Waveform inversion for 3-D Earth structure using a new inverse algorithm

本研究项目的目的是利用数字地震波形进行高精度、高分辨率的地球三维结构反演。我们发展了一种高效的计算合成地震记录及其偏导数的方法(直接解法)和一种新的反演算法。在本研究项目中，我们计划利用这些研究成果，利用宽带地震波形进行三维地球结构的反演。然而，为了高精度地反演地球结构，我们开发了更准确、更高效的计算方法和软件。通过本项目的研究成果，大大提高了合成地震记录计算的精度和效率。主要研究成果如下：1.用直接解法计算了4-5000秒高精度的DSM合成地震记录。我们证明了如果使用DSM可以计算高精度的合成。2.我们推导了数值精确算子(修正算子)应该满足的一般准则，并在不增加带宽的情况下对任意非均匀介质导出了满足该准则的DSM修正算子。3.我们推导了球坐标问题的修正算子，用于反演。利用这些修正算子，我们开发了球对称和三维非均匀地球结构的计算软件。根据这些结果，我们可以在10分钟内(在SPARC20上)计算出高精度的20-5000秒的P-SV合成地震记录。我们发展了以解析解为试函数的理论和软件，用于位移场的扩展。

The purpose of this research project is inverting 3-D earth structure with high accuracy and high resolution using digital seismic waveforms. We have developed an efficient method (Direct Solution Method) which computes synthetic seismograms and their partial derivatives efficiently and a new inverse algorithm. In this research project, we have planed to invert 3-D earth structure using broadband seismic waveforms using these research results. However to invert earth structure with high accuracy, we have developed more accurate and efficient computational methods and softwares. By the research results of this project, the accuracy an the efficiency of computation of synthetic seismograms are greatly improved.We will list chief research results below.1.We have computed 4-5000s highly accurate DSM synthetic seismograms using the Direct Solution Method. We showed that we can compute highly accurate synthetics if we use DSM.2.We have derived a general criterion which should be satisfied by numerically accurate op erators (modified operators), and derived DSM modified operators satisfying this criterion for arbitrarily heterogeneous media without increasing their bandwidth.3.We have derived modified operators for spherical coordinate problems which will be used for inversions. We have developed softwares using these modified operators for sphericall symmetric and 3-D heterogeneous earth structure. By these results, we came to be able to compute highly accurate 20-5000s P-SV synthetic seismograms in 10 minutes (on SPARC 20). We came to be able to compute highly accurate synthetics for 3-D heterogeneous structure.4.We have developed theory and softwares which uses analytical solutions as a trial function which are used for expansion of the displacement field.