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The full waveform synthetic seismogram of multiple scatteredSH waves by many cylindrical cavities in two-dimensional homogeneous elastic media is computed. We used the so-called single-layer potential integral representation of the scattered field and a discretization scheme with line source distribution for each cavity. The total field is the sum of the incident wave plus the field radiated from all sources, each multiplied by an unknown complex constant representing its strength. These constants are determined by imposing the appropriate boundary conditions in the least-squares sense. Here we solve scattering problems involving one, two, four, twelve and fifty cavities regularly distributed in a half-space. The seismograms computed along the free-surface show regions where the incident wave is strongly attenuated, as well as the arrivals of all multiple scattered phases. The accuray of the method is estimated from the degree of agreement of our solution for one cavity with the corresponding analytical solution, and also from the magnitude of the residual tractions along the boundaries of two cavities separated at various distances. Finally we apply the method to compute the case of fifty cylindrical cavities, each of radiusa, randomly distributed in a region 80a wide by 30a deep in a half-space. The value of scattering loss is obtained from the amplitude decay of the primary wave with distance for wavelengths in the range from 1.7a to 13.3a, using the synthetic seismogram calculated for the same distribution of 50 cavities as above, but in full-space. 相似文献
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Keiiti Aki 《Pure and Applied Geophysics》1995,145(3-4):647-676
In order to develop capabilities for predicting earthquake processes on the basis of known fault zone structures and stress conditions, we need to find relations between seismogenic structures and processes. In the present paper we search for the scale dependence in various earthquake phenomena with the hope to find some structures in the earth that may control the earthquake processes. Among these phenomena, we shall focus on (1) geologic structures which play some role in nucleation and stopping of earthquake fault rupture, (2) depth ranges of the brittle seismogenic zone, (3) asperities and barriers distributed over a fault plane, (4) source-controlledf
max effect, (5) nonfractal behavior of creep events, and (6) temporal correlation between codaQ
–1 and seismicity of earthquakes with magnitude characteristic to a given area. Our review of various scale-dependent phenomena leads us to propose a working hypothesis that the temporal change in codaQ
–1 may reflect the activity of creep fractures near the brittle-ductile transition zone. 相似文献
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In this study, we present a new and effective method to determine the dynamic source parameters (i.e., stress drop and strength distribution). We first assume that the kinematic source parameters, i.e., the slip and rupture time distributions on the fault plane, are known from the previous source inversion studies. Then, using the seismic source representation theorem we determine the dynamic stress field on a fault plane from known kinematic parameters. Finally, we determine the strength of the fault defined as the peak stress just before the rupture. We have tested the validity of this method by using an illustrative two-dimensional analytical example. To assess the applicability of this method, we have applied it to study the 1979 Imperial Valley earthquake, and obtained consistent results with those ofMiyatake's (1992) andQuin's (1990). Compared with previous methods, this new method is simple, straightforward and accurate, and needs much less calculation. Therefore, it is expected to be useful in exploring the seismic source process. 相似文献
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Keiiti Aki Mike Fehler Shamita Das 《Journal of Volcanology and Geothermal Research》1977,2(3):259-287
We propose a model for the mechanism of magma transport based on a fluid-filled tensile crack driven by the excess pressure of fluid. Such a transport mechanism can generate seismic waves by a succession of jerky crack extensions, if the fracture strength of rock varies in space, or if there is a difference between the dynamic and static values of the critical stress intensity factor. We also find that the opening and closing of a narrow channel connecting two fluid-filled cracks may be a source of seismic waves. Using the finite-difference method, we calculated the vibration of dry and fluid-filled cracks generated by: (1) a jerky extension at one end or at both ends and (2) a jerky opening of a narrow channel connecting two cracks. We then calculated the far-field and near-field radiation from these vibrating cracks. The spectra show peaked structures, but interestingly, most high-frequency peaks are only present in the near-field and cannot be transmitted to the far-field. The spectral features described above are often observed for volcanic tremors and in some cases for seismic signals associated with hydraulic fracturing experiments.We first consider as a model of volcanic tremor randomly occurring jerky crack extensions, and derive a formula relating the tremor amplitude to the excess pressure in the magma, the incremental area in each extension, and the frequency of extensions. These parameters are also constrained by other observations, such as the rate of magma flow.Our model was tested quantitatively against observations made in one of the best-described case histories of volcanic tremor: the October 5–6, 1963 Kilauea flank eruption. We found that a single, long crack extending from the summit to the eruptive site cannot explain the observations. The model of a steadily expanding crack ran into difficulties when quantitative comparisons were made with observations. The extension of crack area needed to explain the amplitude of volcanic tremor should accompany a large increase in tremor period which was not observed.Our second model is a chain of cracks connected by narrow channels which open and close. The length of each crack is around 1 km, the channel area connecting neighboring cracks is about 103m2, and the channel opens jerkily with the magmatic excess pressure of about 20 bars. The frequency of jerky opening of each channel is about once in 15 seconds. The channel is closed after each jerky opening, as soon as magma is moved through the channel. 相似文献
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The dynamic motions and stabilities of a single-degree-of-freedom elastic system controlled by different friction laws are compared. The system consists of a sliding block connected to an elastic spring, driven at a constant velocity. The friction laws are a laboratory-inferred friction law called the rate-and-state-dependent friction law, proposed by Dieterich and Ruina, and a simple friction law described by dynamic and static frictions. We further extend the solution to a one-dimensional mass-spring model which is an analog of a fault controlled by the rate-and-state-dependent friction law. This model predicts non uniform slip and stress drop along the rupture length of a heterogeneous fault. This result is very different from some earlier modelings based on the simple friction law and a slip weakening friction law. In those earlier modelings the stress and slip functions become smoother with time along the length of the fault rupture, owing to the interactions between fault segments during slip. Because of this smoothing process the number of small events will decrease with time, and the universilly observed stationary magnitude-frequency relation cannot be explained. The interaction between a fault segment and its neighboring segments can be measured when the post-slip stress on this segment is compared with the stress on an identical segment (represented by a block in this modeling) without neighboring segments. If the post-slip stress of the former is much higher than that of the latter, strong interaction exists; if the two are close, only weak interaction exists. The interaction is determined by the relative motion between fault segments and the time duration of interaction. Our new modeling with the rate-and-state-dependent friction law appears to show no such smoothing effect and provides a physical mechanism for the roughening process in the difference between the fault strength and stress that is necessary to explain the observed stationary magnitude-frequency relation. The noninstantaneous healing predicted by the rate-and-state-dependent friction law may be repsonsible for the recurring nonuniform slip and stress drop, and may be explained by the reduction of interaction among fault segments due to the low frictional strength during the fault stopping. The very low friction during slip stopping allows much longer times than does the higher friction due to instantaneous healing for the fault segments to adjust their motions from an upper-limit slip velocity to almost rest. According to newton's second law, a process with fixed masses and constant velocity changes involves low forces and weak interactions if it is accomplished in a long time period, and vice versa. Our modeling also indicates that the existence of strong patches with higher effective stress on a fault is needed for the occurrence of major events. The creeping section of a fault, such as the one along the San Andreas fault in central California, on the other hand, can be simulated with the rate-and-state-dependent friction law by certain model parameters, which, however, must not include strong patches. In this case small earthquakes and aseismic creep relieve the accumulating strain without any large events. 相似文献