ALBERT

Notes: Abstract 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.

Notes: Abstract A set of acceleration source spectra is constructed using the observed parameters of the specific barrier model of Papageorgiou and Aki. The spectra show a significant departure from the ‘ω2-model’ at the high frequency range. Specifically, the high frequency spectral amplitudes of seismic excitation are higher as compared to the level predicted by the ‘ω2-model’. This is also supported by other observational evidence. The high frequency amplitudes of acceleration scale proportionally to the square root of the rupture areaS, to the rupture spreading velocityv, and to the local strain drop (Δσ/μ) (=strain drop in between barriers). The local strain drop in between barriers is not related in a simple way to the global strain drop, which is the strain drop estimated by assuming that it is uniform over the entire rupture area. Consequently, the similarity law does not apply. Using the source spectra which we constructed, we derive expressions for high frequency amplitudes of acceleration such asa rms anda max. Close to the fault both are independent of fault dimensions and scale as (Δσ/µ)(Δf)1/2, while away from the fault plane they scale asW 1/2(Δσ/µ)(Δf)1/2, whereW is the width of the fault and Δf is the effective bandwidth of the spectra.

Notes: Abstract In this paper we show evidences of the fractal nature of the 3-D inhomogeneities in the lithosphere from the study of seismic wave scattering and discuss the relation between the fractal dimension of the 3-D inhomogeneities and that of the fault surfaces. Two methods are introduced to measure the inhomogeneity spectrum of a random medium: 1. the coda excitation spectrum method, and 2. the method of measuring the frequency dependence of scattering attenuation. The fractal dimension can be obtained from the inhomogeneity spectrum of the medium. The coda excitation method is applied to the Hindu-Kush data. Based on the observed coda excitation spectra (for frequencies 1–25 Hz) and the past observations on the frequency dependence of scattering attenuation, we infer that the lithospheric inhomogeneities are multiple scaled and can be modeled as a bandlimited fractal random medium (BLFRM) with an outer scale of about 1 km. The fractal dimension of the 3-D inhomogeneities isD 3=31/2–32/3, which corresponds to a scaling exponent (Hurst number)H=1/2–1/3. The corresponding 1-D inhomogeneity spectra obey the power law with a powerp=2H+1=2–5/3. The intersection between the earth surface and the isostrength surface of the 3-D inhomogeneities will have fractal dimensionD 1=1.5–1.67. If we consider the earthquake fault surface as developed from the isosurface of the 3-D inhomogeneities and smoothed by the rupture dynamics, the fractal dimension of the fault trace on the surface must be smaller thanD 1, in agreement with recent measurements of fractal dimension along the San Andreas fault.

Notes: Abstract A temporal and spatial change of codaQ −1 associated with the occurrence of the North Palm Springs earthquake of July 8, 1986 was studied by using 242 small local earthquakes in the vicinity of the mainshock. We found that the codaQ −1 of earthquakes which occurred before the mainshock was significantly higher than that of the aftershocks in the mainshock area while the codaQ −1 for the surrounding area remained almost constant throughout 1986. CodaQ −1 was determined separately for the lapse time windows of 10 to 20 sec. and 15 to 40 sec. for the period from 1981 to 1987. The result for the time window 10 to 20 sec. showed a peak in codaQ −1 before the time of mainshock at all frequencies. The peak appeared earlier at lower frequencies. There was no significant change in codaQ −1 for the time window 15 to 40 sec., probably because the change was restricted to a small area.

Notes: Abstract 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.

Notes: Abstract Dieterich simulated aftershocks numerically, using a one-dimensional mass-spring model with a time-dependent friction law. But an important precursory phenomenon called ‘quiescence’ cannot be produced by this model unless, as Mikumo and Miyatake showed with a three-dimensional continuum model, a somewhat arbitrary bimodal distribution of frictional strength is assumed. Here we used the friction law proposed by Stuart, which is a displacement hardening-softening model, and simulated the quiescence. By varying the parameters of the friction law in our mass-spring model, we found a variety of seismicity patterns. When we choose extremely large critical displacement we get a recurrent sequence of creep followed by mainshock without small earthquakes. But when we choose a critical displacement in the same order of magnitude as the slip-weakening critical displacement estimated by Papageorgiou and Aki from strong motion data, we get a normal seismicity pattern, including quiescence before large events. This simple model points to a promising approach for the interpretation of the rupture process during an earthquake by the same physical model.

Notes: Abstract 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.

Notes: Abstract Recent observations made by Kanamori and Allen about earthquake recurrence time and average stress drop revealed a very interesting relation: earthquakes with longer recurrence times have higher average stress drops. They attributed the difference in stress drop to the difference in long-term average slip rate. To interpret their result in terms of the healing effect, we simulated earthquake recurrence with a one-dimensional mass-spring model, incorporating a recently developed rate-and-state dependent friction law for different loading rates and heterogeneous strength distributions. We first calculated the stress drop and recurrence time as functions of loading rate for a homogenous fault model. We found that the stress drop increases up to 30% when the loading rate decreases from 10 cm/yr to 0.01 mm/yr. Thus, the observed great variability of stress drop, from a few bars to a few hundred bars, which is obtained by replotting the data of Kanamori and Allen in the form of stress drop versus long-term slip rate, may not be attributable to the healing effect alone. Our numerical simulation shows that the variability may be due primarily to the spatial heterogeneity of strength on the fault. Our simulation also suggests that of the two empirical laws that were inferred from the same laboratory friction data, called the power law and the logarithmic law by Shimamoto and Logan, the former can explain the observed relation between stress drop and slip rate better than can the latter, at least for strike-slip fault. The logarithmic law is an earlier and simpler version of the rate-state-dependent friction law.