Open AccessThe Seismological Effects of Elastic Pre‐Straining within the Earth
Author(s) -
Walton K.
Publication year - 1974
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1974.tb00619.x
Subject(s) - seismic wave , context (archaeology) , magnitude (astronomy) , infinitesimal , shear (geology) , geology , stress (linguistics) , shear waves , mechanics , physics , plane (geometry) , geophysics , seismology , geometry , mathematical analysis , mathematics , petrology , paleontology , linguistics , philosophy , astronomy
Summary It is known that large elastic strains exist in the vicinity of a fault prior to the occurrence of an earthquake. The purpose of this paper is to study some effects of this strain on the subsequent seismic radiation. The mathematical model used is that of infinitesimal motions due to a small perturbing force superimposed on an already existing state of finite strain in an elastic medium. The suitability of this particular model is first discussed in detail in the context of the real Earth. The governing equations of motion are found to be soluble for the P ‐wave by means of the technique of ray expansions. The success of this approach is due to the fact that we consider a pre‐strained , as opposed to a pre‐stressed , Earth. In the former case, the material becomes unstrained when the stress is removed; in the latter, this is not so. In this manner, expressions for the P ‐wave front, the bicharacteristic rays and the nodal surface are obtained. The consequences of these results for the fault‐plane method are then discussed. In general, the magnitude of the effect of the pre‐strain is of the order of the magnitude of the shear strain at the source. However, in one particular region, it is found to be of higher order. One effect of pre‐straining is that two quasi‐ S ‐waves appear. A study of the difference between the two corresponding characteristic equations yields an approximate expression for the difference in arrival times of these two waves.