seismograms through two-dimensional media. The routine is economical and easy to run, and is intended for use as a practical tool in the interpretation of seismic refraction data. The velocity structure is represented by large polygonal blocks, and within each block the velocity gradient is uniform and of arbitrary orientation. Simple analytical expressions are thus used for both ray tracing and amplitude computations. For reflected and refracted rays, amplitudes are determined by using zero-order asymptotic ray theory. For calculating the geometrical spreading function, the width of the ray tube in the in-plane direction is determined by shooting two closely spaced rays for every receiver location. This enables an estimate of the partial derivative of range with respect to starting angle to be made. The ray tube width in the out-of-plane direction is evaluated using expressions valid for the specific case of two-dimensional models with linear velocity gradients. Head wave amplitudes are determined using first-order asymptotic ray theory. Each block of the model is reparameterized as a series of thin homogeneous layers perpendicular to the direction of the velocity gradient. Amplitudes are then determined by analytic expressions valid for models of homogeneous layers with plane dipping boundaries. The reparameterized model also may be used in an alternative method of calculating amplitudes for reflected rays and for refracted rays with no turning points.