Post-seismic rebound of a spherical Earth: new insights from the application of the Post-Widder inversion formula
Post-seismic rebound of a spherical Earth: new insights from the application of the Post-Widder inversion formula
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DOI：
10.1111/j.1365-246x.2008.03847.x
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发表时间：
2008-08
影响因子：
2.8
通讯作者：
D. Melini;V. Cannelli;A. Piersanti;G. Spada
中科院分区：
文献类型：
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作者：
D. Melini;V. Cannelli;A. Piersanti;G. Spada
摘要粘弹性地球对地震位错的震后响应可以在简正波框架内基于传播算子方法的应用进行分析计算。这种技术，广泛记载在文献中，有几个缺点;主要的缺点是有关长期方程的数值解，其程度随粘弹性层的数量线性增加，使只有粗分层模型实际上是可解的。最近，一个可行的替代标准的正常模式的方法，基于后Widder拉普拉斯反演公式，已被提出在冰后期反弹模型的领域。这种方法的主要优点是绕过长期方程的显式解，同时保留传播子形式主义的分析结构。同时，数值计算大大简化，使得可以简单地实现诸如线性非麦克斯韦流变学的附加特征。在这项工作中，第一次，我们应用后Widder拉普拉斯反演公式地震后反弹模型。我们测试的方法对标准的正常模式的解决方案，我们执行各种基准，旨在调整算法和优化计算性能，同时确保解决方案的稳定性。作为一个应用程序，我们解决的问题，找到最小数量的层与不同的弹性特性需要准确地描述一个现实的地球模型的地震后放松。最后，我们证明了我们的代码的潜力，通过模拟地震后的放松后，2004年苏门答腊-安达曼地震比较结果的基础上麦克斯韦和伯格斯流变学。
SUMMARY The post-seismic response of a viscoelastic Earth to a seismic dislocation can be computed analytically within the framework of normal-modes, based on the application of propagator methods. This technique, widely documented in the literature, suffers from several shortcomings; the main drawback is related to the numerical solution of the secular equation, whose degree increases linearly with the number of viscoelastic layers so that only coarse-layered models are practically solvable. Recently, a viable alternative to the standard normal-mode approach, based on the Post–Widder Laplace inversion formula, has been proposed in the realm of postglacial rebound models. The main advantage of this method is to bypass the explicit solution of the secular equation, while retaining the analytical structure of the propagator formalism. At the same time, the numerical computation is much simplified so that additional features such as linear non-Maxwell rheologies can be simply implemented. In this work, for the first time, we apply the Post–Widder Laplace inversion formula to a post-seismic rebound model. We test the method against the standard normal-mode solution and we perform various benchmarks aimed to tune the algorithm and to optimize computation performance while ensuring the stability of the solution. As an application, we address the issue of finding the minimum number of layers with distinct elastic properties needed to accurately describe the post-seismic relaxation of a realistic Earth model. Finally, we demonstrate the potentialities of our code by modelling the post-seismic relaxation after the 2004 Sumatra–Andaman earthquake comparing results based upon Maxwell and Burgers rheologies.