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

快速多极子方法(FMMS)被广泛应用于许多科学和技术分支，但需要通用的、有充分记录的开放源码优化版本的方法，适用于地球科学和其他领域。使用FMMS的迫切需要之一是对许多地震在很长一段时间内的发生进行大规模数学模拟。这样的模拟将产生一个综合的地震目录，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，目标都是使用基本的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的非线性地球系统有了足够的了解，才有可能进行现实的地震模拟，并根据观测到的地震行为对其进行测试。现在，这些模拟有可能在细节上足够逼真，在规模上足够大，从而有助于理解地震的物理以及地震发生的可能性，这些理解具有重要的社会效益。这个项目将开发FMM算法，并将它们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。我们创建的软件将对科学和工程中的其他各种应用程序有用，而不仅仅是我们所关注的应用程序；我们将在一个开放的网站上向我们的文档化图书馆提供示例问题，并向科学界宣传这一点。该项目将开发、测试和应用新一代高效的计算机程序，这些程序可以生成迄今不可能产生的长时间人工地震历史。这些历史将使科学家能够了解地震发生的模式，这些模式可用于估计地震对人类生命和财产构成的危险。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，目前它对地震发生概率的估计基于的是许多专家认为不充分的方法。专家认为，能够创建计算机模型来生成许多长时间的地震序列，是提高我们对美国和国外许多地震多发地区何时何地可能发生地震的理解的下一个重要步骤。在许多方面，这种方法与基于计算机的天气和气候预测相似，目前计算机天气和气候预测比地震发生预测先进得多。该项目涉及数学家和地震科学家之间的一种新的紧密合作，他们之前一直在各自领域独立开发最先进的方法。所生产的计算机程序将提高制作快速有效的计算机模型的能力或社会，这些计算机模型在一系列科学和工程应用中除了在理解地震方面有用外，还将带来好处。这些计划将被记录下来，公之于众，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.