CMG Collaborative Research: Fast Multipole Algorithms for Geophysical Stress Modeling and Their Use in Large-Scale Simulation of Earthquake Occurrence

快速多极方法 (FMM) 广泛应用于科学技术的许多分支，但需要该方法的优化版本的通用、记录良好的开源实现，适合在地球科学和其他领域使用。使用 FMM 的迫切需求之一是对长时间内发生的许多地震进行大规模数学建模。这种模拟将产生地震的综合目录，其在空间和时间上的统计特性可能与自然界发生的地震的实际分布相似。这种模拟类似于气象学家和气候科学家用来模拟天气和气候的全球环流模型。在这两种情况下，目标都是使用基本物理定律来模拟大型复杂自然系统的行为。我们最近才对产生地震的复杂非线性地质系统有了足够的了解，因此可以进行真实的地震模拟并根据观察到的地震行为对其进行测试。现在，模拟的细节可能足够真实，规模足够大，有助于理解地震的物理原理以及地震发生的概率，这些理解具有重要的社会效益。该项目将开发 FMM 算法并实现它们以与地震模拟器代码一起使用。这些改进的代码还将用于进行大大改进的地震模拟。我们创建的软件将可用于科学和工程领域的各种其他应用，而不仅仅是我们关注的应用；我们将在开放网站上向我们的文档库提供示例问题，并向科学界公开。该项目将开发、测试和应用新一代高效计算机程序，这些程序可以生成迄今为止不可能的长期人工地震历史。这些历史将使科学家能够了解地震的发生模式，并可用于估计地震对人类生命和财产造成的危害。例如，加州地震局制定的地震保险费率对加州和全世界都有数十亿美元的影响，但目前对地震发生概率的估计所采用的方法很多专家认为是不够的。专家们认为，创建能够生成许多长地震序列的计算机模型的能力是提高我们对美国和国外许多地震多发地区可能发生地震的时间和地点的了解的下一个重要步骤。在许多方面，这种方法类似于基于计算机的天气和气候预测，目前比地震发生的预测先进得多。该项目涉及数学家和地震科学家之间的新的紧密合作，他们之前一直在各自领域独立开发最先进的方法。所产生的计算机程序将增强社会建立快速有效的计算机模型的能力，除了在理解地震方面的有用性之外，还可以在一系列科学和工程应用中受益。这些计划将被记录、公布并在网站上免费提供。

Fast Multipole Methods (FMMs) are widely used in many branches of science and technology, but there is a need for general-purpose, well-documented open source implementations of optimized versions of the method, suitable for use in the geosciences and other fields. One of the pressing needs for using FMMs is in conducting large-scale mathematical modeling of the occurrence of many earthquakes over a long period of time. Such simulations would produce a synthetic catalog of earthquakes, whose statistical properties, in both space and time, may be similar to the actual distribution of earthquakes that occur in nature. Such simulations are analogous to the global circulation models used by meteorologists and climate scientists to simulate weather and climate. In both cases, the objective is to use basic physical laws to simulate the behavior of a large and complex natural system. We have only recently gained enough knowledge about the complex non-linear geosystem that generates earthquakes that it is possible to conduct realistic earthquake simulations and test them against observed earthquake behavior. It is now possible that the simulations can be sufficiently realistic in detail and large enough in scale that they can be useful in understanding the physics of earthquakes as well as the probabilities of earthquake occurrence, understandings that have important societal benefits. This project will develop FMM algorithms and implement them for use with earthquake simulator codes. These improved codes will also be used to conduct much-improved earthquake simulations. The software we create will be useful for a variety of other applications in science and engineering beyond the one we focus on; we will provide our documented libraries with example problems on an open website and will publicize this to the scientific community.This project will develop, test, and apply new generations of efficient computer programs that can generate hitherto impossible long artificial histories of earthquakes. These histories will enable scientists to understand patterns of occurrence that can be used for estimating the hazard that earthquakes pose to human life and property. For example, the California Earthquake Authority, which sets earthquake insurance rates with billions of dollars of implications for California and the world, presently bases its estimates of the probability of earthquake occurrence on methodology that many experts feel is inadequate. The ability to create computer models that generate many long sequences of earthquakes is regarded by experts as the next important step in improving our understanding of when and where earthquakes may occur in many earthquake prone regions of the USA and abroad. In many ways this approach is similar to the computer-based forecasts of weather and climate that are presently much more advanced than are forecasts of earthquake occurrence. The project involves a new and tight collaboration between mathematicians and earthquake scientists who previously have been developing state-of-the-art approaches in their fields independently. The computer programs that are produced will enhance the ability or society to make fast and efficient computer models with benefits in a range of scientific and engineering applications in addition to their usefulness in understanding earthquakes. The programs will be documented, publicized, and made freely available on a web site.