横方向不均質媒体における波動場の最新の計算法

―ガウシアンビームを中心として―

抄録

This paper reviews recent developments in computational techniques for wavefields in laterally heterogeneous media, mainly the Gaussian beam method. We start with a solution by the asymptotic ray theory as a high-frequency limit, and point out two major defaults in this approach. The first problem is a two-point ray tracing or time-consuming search for the ray connecting source and receiver. This difficulty can be removed by the paraxial ray approximation, extrapolating wavefields outsides of rays. The second is due to singularity in some critical regions such as caustics and shadow zones. By combining a point-source wave with a plane wave, the Gaussian beam method can avoid such singularity. Also, superposition of many beams naturally smooths out heterogeneities of media, simulating the effect of finite wavelength. In laterally homogeneous media, this superposition corresponds to the WKBJ seismogram of Chapman as a limit. The real difficulty lies in ambiguous weighting factors for the two wavefields: a point-source wave and a plane wave. No studies have ever revealed any physical basis to find appropriate values of the weighting factors. In the near future, one must develop any method to globally estimate those values, rather than empirically, by matching boundary conditions of wavefields on free surface or on interface, which will eventually give more reliable results.