Finite-fault Inversion Research Articles

Signatures of the Seismic Source in EMD-Based Characterization of the 1994 Northridge, California, Earthquake Recordings

In this article we use empirical mode decomposition (EMD) to charac- terize the 1994 Northridge, California, earthquake records and investigate the sig- natures carried over from the source rupture process. Comparison of the current study results with existing source inverse solutions that use traditional data processing suggests that the EMD-based characterization contains information that sheds light on aspects of the earthquake rupture process. We first summarize the fundamentals of the EMD and illustrate its features through the analysis of a hypothetical and a real record. Typically, the Northridge strong-motion records are decomposed into eight or nine intrinsic mode functions (IMF's), each of which emphasizes a different oscillation mode with different amplitude and frequency content. The first IMF has the highest-frequency content; frequency content decreases with an increase in IMF component. With the aid of a finite-fault inversion method, we then examine aspects of the source of the 1994 Northridge earthquake that are reflected in the second to fifth IMF components. This study shows that the second IMF is predominantly wave motion generated near the hypocenter, with high-frequency content that might be related to a large stress drop associated with the initiation of the earthquake. As one progresses from the second to the fifth IMF component, there is a general migration of the source region away from the hypocenter with associated longer-period signals as the rupture propagates. This study suggests that the different IMF components carry information on the earthquake rupture process that is expressed in their different frequency bands.

A detailed slip model for the 1995, October 1, Dinar, Turkey, earthquake determined from inversion of teleseismicPandSHwaveforms

Summary Teleseismically recorded P and SH waveforms of the 1995, October 1 Dinar, Turkey, earthquake are inverted to find detailed coseismic slip distribution on the ruptured part of the Dinar-Civril fault. For this purpose a linear finite-fault inversion procedure with time window approach is used to allow variable rise time and rupture velocity on the model fault. The source is represented by a 24 × 21 km rectangle fault plane, which is divided into 56 equal size subfaults. The strike and the dip of the fault plane are assumed as determined by a previous study. The amount of slip and the rake angle on each subfault is retrieved through fitting the observed and synthetic seismograms in a least-squares sense. The previous inversion studies indicated that the earthquake was associated with two subevents, with a 6 s time lag of the NW subevent. Therefore, the model fault plane is also divided into two separate equal-area segments, the SE and the NW segments, to delay the rupture propagation over the NW segment. We tried several models to fix the delay time and hypocentral depth and to explain the waveforms. The smallest misfit error resulted from a model with 5 s delay time and 7.5 km hypocentral depth. The preferred solution suggests that the earthquake is associated with breaking of two asperities and the coseismic slip occurred mostly above the depth of 10 km. The smaller asperity is located to the SE just beneath Dinar town with peak slip of 26 cm while the larger one is located to the NW with peak slip of 41 cm. The observed surface rupture coincides with the location of the smaller asperity. The seismic moment for our slip model is 2.8 × 1018 N m. The modelling yields an average rake angle of −102° and almost no difference between the average rake angles of the two asperities.

Finite fault inversion of the September 25, 1999 (Mw = 6.4) Taiwan earthquake: Implications for GPS displacements of Chi‐Chi, Taiwan earthquake sequence

The September 25, 1999 Chi‐Chi Taiwan aftershock (Mw = 6.4) occurred on a down dip extension of the fault ruptured in the mainshock. Strong motion data were used to invert for the finite‐source process and test for the causative fault plane. We performed a grid‐search over a range of focal mechanisms and found a preferred model (strike = 5°, dip = 30°, slip = 100°) different from teleseismic studies (strike = 28±10°, dip = 27±5°, slip = 106±9°) but similar to the mainshock (strike = 5°, dip = 34°, slip = 65°). The aftershock asperity has a dimension of 10 km × 10 km with a maximum slip of ∼1.8 m and a static stress drop of 8 MPa. We forward‐predict the GPS displacements and found up to 0.033 m of surface horizontal displacements at some GPS sites, indicating that studies of post‐seismic deformation may need to account for the effects of large aftershocks.

Source Description of the 1999 Hector Mine, California, Earthquake, Part I: Wavelet Domain Inversion Theory and Resolution Analysis

We present a new procedure for the determination of rupture complexity from a joint inversion of static and seismic data. Our fault parameterization involves multiple fault segments, variable local slip, rake angle, rise time, and rupture velocity. To separate the spatial and temporal slip history, we introduce a wavelet transform that proves effective at studying the time and frequency characteristics of the seismic waveforms. Both data and synthetic seismograms are transformed into wavelets, which are then separated into several groups based on their frequency content. For each group, we use error functions to compare the wavelet amplitude variation with time between data and synthetic seismograms. The function can be an L1 + L2 norm or a correlative function based on the amplitude and scale of wavelet functions. The objective function is defined as the weighted sum of these functions. Subsequently, we developed a finite-fault inversion routine in the wavelet domain. A simulated annealing algorithm is used to determine the finite-fault model that minimizes the objective function described in terms of wavelet coefficients. With this approach, we can simultaneously invert for the slip amplitude, slip direction, rise time, and rupture velocity efficiently. Extensive experiments conducted on synthetic data are used to assess the ability to recover rupture slip details. We, also explore slip-model stability for different choices of layered Earth models assuming the geometry encountered in the 1999 Hector Mine, California, earthquake.

Compound rupture of the great 1998 Antarctic plate earthquake

The March 25, 1998, Antarctic plate earthquake ruptured a portion of the Antarctic plate more than 200 km west of its boundary with the Australian plate. The Harvard centroid moment tensor solution indicates that the earthquake was primarily a strike‐slip event, but the large non‐double‐couple component of the moment tensor suggests considerable complexity in the rupture process. We use a finite fault inversion method to determine details of the rupture process from teleseismic body waves recorded by the Global Seismic Network. The P waves are poorly fit by one or more subevents having only a strike‐slip mechanism. We find that the presence of a large oblique‐normal faulting subevent located to the east of the hypocenter is necessary to improve the fit. This subevent combines with a larger strike‐slip subevent to the west to comprise the main moment release in the earthquake and is the cause of the large non‐double‐couple component in the long‐period focal mechanism. The earthquake exhibited very high slip and high stress drop compared with most interplate strike‐slip events and the rupture was largely confined to the upper 15–20 km of the lithosphere. Both constituent focal mechanisms indicate that this part of the Antarctic plate is under NW‐SE oriented tension, although the origin of these stresses is unknown.

The fault nature of the Ms 5.4 volcanic earthquake preceding the 1996 subglacial eruption of Grimsvötn volcano, Iceland

The seismic activity preceding and accompanying the September 30, 1996 subglacial eruption of the Grimsvötn volcano, Iceland, developed in three stages. (1) The first stage (first 19 h) included the main shock of magnitude M s 5.4 and its aftershocks along the northern slope of the Bardarbunga volcano, situated about 20 km NW from Grimsvötn. (2) Seismic foci during the next 17 h marked a line connecting two volcanoes, Bardarbunga and Grimsvötn. This stage culminated in the opening of a fissure and the beginning of eruption. (3) The third stage was observed during the eruption (midnight of September 30–October 7), and included continuous seismic activity along the northern slope of the Bardarbunga volcano as well as more western distributed epicenters, which together had clustered the ring-fault epicentral zone. A finite-fault, broadband teleseismic P waveform inversion was applied to the main shock of September 29. The inversion showed that the rupture had developed downdip from the hypocenter in about 3 s, and the main asperity was ruptured at depths between 4 and 6 km. A comparison with the deep distribution of aftershocks showed that their hypocenters were situated above the destroyed asperities at the depths between 0 and 4 km. These space-time seismic patterns and the results of the finite-fault inversion may be interpreted in the following way. There was a magma chamber under Bardarbunga volcano covered by the strong rocks, or asperities. The main shock of September 29 broke the asperity and formed a path for magma transport. Then a fissure was formed connecting the opened magma chamber with the feeding structures of Grimsvötn volcano, and magma was injected laterally to the site of eruption. The continuous seismic activity during the third period was related to the collapse of rocks around the released parts of the magma chamber. The role of the M s 5.4 earthquake in this sequence was decisive.

Fault-slip distribution of the 1995 Colima-Jalisco, Mexico, earthquake

AbstractBroadband teleseismic P waves have been analyzed to recover the rupture history of the large (MS 7.4) Colima-Jalisco, Mexico, shallow interplate thrust earthquake of 9 October 1995. Ground-displacement records in the period range of 1-60 sec are inverted using a linear, finite-fault waveform inversion procedure that allows a variable dislocation duration on a prescribed fault. The method is applied using both a narrow fault that simulates a line source with a dislocation window of 50 sec and a wide fault with a possible rise time of up to 20 sec that additionally allows slip updip and downdip from the hypocenter. The line-source analysis provides a spatio-temporal image of the slip distribution consisting of several large sources located northwest of the hypocenter and spanning a range of rupture velocities. The two-dimensional finite-fault inversion allows slip over this rupture-velocity range and indicates that the greatest coseismic displacement (3-4 m) is located between 70 and 130 km from the hypocenter at depths shallower than about 15 km. Slip in this shallow region consists of two major sources, one of which is delayed by about 10 sec relative to a coherent propagation of rupture along the plate interface. These two slip sources account for about one-third of the total P-wave seismic moment of 8.3 × 1027 dyne-cm (Mw 7.9) and may have been responsible for the local tsunami observed along the coast following the earthquake.

Seismic Subduction of the Nazca Ridge as Shown by the 1996–97 Peru Earthquakes

By rupturing more than half of the shallow subduction interface of the Nazca Ridge, the great November 12, 1996 Peruvian earthquake contradicts the hypothesis that oceanic ridges subduct aseismically. The mainshock’s rupture has a length of about 200 km and has an average slip of about 1.4 m. Its moment is 1.5 ∞ 1028 dyne-cm and the corresponding M w is 8.0. The mainshock registered three major episodes of moment release as shown by a finite fault inversion of teleseismically recorded broadband body waves. About 55% of the mainshock’s total moment release occurred south of the Nazca Ridge, and the remaining moment release occurred at the southern half of the subduction interface of the Nazca Ridge. The rupture south of the Nazca Ridge was elongated parallel to the ridge axis and extended from a shallow depth to about 65 km depth. Because the axis of the Nazca Ridge is at a high angle to the plate convergence direction, the subducting Nazca Ridge has a large southwards component of motion, 5 cm/yr parallel to the coast. The 900–1200 m relief of the southwards sweeping Nazca Ridge is interpreted to act as a “rigid indenter,” causing the greatest coupling south of the ridge’s leading edge and leading to the large observed slip. The mainshock and aftershock hypocenters were relocated using a new procedure that simultaneously inverts local and teleseismic data. Most aftershocks were within the outline of the Nazca Ridge. A three-month delayed aftershock cluster occurred at the northern part of the subducting Nazca Ridge. Aftershocks were notably lacking at the zone of greatest moment release, to the south of the Nazca Ridge. However, a lone foreshock at the southern end of this zone, some 140 km downstrike of the mainshock’s epicenter, implies that conditions existed for rupture into that zone. The 1996 earthquake ruptured much of the inferred source zone of the M w 7.9–8.2 earthquake of 1942, although the latter was a slightly larger earthquake. The rupture zone of the 1996 earthquake is immediately north of the seismic gap left by the great earthquakes (M w ~ 8.8–9.1) of 1868 and 1877. The M w 8.0 Antofagasta earthquake of 1995 occurred at the southern end of this great seismic gap. The M w 8.2 deep-focus Bolivian earthquake of 1994 occurred directly downdip of the 1868 portion of that gap. The recent occurrence of three significant earthquakes on the periphery of the great seismic gap of the 1868 and 1877 events, among other factors, may signal an increased seismic potential for that zone.

The July 12, 1993, Hokkaido‐Nansei‐Oki, Japan, earthquake: Coseismic slip pattern from strong‐motion and teleseismic recordings

We employ a finite fault inversion scheme to infer the distribution of coseismic slip for the July 12, 1993 Hokkaido‐Nansei‐Oki earthquake using strong ground motions recorded by the Japan Meteorological Agency within 400 km of the epicenter and vertical P waveforms recorded by the Global Digital Seismograph Network at teleseismic distances. The assumed fault geometry is based on the location of the aftershock zone and comprises two fault segments with different orientations: a northern segment striking at N20°E with a 30° dip to the west and a southern segment with an N20°W strike. For the southern segment we use both westerly and easterly dip directions to test thrust orientations previously proposed for this portion of the fault. The variance reduction is greater using a shallow west dipping segment, suggesting that the direction of dip did not change as the rupture propagated south from the hypocenter. This indicates that the earthquake resulted from the shallow underthrusting of Hokkaido beneath the Sea of Japan. Static vertical movements predicted by the corresponding distribution of fault slip are consistent with the general pattern of surface deformation observed following the earthquake. Fault rupture in the northern segment accounts for about 60% of the total P wave seismic moment of 3.4 × 1020 N m and includes a large circular slip zone (4‐m peak) near the earthquake hypocenter at depths between 10 and 25 km. Slip in the southern segment is also predominantly shallower than 25 km, but the maximum coseismic displacements (2.0–2.5 m) are observed at a depth of about 5 km. This significant shallow slip in the southern portion of the rupture zone may have been responsible for the large tsunami that devastated the small offshore island of Okushiri. Localized shallow faulting near the island, however, may require a steep westerly dip to reconcile the measured values of ground subsidence.

Finite-fault analysis of the 1979 March 14 Petatlan, Mexico, earthquake using teleseismic P waveforms

SUMMARY Vertical, teleseismic P waves recorded for the 1979 March 14 Petatlan, Mexico, earthquake were used to derive the distribution of coseismic slip using a linear finite-fault inversion scheme that solves for the amount of slip in each of a series of consecutive time windows. Data recorded by six stations of the Global Digital Seismograph Network were inverted in addition to digitized analogue long-period recordings available from nine Worldwide Standardized Seismograph Network stations. The digital data include four broad-band and short-period velocity waveforms reconstructed from the short- and long-period components. The time-window approach allows for a variable rise time on the fault and accounts for the source multiplicity evident in the recorded P waveforms. Synthetic tests conducted using the inversion method on the limited data set, however, reveal that the data are insufficient to identify the exact dislocation duration on the fault. The method is thus implemented by prescribing the fault rise time using five consecutive 1 s time windows. The coseismic slip inferred from the P waves shows a small 70 cm peak near the earthquake hypocentre and a large zone of dislocation (1.2 m maximum) further south-east. The slip pattern covers depths from 3 to 25 km and is located south-east of other recent large interplate ruptures on the Michoacan segment of the Mexican subduction zone. This result indicates that the 1979 Petatlan earthquake broke an independent, adjacent portion of the Cocos-North America plate boundary. The seismic moment of 1.5 × 1027 dyn cm inferred from the P waves is approximately one-half the long-period moment estimated by other investigators from the observed surface waves. Although the discrepancy is within the uncertainty of the seismic-moment estimates, it may suggest the presence of a component of slow interplate motion that did not radiate significant P-wave energy.

Strong motion and broadband teleseismic analysis of the 1991 Sierra Madre, California, earthquake

Short period and broadband teleseismic waveform data and three‐component strong motion records were analyzed to obtain the source parameters of the 1991 Sierra Madre earthquake. Close‐in strong motion velocity records (analyzed from 5 s to 5 Hz) show two distinct pulses about 0.35 s apart, requiring some rupture complexity. The near‐field shear wave displacement pulse from this event has a relatively short duration (about 1 s) for the magnitude of the event, requiring a particularly high average stress drop. To further constrain the rupture process, the data were used in a finite fault source inversion to determine the temporal and spatial distribution of slip. We chose a fault plane orientation striking S 62°W and dipping 50° toward the northwest as required by the distribution of aftershocks, the first motion mechanism and the teleseismic bodywave point source inversion. In addition to the aftershock locations, depth constraints are provided by teleseismic short period and broadband recordings which require a centroid depth of 10–11 km. Our inverse modeling results indicate that both the teleseismic and strong motion data sets can be fit with a compact rupture area, about 12 km2, southwest and up‐dip from the hypocenter. The average slip is approximately 50 cm, and the maximum slip is 120 cm. The seismic moment obtained from either of the separate data sets or both sets combined is about 2.8 ± 0.3 × 1024 dyn cm and the potency is 0.01 km3. Using the area of significant slip estimated from the finite fault inversion, the resulting stress drop is on the order of 150–200 bars.

A broadband seismological investigation of the 1989 Loma Prieta, California, earthquake: Evidence for deep slow slip?

Analysis of regional and teleseismic broadband body waves and long-period surface waves from the 1989 Loma Prieta earthquake demonstrates that a fairly simple average fault model explains most characteristics of seismic wave radiation over a broad period range (1 to 300 sec), but there are some systematic period-dependent characteristics that are not yet understood. Determinations of the preferred point source focal mechanism are consistent for different seismic waves, as long as optimal source-time functions and depths are chosen for each wavetype. The major double couple orientation compatible with the entire period range has a strike = 128 +_ 3 °, dip = 67 _+ 5 ° , and rake = 133 _+ 8% While this source mechanism consistency is encouraging and indicates that the average source process is quite simple, there are some systematic discrepancies in the source parameter estimates from different period waves. The source duration estimated from the principal body-wave ground motions is 8 + 2 sec, compatible with the duration of near-field strong-motion vibrations, but the surface waves indicate total durations of 18 to 30 sec, depending on the earth model selected for computing propagation corrections. The model dependence of the surface-wave results suggests that it may be possible to reconcile the duration estimates with improved earth models, but the discrepancy is quite large. There is some complexity in the source-time function, comprised of three subevents at different depths, but this complexity is only manifested in short-period signals and does not explain the duration discrepancy. Changes of fault geometry or slip direction during rupture, as suggested by recent finite-fault inversions, are unlikely to cause a bias in source duration estimates. The centroid depth determined from our body-wave analysis is 10 to 12 km, consistent with the finite-fault models, which indicate rupture extending from 5 to 18 km. Surface-wave centroid depth estimates (15 to 30 km) vary substantially for different choices of global Q model and lithospheric structure in the source region, but they do tend to be deeper than the body-wave results. It is again not clear whether this depth discrepancy is due to the source process or inadequate earth models. The body-wave and surface-wave seismic moment estimates are also not fully consistent; the moment from our body-wave inversions is 2.4 _+ 0.3 x 1019 N-m, while our surface-wave analysis gives 3.2 _+ 0.5 x 1019 N-m. It is not known whether reasonable changes of the earth models can bring the moment estimates into full agreement. The systematic discrepancies in source duration, centroid depth, and seismic moment, despite the consistency in source orientation, raise the possibility of a deep, relatively slow co-seismic slip component, but trade-offs with modeling assumptions preclude us from confirming this hypothesis at present.