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タイトル: Potential and Gravity Changes Caused by Dislocations in Spherically Symmetric Earth Models
その他のタイトル: 球対称地球モデルの中におかれたPoint Dislocationによって生じるポテンシャルと重力変化
著者: Sun, Wenke
著者(別言語): 孫, 文科
発行日: 1992年9月30日
出版者: 東京大学地震研究所
掲載誌情報: 東京大学地震研究所彙報. 第67冊第2号, 1992.9.30, pp. 89-238
抄録: This thesis studied for the first time the potential and gravity changes caused by dislocations in spherically symmetric earth models. We introduced equations of equilibrium with an arbitrary body force in a SNREI model as well as boundary conditions. Integration of the fundamental equations with the body force was divided into two parts: one to solve the basic equations of equilibrium without considering the body force; the another to consider it as initial values. We defined dislocation Love numbers to describe the elastic deformation of the earth raised by source functions. We proved that only four components of the nine-part solution are independent in a general dislocation model. We discuss the shear dislocation, tensile dislocation and explosion, which can be expressed by the four independent components corresponding (in this paper) to a vertical strike-slip, a vertical dip-slip, a dip-slip at a 45° dipping plane, and a tensile opening at the horizontal plane. Based on the above-mentioned equations of equilibrium and the dislocation models, we derived expressions of the potential and gravity changes caused by dislocations buried in a spherically symmetric earth model. We derived general formulas for practical applications. We discussed the special case of a point source on the earth's surface. We handled particularly the case of n=1 using principle of conservation of the mass center. In our integrations and summations, we used some techniques to truncate the infinite series and to accelerate the covergence, such as normalization, truncation of harmonic degree n, the disk factor, Euler transformation, interpolation, and asymptotic solutions. We started our calculations with a homogeneous earth model by comparing the results from those obtained from flat-earth theory. We showed that they coincide very well, at least within 1°. The far-field results indicated no larger than a 10% difference within 10°. We conclude that in this case it is the same to use both the spherical and flat-earth theories in the near field, while it is reasonable to use spherical theory for a global calculation. After that, we proceeded to undertake calculations with a radially heterogeneous earth model (Model 1066A). The results are, as a whole, similar to those for a homogeneous sphere. In some cases, however, the difference between the two becomes very large. For example, the locations of the nodal lines of the gravity change differ significantly between the two models. This indicates that the vertical layering can cause considerable effects on the deformation fields. As main numerical results of the study, we list the dislocation Love numbers in Appendix D and the deformations including the radial displacement, potential and gravity changes in Appendix E. We extended the theory of the point dislocation to that of a finite fault, and used it to calculate the gravity changes caused by the 1964 Alaska earthquake. The computed results are in excellent agreement with the observed gravity changes during the earthquake. In the far field (epicentral distance ≫ fault dimension), we also demonstrate that the gravity change is large enough to be detected by a superconducting gravimeter.
この研究では,球対称地球モデルの中に発生したディスロケーションによってひきおこされるポテンシャルおよび重力の変化をとりあつかった.この変化の数式化をおこなった.ディスロケーションLove数(hdn, ldn, kdn)を定義する.これを利用して,点源関数により地球に生じる弾性変形を記述する.
URI: http://hdl.handle.net/2261/13101
ISSN: 00408972


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