Extrapolation of Time-Dependent Waveforms along their Path of Propagation

作者：Jon F. Claerbout, Ansel G. Johnson · 发表于：Geophysical Journal of the Royal Astronomical Society · 年份：2007 · DOI：10.1111/j.1365-246x.1971.tb03402.x · 被引用次数：49 · 研究领域：Seismic Imaging and Inversion Techniques、Seismic Waves and Analysis、Geophysical Methods and Applications

Summary Time-dependent waveforms are commonly extrapolated in space by means of rays and occasionally by means of diffraction integrals. It is possible to extrapolate time-dependent waves in space with a partial differential equation derived from the wave equation. There are stable numerical approximations. An example illustrates a mechanism for ' signal-generated noise ' which is consistent with observations. When a wave propagates in an inhomogeneous medium the waveform changes. Given that the wave has been observed at a suitable number of points in space we may attempt to solve two types of problems. First we may attempt to ascertain the nature of material inhomogeneity along the wave paths, and second, we may attempt to extrapolate the disturbance back to the source in an attempt to discover the nature of the source. With few exceptions, the methods used during the past decade for doing this kind of geophysical work may be summarized as follows: when wave equations are to be used, separability is achieved by considering cases in which the material inhomogeneity is a function of only one spatial co-ordinate. When higherdimensional inhomogeneity is so severe that it cannot be ignored, then the wave equations are almost always specialized to ray theory. Ray theory is especially useful when only the travel time is required. Although the amplitude may also be obtained by ray theory it is often of marginal utility because amplitude measurement is made ambiguous by changing wave...