Determination of discontinuous seismic structure using waveform inversion

这个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。，包括地震不连续面。要实现这一目标，需要精确而有效的方法来计算合成地震记录及其偏导数，并进行地震结构模型的反演。我们在这些领域取得了以下进展：正演计算：(1)在以往的许多数值方法中，如果震源没有精确定位在计算网格的某个节点上，合成地震记录的精度会严重下降。我们已经开发了一种方法，可以对任意位置的震源进行计算，其精度与网格点的震源相同。(2)当岩性不连续面与计算网格不完全重合时，许多有限差分格式的精度会严重降低。我们为包含节点间岩性不连续的元素开发了最精确的数值算子。反演：(1)我们开发了一个精确的方案，以一个有限的扰动岩性不连续。(2)在大多数全球研究中，震源和观测站的分布并不均匀。在进行地震反演时，我们开发了一种加权方案来解释这种不均匀分布，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.