Mathematical and Numerical Problems in Seismic Imaging

地震成像中的数学和数值问题

基本信息

批准号：
1939770
负责人：
金额：
--
依托单位：
University of Bath
依托单位国家：
英国
项目类别：
Studentship
财政年份：
2017
资助国家：
英国
起止时间：
2017 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=studentship-1939770
关键词：
Mathematical Numerical Problems Seismic Imaging

项目摘要

GENERAL FIELDThis project is in general area of the numerical analysis ofwave-propagation problems. More specifically, the project focuses on seismic imaging. The context is as follows: Aspart of the seismic exploration process, waves are emitted from a source into the earth and then the reflections ofthese waves from the subsurface of the earth are measured by sensors. For seismic exploration in a marineenvironment, the source and measurement sensors are towed behind boats. The seismic waves can be described bypartial differential equations (PDEs), formulated in the time or frequency domain. Given the sensor measurements,the seismic properties of the subsurface may be inferred. This process is termed Full Waveform Inversion (FWI). FWIrequires the numerical solution of the PDE, to generate predicted data, and an optimisation step, in which thedifference between the predicted and measured data is minimised to obtain an improved modelof the subsurface.EARLY TRAININGAs a student in the CDT SAMBa, Shaunagh will undertake the SAMBa training programme for first-year PhDstudents, including participating in an Integrative Think Tank, and taking units relevant to her project area. Inparticular she will take a reading course on the wave equation and will do a relevant Level 4 course on large-scaleoptimisation. Further details of the training she will undergo are given in the section "Training Requirements" below.FINAL AIMS AND METHODOLOGYThis project will consider different mathematical and numericalproblems in seismic imaging, in particular related to the process of FWI. The mathematical tools used will bemethods from numerical analysis, optimisation, and analysis of PDEs. One initial problem we seek to investigate,which is of great practical interest in petroleum prospecting, and is not considered in the standard approach to FWI,is the optimal positioning of the sensors in order to obtain the best return from the seismic exploration process. Thekey question in this problem would be "given prior information about the likely make-up of the subsurface (in the formof a class of generic models), can one optimise the location of the sensors to retrieve sufficient information about thesubsurface?''

通用现场项目是波浪传播问题的数值分析的一般领域。更具体地说，该项目着重于地震成像。上下文如下：地震勘探过程的Aspart，从一个源向地球发出波，然后通过传感器测量这些波浪的反射。为了在海洋环境中进行地震探索，来源和测量传感器被拖到船后。地震波可以描述在时间或频域中配制的季节微分方程（PDE）。给定传感器测量值，可以推断地下的地震特性。该过程称为完全波形反转（FWI）。 FwireQuires PDE的数值解决方案，生成预测的数据和优化步骤，在该步骤中，将预测数据和测量数据之间的差异最小化以获得地下培训的改进模型。在CDT Samba中，Shaunagh将对SAMBA培训计划进行一年级的培训计划，以将samba培训与一年级的参与者进行集成，并在包括一个集成的脑海中，并将其组合成整合。她将在波动方程式上进行阅读课程，并在大阶段进行大规模化的4级课程。在下面的“培训要求”部分中给出了她将要接受的培训的更多细节。最终目标和方法论这个项目将考虑地震成像中的数学和数字问题，特别是与FWI过程有关。所使用的数学工具将对PDE的数值分析，优化和分析进行a虫。我们试图调查的一个最初的问题，这是对石油勘探具有极大实际兴趣的最初问题，而在FWI的标准方法中没有考虑到传感器的最佳定位，以便从地震探索过程中获得最佳回报。此问题中的键问题将“给出有关地下可能构成的事先信息（以一类通用模型的形式），可以优化传感器的位置以检索有关ThesubSurface的足够信息吗？”