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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?''

这个项目是波传播问题的数值分析的一般领域。更具体地说，该项目的重点是地震成像。内容如下：作为地震勘探过程的一部分，波从震源发射到地球上，然后用传感器测量这些波从地球地下的反射。对于海洋环境中的地震勘探，震源和测量传感器被拖到船后。地震波可以用时间域或频率域中的偏微分方程(PDE)来描述。根据传感器的测量结果，可以推断地下的地震性质。这个过程被称为全波形反转(FWI)。FWI需要PDE的数值解，以生成预测数据，并进行优化步骤，在此步骤中，预测数据和测量数据之间的差异被最小化，以获得改进的次表面模型。EARLY TRAING作为CDT Samba的学生，Shaunagh将承担针对博士一年级学生的Samba培训计划，包括参加综合智库，并选择与她的项目领域相关的单元。特别是，她将参加一门关于波动方程的阅读课程，并将参加一门关于大规模优化的相关4级课程。她将接受的培训的更多细节在下面的“培训要求”一节中给出。FINAL AIMS和METHODOLOGY这个项目将考虑地震成像中的不同数学和数值问题，特别是与FWI过程相关的问题。所使用的数学工具将从偏微分方程组的数值分析、优化和分析中获得方法。我们试图研究的一个初始问题是传感器的最佳位置，以便从地震勘探过程中获得最佳回报，这在石油勘探中具有很大的实际意义，但在FWI的标准方法中没有考虑到。这个问题的关键问题将是“给出关于地下表面可能组成的先验信息(以一类通用模型的形式)，人们能否优化传感器的位置，以检索关于地下表面的足够信息？”