Determination of discontinuous seismic structure using waveform inversion

这项研究项目的目的是分析宽带地震数据，以确定地球内部的精细结构，包括地震间断。为了实现这一目标，需要准确和有效的方法来计算合成地震记录及其偏导数，并对地震结构模型进行反演。我们在这些方面取得了以下进展。正演计算：(1)在以前的许多数值方法中，如果震源不精确地位于计算网格的一个节点上，合成地震记录的精度就会严重下降。我们已经开发了一些方法，使任意位置的震源的计算精度与网格点上的震源的计算精度相同。(2)如果岩性不连续面与计算网格不完全重合，许多以前的有限差分格式的精度将严重下降。对于含有节点间岩性不连续的单元，我们发展了最优精度的数值算符。(2)在大多数全球研究中，震源和观测站的分布并不均匀。我们开发了一种加权方案来考虑进行地震反演时的这种不均匀分布，并将其应用于观测数据集，以获得无偏的三维地球模型。

The purpose of this research project was to analyze broadband seismic data to determine the fine structure of the Earth's interior., including seismic discontinuities. Progress towards this goal requires accurate and efficient methods for calculating synthetic seismograms and their partial derivatives, and for conducting inversion for seismic structure models. We achieved the following progress in these areas.Forward calculations : (1)In many previous numerical methods the accuracy of synthetic seismograms seriously degraded if the seismic source was not located exactly at a node of the computational grid. We have developed methods that allow calculations for arbitrarily located seismic sources with the same accuracy as for seismic sources at grid points. (2)The accuracy of many previous finite difference schemes was seriously degraded if lithological discontinuities did not coincide exactly with the computational grid. We developed optimally accurate numerical operators for elements containing inter-node lithological discontinuities.Inversion : (1)We developed an accurate scheme for a finite perturbation to a lithological discontinuity. (2)In most global studies seismic sources and observatories are not uniformly distributed. We developed a weighting scheme to account for this uneven distribution when carrying out seismic inversion, and applied it to an observed dataset to obtain an unbiased 3-D Earth model.