Mitsuhiro Matsu'ura

Maximum-likelihood estimation of hypocenter with origin time eliminated using nonlinear inversion technique

Abstract A new algorithm is applied to inverting arrival time data for hypocenter location. The algorithm incorporates both observed and prior data from a Bayesian point of view. We define marginal probability density function (pdf) to eliminate the origin time from the location problem; the posterior pdf of hypocenter parameters is integrated over the whole range of the origin time. The best estimate of the hypocenter is defined as a set of spatial coordinates which maximizes the marginal pdf. Assuming Gaussian errors in both observed and prior data, we obtain a simple algorithm. Estimation errors of parameters are evaluated by an asymptotic covariance matrix, with which an asymptotic posterior pdf is computed. The algorithm is applied to observed data and is tested. An example of analysis is given for aftershocks of the 1969 Gifuken-chubu earthquake (M = 6.6) reported by the Japan Meteorological Agency (JMA). The spatial distribution of the aftershocks is supposed to be Gaussian with standard deviation of 15 km. A center of the aftershock distribution, which gives the prior estimates of hypocenters, is also estimated from observed data. Results of the nonlinear inversion of arrival time data are examined in terms of the asymptotic posterior pdf. We found that relocated hypocenters of the aftershocks are concentrated in a narrow region of 2–3 km in width, while the hypocenters previously reported by JMA have a wide distribution of 5–7 km.

Spontaneous processes for nucleation, dynamic propagation, and stop of earthquake rupture

We developed a model which can naturally explain the entire process of nucleation, dynamic propagation, and stop of earthquake rupture. In this model we represent frictional interaction between fault surfaces by a slip-dependent constitutive relation, and use it as the fundamental law governing the entire process of earthquake rupture. We considered a broad weak zone with a locally strong part (asperity) on a fault plane and examined the entire rupture process proceeding with the increase of external shear stress through numerical simulations. The nucleation process first proceeds quasi-statically at the weakest portion with the increase of external stress and brings about high stress concentration at the asperity. Then dynamic rupture starts at the asperity, but this dynamic rupture is arrested soon. After the arrest of the local dynamic rupture, the quasi-static nucleation process proceeds again and brings about high stress concentration at both ends of the weak zone. When the stress concentration reaches a critical level, dynamic rupture starts at the endzones and propagates outward. The rupture propagation is gradually accelerated to S-wave velocity until it reaches much stronger parts (barriers). The dynamic rupture is decelerated and finally arrested, with it propagating into the barrier. Our model successfully describes the transition process from nucleation to dynamic rupture propagation observed in laboratory experiments of stick-slip.

Selectivity of spontaneous rupture propagation on a branched fault

We simulated spontaneous dynamic rupture propagation on a branched fault system using the boundary integral equation method (BIEM) in 3D homogeneous, unbounded elastic medium. From the numerical experiments, we found that slightly heterogeneous preload stress field on the branches caused selective rupture propagation. Dynamic rupture propagation spontaneously on both branches requires very delicate conditions for the initial stress field as well as for the fracture criterion on them.

A maximum likelihood approach to nonlinear inversion under constraints

Abstract Nonuniqueness in geophysical inverse problems is naturally resolved by incorporating prior information about unknown models into observed data. In practical estimation procedures, the prior information must be quantitatively expressed. We represent the prior information in the same form as observational equations, nonlinear equations with random errors in general, and treat as data. Then we may define a posterior probability density function of model parameters for given observed data and prior data, and use the maximum likelihood criterion to solve the problem. Supposing Gaussian errors both in observed data and prior data, we obtain a simple algorithm for iterative search to find the maximum likelihood estimates. We also obtain an asymptotic expression of covariance for estimation errors, which gives a good approximation to exact covariance when the estimated model is linearly close to a true model. We demonstrate that our approach is a general extension of various inverse methods dealing with Gaussian data. By way of example, we apply the new approach to a problem of inferring the final rupture state of the 1943 Tottori earthquake (M = 7.4) from coseismic geodetic data. The example shows that the use of sufficient prior information effectively suppresses both the nonuniqueness and the nonlinearity of the problem.

Study on coseismic and postseismic crustal movements associated with the 1923 Kanto earthquake

Abstract The Kanto earthquake of 1923 (M = 7.9) occurred in the southern part of the Kanto district, Japan. This earthquake was accompanied by the transient crustal movements which follow instantaneous elastic deformations at the time of faulting. The coseismic and postseismic crustal movements associated with the Kanto earthquake are well interpreted by a dislocation source model in a composite medium which consists of an elastic surface layer (lithosphere), an intervening Maxwellian viscoelastic layer (asthenosphere) and an elastic substratum. An optimum fault model of the Kanto earthquake is obtained from the coseismic crustal movements by using a method of inversion analysis, in which effects of systematic errors caused by the movements of reference points in geodetic measurement are taken into account. It is found that the fault motion of this earthquake is a reverse, right-lateral slip of 4.8 m with a slip-angle of 140° on a fault plane which dips 25° towards N24°E, where the slip-angle is measured counterclockwise from the fault strike. The fault length, the fault width, and the depth to the upper fault edge are determined as 95 km, 54 km, and 2.0 km, respectively. The postseismic transient crustal movements are considered to be controlled by a quasi-static relaxation process of stress changes due to faulting in the earths asthenosphere. In such a quasi-static problem, the surface motion caused by a dislocation source consists of instantaneous elastic deformation at the time of faulting and transient viscoelastic movement after the event. The viscoelastic part of the surface displacement field is calculated for the optimum fault model in a three-layered composite medium with an intervening viscoelastic layer, and compared with the observed data. The transient crustal movements after the Kanto earthquake are adequately explained by the present model, taking the thickness of the lithosphere as 60 km, and the thickness and viscosity of the asthenosphere as 180 km and 1020 poise, respectively.

LOADING MECHANISM AND SCALING RELATIONS OF LARGE INTERPLATE EARTHQUAKES

We have done a numerical simulation of tectonic loading at transform plate boundaries with a lithosphere-asthenosphere coupling model subject to steady relative plate motion. In this model a seismic fault is represented by a locked patch with a finite length on an infinitely long vertical dislocation surface cutting the entire lithosphere. Through the numerical simulation we have obtained the following results. Stress accumulation on the fault is partly due to viscous drag at the base of the lithosphere (base loading) and partly due to dislocation pile-ups at horizontal edges of the fault (edge loading). If the viscosity of the asthenosphere is less than 1018 Pa s, the base loading is not effective, since its rate exponentially decays very soon. If the viscosity of the asthenosphere is greater than 1020 Pa s, both types of loading are effective, and then the stress accumulation rate in the early stage of loading is formally written as dτdt = Vpl(a + bL), where Vpl is a rate of relative plate motion and L is a fault length. When the fault length L is small, the effect of edge loading (the second term) is dominant, and the stress accumulation rate is in proportion to the inverse of L. When the fault length L is large, the effect of base loading (the first term) becomes dominant, and the stress accumulation rate is independent of L. It is well-known that the general L-cubed dependence of seismic moment M0 breaks for large interplate earthquakes. This break in the moment-length relation can be ascribed to difference in loading mechanism between small and large earthquakes. From the results of numerical computation, if interplate earthquakes have the same stress drop regardless of their fault lengths, we may derive a L-squared dependence of M0 for large interplate earthquakes and a linear L-dependence of M0 for very large interplate earthquakes.

Foreshocks and pre‐events associated with the nucleation of large earthquakes

We propose a theoretical model which can explain the occurrence of foreshocks and pre-events associated with the nucleation of large earthquakes. We consider a broad weak zone with a locally strong part (asperity) on a fault plane in a two-dimensional framework and examine the transition process from quasistatic nucleation to high-speed rupture propagation through numerical simulations. The dynamic rupture of the asperity occurs in three different manners, as aseismic slip, foreshock or pre-event, depending on the peak stress of the asperity. In all cases the rupture of the asperity accelerates the nucleation of main rupture.

Interplate coupling in the Kanto district, central Japan, deduced from geodetic data inversion and its tectonic implications

Abstract Interplate coupling between the Philippine Sea (PHS), the North American (NAM), and the Pacific (PAC) plates in the Kanto district, central Japan, has been investigated through the inversion analysis of geodetic data using Akaikes Bayesian Information Criterion (ABIC). The data used for the analysis are annual rates of level changes (1972–1985) and horizontal length changes (1973–1990), which presumably represent average crustal movements during the interseismic period. Disregarding effects of steady plate subduction, we may ascribe the observed crustal movements to the effects of locking or faulting on some parts of the plate boundaries. In our model, the effect of locking is represented by back slip on the plate boundary, and that of faulting by forward slip. The results of the inversion analysis show the existence of a strongly coupled area on the southwestern, shallower part of the NAM-PHS plate boundary, which almost coincides with the faulting area of the 1923 Kanto earthquake ( M 7.9), and a notable faulting area on the northeastern, deeper part of the PHS-PAC plate boundary. In the southwestern strongly coupled area, the rate of back slip reaches 3.5 cm/yr, and its direction is oriented N33°W, which is almost opposite to the direction of fault slip (S29°E) at the time of the 1923 event. This suggests that tectonic stress accumulation for the next large event is effectively proceeding there, and its recurrence time is roughly estimated as 245 years. The strongly coupled region is also recognized as corresponding to a recent seismic gap. The inverted forward-slip distribution on the PHS-PAC plate boundary, which has the average rate of 1.9 cm/yr and the average direction of N56°E, may be explained by aseismic northeastward slip in relation to the process to form a peculiar configuration of downward bend of the PHS plate beneath the Kanto district.

Crustal movements on Shikoku, southwestern Japan, inferred from inversion analysis of levelling data using ABIC

Abstract With an inversion technique based on Akaikes Bayesian Information Criterion (ABIC) we analyzed levelling data for 1893–1983 on Shikoku, southwestern Japan, where large interplate earthquakes have periodically occurred at intervals of about 120 years, releasing tectonic stress produced by steady relative motion of the Philippine Sea and the Eurasian plates. Through the inversion analysis we reconstructed the pattern of crustal movements on Shikoku over the last 120 years, including the occurrence of the 1946 Nankaido earthquake (M 8.1). The result clearly shows that the crustal movements on Shikoku include significant secular vertical motion (uplift in the south and subsidence in the north) in addition to cyclic motion related to the periodic occurrence of interplate earthquakes at the Nankai trough. Contrary to the widely accepted theory, we could not find any correlation between the secular vertical motion and the coseismic vertical displacement. The secular uplift motion on southern Shikoku estimated from the levelling data completely agrees with that inferred from the present heights of marine terraces formed by eustatic sea level changes and crustal uplift for the last 105 yr. This suggests that the fundamental causes of the short-term (102 yr) and long-term (105 yr) movements on southern Shikoku are the same, the steady subduction of the Philippine Sea plate at the Nankai trough. On northern Shikoku, on the other hand, the pattern of secular crustal motion estimated from the levelling data is quite different from that of the Quaternary uplift inferred from the present heights of eroded flat surfaces, indicating the existence of some unknown tectonic process controlling the very long-term (106 yr) crustal movements.

Aseismic crustal deformation in the Transverse Ranges of southern California

Abstract Geodetic data at a plate boundary can reveal the pattern of subsurface displacements that accompany plate motion. We model these displacements as the sum of rigid block motion and the elastic effects of frictional drag between blocks. The frictional interactions are represented by uniform dislocation on each of several rectangular fault patches. We then estimate the block velocities and fault parameters from geodetic data. Our Bayesian inversion procedure employs prior estimates based on geological and seismological data. We apply the method to the Transverse Ranges, using prior data from Bird and Rosenstock (1984) and geodetic data from the USGS trilateration networks and NASA VLBI measurements. Our model consists of 12 blocks and 27 rectangular fault patches. The block motion inferred from the geodetic data has the same order of magnitude as the geologic estimates, and for many faults the agreement is excellent. However, the geodetic data imply a displacement rate of about 20 mm yr −1 across the San Andreas fault, while the geologic estimates exceed 30 mm yr −1 . The final model implies about 6 mm yr −1 of crustal shortening normal to the trend of the San Andreas fault; this is about half the rate implied by the prior model. Most of this shortening occurs on the Sierra Madre-Cucamonga and the White Wolf fault systems. Aseismic fault motion is a major contributor to plate motion, and the thickness of the frictional surface varies considerably from one fault to another. The geodetic data can help to identify faults that are suffering rapid stress accumulation; in the Transverse Ranges those faults are the San Andreas, San Gabriel, Sierra Madre, Pleito, and White Wolf faults.