Eiichi Fukuyama

Stress-Breakdown Time and Slip-Weakening Distance Inferred from Slip-Velocity Functions on Earthquake Faults

We estimate the critical slip-weakening distance on earthquake faults by using a new approach, which is independent of the estimate of fracture energy or radiated seismic energy. The approach is to find a physically based relation between the breakdown time of shear stress Tb, the time of peak slip-velocity Tpv, and the slip-weakening distance Dc, from the time histories of shear stress, slip, and slip velocity at each point on the fault, which can be obtained from dynamic rupture calculations using a simple slip-weakening friction law. Numerical calculations are carried out for a dynamic shear crack propagating either spontaneously or at a fixed rupture velocity on a vertical fault located in a 3D half-space and a more realistic horizontally layered structure, with finite-difference schemes. The results show that Tpv is well correlated with Tb for faults even with a heterogeneous stress-drop dis- tribution, except at locations near strong barriers and the fault edges. We also inves- tigate this relation for different types of slip-weakening behavior. We have applied the method to two recent, strike-slip earthquakes in western Japan, the 2000 Tottori and the 1995 Kobe events. We integrated the slip-velocity functions on the vertical fault obtained from kinematic waveform inversion of strong- motion and teleseismic records from the arrival time of rupture Tr to the time of the peak-slip velocity Tpv, and we then corrected the slip obtained at Tpv for the errors expected from the dynamic calculations. It was found that the slip-weakening dis- tance D c estimated in the frequency window between 0.05 and 0.5 Hz ranges between 40 and 90 cm on the two earthquake faults. However, if we consider the limited frequency resolution of the observed waveforms, probable time errors in the slip- velocity functions obtained from kinematic inversion, and the uncertainty of the slip- weakening behavior, the above estimates may be those located between the minimum resolvable limit and the upper bound of their real values. The estimated Dc values do not necessarily seem to indicate larger values in the shallower part and smaller values in the deeper part of the fault, but rather a spatially heterogeneous distribution that appears to be dependent on the local maximum slip. This possible dependence might be interpreted by the frictional properties of the fault such as the degree of roughness or the thickness of gouge layers, in addition to stress heterogeneities.

NIED seismic moment tensor catalogue for regional earthquakes around Japan: quality test and application

Abstract We have examined the quality of the National Research Institute for Earth Science and Disaster Prevention (NIED) seismic moment tensor (MT) catalogue obtained using a regional broadband seismic network (FREESIA). First, we examined using synthetic waveforms the robustness of the solutions with regard to data noise as well as to errors in the velocity structure and focal location. Then, to estimate the reliability, robustness and validity of the catalogue, we compared it with the Harvard centroid moment tensor (CMT) catalogue as well as the Japan Meteorological Agency (JMA) focal mechanism catalogue. We found out that the NIED catalogue is consistent with Harvard and JMA catalogues within the uncertainty of 0.1 in moment magnitude, 10 km in depth, and 15° in direction of the stress axes. The NIED MT catalogue succeeded in reducing to 3.5 the lower limit of moment magnitude above which the moment tensor could be reliably estimated. Finally, we estimated the stress tensors in several different regions by using the NIED MT catalogue. This enables us to elucidate the stress/deformation field in and around the Japanese islands to understand the mode of deformation and applied stress. Moreover, we identified a region of abnormal stress in a swarm area from stress tensor estimates.

A Kinematic Source-Time Function Compatible with Earthquake Dynamics

We propose a new source-time function, to be used in kinematic modeling of ground-motion time histories, which is consistent with dynamic propagation of earthquake ruptures and makes feasible the dynamic interpretation of kinematic slip models. This function is derived from a source-time function first proposed by Yoffe (1951), which yields a traction evolution showing a slip-weakening behavior. In order to remove its singularity, we apply a convolution with a triangular function and obtain a regularized source-time function called the regularized Yoffe function. We propose a parameterization of this slip-velocity time function through the final slip, its duration, and the duration of the positive slip acceleration ( Tacc ). Using this analytical function, we examined the relation between kinematic parameters, such as peak slip velocity and slip duration, and dynamic parameters, such as slip-weakening distance and breakdown-stress drop. The obtained scaling relations are consistent with those proposed by Ohnaka and Yamashita (1989) from laboratory experiments. This shows that the proposed source-time function suitably represents dynamic rupture propagation with finite slip-weakening distances.

Detailed Fault Structure of the 2000 Western Tottori, Japan, Earthquake Sequence

We investigate the faulting process of the aftershock region of the 2000 western Tottori earthquake ( M w 6.6) by combining aftershock hypocenters and moment tensor solutions. Aftershock locations were precisely determined by the double difference method using P - and S -phase arrival data of the Japan Meteorological Agency unified catalog. By combining the relocated hypocenters and moment tensor solutions of aftershocks by broadband waveform inversion of FREESIA (F-net), we successfully resolved very detailed fault structures activated by the mainshock. The estimated fault model resolves 15 individual fault segments that are consistent with both aftershock distribution and focal mechanism solutions. Rupture in the mainshock was principally confined to the three fault elements in the southern half of the zone, which is also where the earliest aftershocks concentrate. With time, the northern part of the zone becomes activated, which is also reflected in the postseismic deformation field. From the stress tensor analysis of aftershock focal mechanisms, we found a rather uniform stress field in the aftershock region, although fault strikes were scattered. The maximum stress direction is N107°E, which is consistent with the tectonic stress field in this region. In the northern part of the fault, where no slip occurred during the mainshock but postseismic slip was observed, the maximum stress direction of N130°E was possible as an alternative solution of stress tensor inversion.

Stress field along the Ryukyu Arc and the Okinawa Trough inferred from moment tensors of shallow earthquakes

Abstract We investigated the stress field along the Ryukyu Arc and the Okinawa Trough using regional (NIED MT) and global (Harvard CMT) moment tensor catalogs. Using the combined dataset of 4 years of data from the NIED MT catalog and 24 years of data from the Harvard CMT catalog, we found an arc-parallel extensional stress province along the forearc of the Ryukyu Arc and observed a detailed extensional stress field in the Okinawa Trough. This arc-parallel extension is observed in the entire region of the Ryukyu Arc except at its northeastern end. This stress field is clearly separated from the backarc extensional stress field in the Okinawa Trough by the volcanic chain. Since it exists in a normal subduction region as well as in a region of weakly coupled subduction, the effects of oblique subduction might not be enough to explain the formation of the arc-parallel extension. Thus, we consider that the backarc opening process should play an important role in this arc-parallel extension. Along the Okinawa Trough, an arc-perpendicular extensional stress field is observed in the southeastern and central Ryukyu Arc, while in the northeastern Okinawa Trough, the direction of the extensional axis is oblique to both the arc normal direction and the direction of plate motion. Two-dimensional mechanical interaction models which consider the interactions between the subducting plate, forearc and backarc are inadequate because an arc-parallel extensional stress field is observed in the entire Ryukyu Arc, and the extension axis in the northeastern Okinawa Trough is oblique to the arc trend. The oblique backarc stress may originate beneath the backarc or on the continental side of the backarc. One of the simplest ways to explain this observation might be active rifting in the northeastern Okinawa Trough.

Estimation of the Critical Slip-Weakening Distance: Theoretical Background

It has been shown that a trade-off exists between estimates of the break- down strength drop and the critical slip-weakening distance (e.g., Guatteri and Spu- dich, 2000). For this reason, only the fracture energy, proportional to these two parameters, may be estimated from waveform modeling. However, Mikumo et al. (2003) proposed a new technique to estimate the slip-weakening distance of earth- quakes, separate from the fracture energy. For this method to be valid, the peak slip- velocity time must be close to the stress breakdown time. Here we explain the theo- retical background of this assumption and clarify the limitations of this technique using numerical simulations based on the boundary integral equation method. The theoretical analysis using the boundary integral equation and some numerical tests indicates that a rather smooth rupture process and relatively sharp change in stress at the stress breakdown time in the slip-weakening curve ensure the validity of the method.

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.

Performance test of an automated moment tensor determination system for the future “Tokai” earthquake

We have investigated how the automated moment tensor determination (AMTD) system using the FREESIA/KIBAN broadband network is likely to behave during a future large earthquake. Because we do not have enough experience with a large (M > 8) nearby earthquake, we computed synthetic waveforms for such an event by assuming the geometrical configuration of the anticipated Tokai earthquake and several fault rupture scenarios. Using this synthetic data set, we examined the behavior of the AMTD system to learn how to prepare for such an event. For our synthetic Tokai event data we assume its focal mechanism, fault dimension, and scalar seismic moment. We also assume a circular rupture propagation with constant rupture velocity and dislocation rise time. Both uniform and heterogeneous slip models are tested. The results show that performance depends on both the hypocentral location (i.e. unilateral vs. bilateral) and the degree of heterogeneity of slip. In the tests that we have performed the rupture directivity appears to be more important than slip heterogeneity. We find that for such large earthquakes it is necessary to use stations at distances greater than 600 km and frequencies between 0.005 to 0.02 Hz to maintain a point-source assumption and to recover the full scalar seismic moment and radiation pattern. In order to confirm the result of the synthetic test, we have analyzed the 1993 Hokkaido Nansei-oki (MJ7.8) and the 1995 Kobe (MJ7.2) earthquakes by using observed broadband waveforms. For the Kobe earthquake we successfully recovered the moment tensor by using the routinely used frequency band (0.01–0.05 Hz displacements). However, we failed to estimate a correct solution for the Hokkaido Nansei-oki earthquake by using the same routine frequency band. In this case, we had to use the frequencies between 0.005 to 0.02 Hz to recover the moment tensor, confirming the validity of the synthetic test result for the Tokai earthquake.

DYNAMIC RUPTURE ANALYSIS : INVERSION FOR THE SOURCE PROCESS OF THE 1990 IZU-OSHIMA, JAPAN, EARTHQUAKE (M=6.5)

A waveform inversion has been applied to strong motion data using a dynamic shear crack model. We studied the 1990 Izu-Oshima earthquake (MJMA = 6.5), which has vertical strike-slip faulting with unilateral rupture propagation. The inversion has two steps, a waveform inversion and a crack inversion, that are applied iteratively. A waveform inversion is used to determine the distribution of rupture starting times and slip dislocations using the slip functions calculated by the initial crack model, or by previous crack inversion. A crack inversion is used to calculate dynamic crack propagation that explains the results of the above inversion. In this step, we use the estimated rupture times as a locking fracture criterion; the maximum shear stress attained before a fault segment breaks gives a lower bound estimate of the peak shear strength at each fault segment. Then the dynamic stress drop distribution is estimated from the slip distribution obtained from waveform inversion assuming a dynamic crack model. From the results, we determine the rise time distribution and the distribution of a dimensionless stress ratio S defined as (strength excess)/(stress drop). Our analysis gives the following picture of the rupture process of the 1990 Izu-Oshima earthquake: (1) An asperity-type faulting having large slip and high stress drop was detected in the region around the initiation point of rupture. (2) South of the asperity zone, barrier-type faulting characterized by incoherent propagating rupture, small slip, long rise time, and high strength excess was detected. This zone corresponds to the intersection of the fault with the 1978 earthquake (MJMA = 7.0).

The dependence of traction evolution on the earthquake source time function adopted in kinematic rupture models

[1] We compute the temporal evolution of traction by solving the elasto-dynamic equation and by using the slip velocity history as a boundary condition on the fault plane. We use different source time functions to derive a suite of kinematic source models to image the spatial distribution of dynamic and breakdown stress drop, strength excess and critical slip weakening distance (D c ). Our results show that the source time functions, adopted in kinematic source models, affect the inferred dynamic parameters. The critical slip weakening distance, characterizing the constitutive relation, ranges between 30% and 80% of the total slip. The ratio between D c and total slip depends on the adopted source time functions and, in these applications, is nearly constant over the fault. We propose that source time functions compatible with earthquake dynamics should be used to inter the traction time history.