散乱理論の応用とトモグラフィー

Abstract

Tomographic inverse schemes, in particular travel-time tomography techniques, havebecome standard ones to image subsurface structures with respect to anomalies in seismicvelocities. In contrast to these ray-theoretical approaches, there exist wave-theoretical schemeswhere seismic waveforms are analyzed in terms of their relation to structural anomalies. In tomographic application of wave theories, Devaney (1984) proposed a method calleddiffraction tomography in which seismic wave-forms are composed of incident and scatteredwave-fields. Since several tens to hundred times much information might be included inseismic wave-forms, it is natural to think that there exists a strong necessity to utilize ofwave-forms in structural analyses.A theoretical jump from ray-theoretical travel-time to wave-theoretical diffraction tomographycan be examined by introducing a simple seismic scattering theory. Since thesetechniques are utilizing seismic signals, results obtained by these methods on the same datamight be considered as the derivation of the same physical properties of unknown targetmaterial in the subsurface. The resolution can also be compared between these two kindsapproaches in seismic tomography through the seismic scattering theory. The theory wasintroduced by a solution to the seismic scattering problem of a compressional plane wavetraveling in a homogeneous medium including a point scatterer, and three types of scatteredwaves were found generated depending on the contrasts in its lithological properties (the Lame's constants and the density) to the surrounding medium. They are equivalent towaves generated by three different kinds of seismic sources. Contrasts between the point scattererand the surrounding medium in bulk modulus, in density, and in rigidity work as a pole, asingle force, and a single couple, respectively. The relation of these parameters to observedscattered waves was found linear and thus invertible. The results obtained through this relationin the analysis of subsurface structure of Izu-Oshima volcano have shown the good resolutionwhich can only be achieved by wave-theoretical methods. It is concluded that seismic scatteringphenomena can be used for the following purposes:(1) to clarify the effects of inhomogeneitieson the observed seismic signals, (2) to find the inverse relation to the scatteringproblems, (3) to understand a link between the seismic methods, i. e., traveltime tomography, waveform tomography and reflection analyses.