New generation finite element methods for seismic forward modelling

用于地震正演模拟的新一代有限元方法

• 批准号: NE/G012628/1
• 金额: $ 8.4万
• 依托单位: University of Reading
• 依托单位国家: 英国
• 项目类别: Training Grant
• 财政年份: 2010
• 资助国家: 英国
• 起止时间: 2010 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=NE%2FG012628%2F1
• 关键词: New; generation; finite; element; methods

This project is concerned with developing and prototyping new, more effective computer simulation methods for modelling the propagation and reflection of seismic waves in the earth subsurface. The pull for this research comes from the CASE partner, Schlumberger Cambridge Research, who wish to develop more efficient methods for imaging the subsurface below land or marine deposits in order to locate hydrocarbon-bearing rocks. In particular, for accurate imaging in more complex geometries where seismic reflectivity is poor, for instance imaging below basalt or salt structures, the state-of the art is to use imaging methods which proceed iteratively, solving the full mathematical equations describing the wave propagation and reflection at each step. Unfortunately, this full simulation of seismic propagation and reflection by standard numerical methods is hugely expensive in computing resources, because of the complex subsurface geometry and the large 3D region that must be simulated. Large, that is, in diameter in comparison with the wavelengths of the seismic waves, so that a very high resolution is needed to visualise the wave propagation accurately using standard computational methods. These standard methods include so-called 'finite element methods', computer simulation methods in which the earth subsurface is thought of as composed of a large number (e.g. 1,000,000-100,000,000) of small pieces (the 'finite elements') in each of which the seismic wave has a very simple behaviour, e.g. is approximately constant. This project is concerned with exploring the use, for seismic simulations, of a new, more sophisticated class of finite element method. This new class of method differs in using a more sophisticated assumed behaviour in each element, namely a certain standard wave-like behaviour (that of a plane wave or a combination of plane waves). To keep the project to a manageable size, one suitable for proof of concept, and suitable for a PhD student to complete in 3 1/2 years, the modelling will be restricted to two-dimensional simulations (where it is assumed that the geometry is constant in one horizontal direction), and to a simplified acoustic model of the seismic propagation. Main objectives of the project will be: i) To extend previous work of this type, namely the so-called Ultra Weak Variational Formulation, so that the method can deal with spatially varying seismic properties (that is, where the wave speed varies gradually or suddenly with position in the subsurface). This (significant) extension to the current method, which will need both strong mathematical and computing skills, will be essential for the method to be of use for general purpose seismic modelling. ii) To apply a combination of sophisticated mathematics and numerical experiments so as to understand the behaviour of the new algorithm. iii) To test the new method on representative acoustic 2D geological models supplied by Schlumberger, comparing the performance of the new algorithms, as implemented in computer software, with existing methods, based on standard finite elements and so-called finite difference modelling. These standard methods Schlumberger has implemented in existing computer software. In the first 18 months of the PhD the student will receive training, in superb research environments at Reading and Schlumberger, in the mathematics, computing, and knowledge of standard methods for modelling seismic propagation, that will be necessary for completion of the project. In this, the student at Reading will benefit from access to courses forming part of our MSc in Mathematics of Scientific and Industrial Computation, from our membership of an advanced graduate level training consortium in Mathematics (the MAGIC group), and from membership of a large community of academic and research staff and PhD students working on many exciting applications of the mathematics of waves, and the use of waves in imaging.

该项目涉及开发和原型制作新的、更有效的计算机模拟方法，以模拟地震波在地下的传播和反射。这项研究的推动力来自CASE的合作伙伴斯伦贝谢剑桥研究中心，他们希望开发更有效的方法来对陆地或海洋沉积物下方的地下进行成像，以定位含烃岩石。特别是，为了在地震反射率较差的更复杂几何形状中进行准确成像，例如在玄武岩或盐结构下方成像，最新技术是使用迭代进行的成像方法，求解描述波传播的完整数学方程和反射在每一步。不幸的是，这种通过标准数值方法对地震传播和反射的完全模拟在计算资源上是非常昂贵的，因为必须模拟复杂的地下几何形状和大的3D区域。大，也就是说，与地震波的波长相比，直径大，因此需要非常高的分辨率来使用标准计算方法准确地可视化波的传播。这些标准方法包括所谓的“有限元方法”，即计算机模拟方法，其中地球地下被认为是由大量（例如1，000，000 - 100，000，000）小块（“有限元”）组成，在每个小块中地震波具有非常简单的行为，例如近似恒定。这个项目是关于探索使用，地震模拟，一个新的，更复杂的一类有限元法。这类新方法的不同之处在于在每个单元中使用更复杂的假设行为，即某种标准的类波行为（平面波或平面波组合的行为）。为了将项目保持在可管理的规模，一个适合于概念验证的规模，并且适合于博士生在3年半内完成，建模将限于二维模拟（假设几何形状在一个水平方向上是恒定的），以及地震传播的简化声学模型。该项目的主要目标将是：（一）扩展以前的这类工作，即所谓的超弱变分公式，使该方法能够处理空间变化的地震特性（即波速随着地下位置的变化而逐渐或突然变化）。这种对目前方法的（重要的）扩展将需要很强的数学和计算技能，对于该方法用于通用地震建模至关重要。ii）应用复杂的数学和数值实验相结合，以了解新算法的行为。㈢在斯伦贝谢公司提供的有代表性的二维声学地质模型上测试新方法，将计算机软件中执行的新算法的性能与基于标准有限元和所谓有限差分建模的现有方法进行比较。斯伦贝谢已经在现有的计算机软件中实现了这些标准方法。在博士学位的前18个月，学生将在阅读和斯伦贝谢的一流研究环境中接受培训，学习数学，计算和地震传播建模标准方法的知识，这对于完成项目是必要的。在这一点上，学生在阅读将受益于访问形成我们的科学和工业计算数学硕士课程的一部分，从我们的高级研究生水平的培训联盟在数学（魔术组）的成员，并从学术和研究人员和博士生工作的许多令人兴奋的应用程序的一个大社区的成员波，并在成像中使用波。