Estimated Slip Distribution Research Articles

Re-Estimating a Source Model for the 1923 Kanto Earthquake by Joint Inversion of Tsunami Waveforms and Coseismic Deformation Data

ABSTRACT The 1923 Kanto earthquake generated not only strong motions that caused a devastating disaster around the metropolitan Tokyo area but also a large tsunami. Although the slip distribution of the 1923 Kanto earthquake has been estimated by several researchers, tsunami waveforms observed at tide gauges near the source have never been used. In this study, the slip distribution of the 1923 Kanto earthquake was estimated using joint inversion of tsunami waveforms and vertical crustal deformations reported in historical documents. The estimated slip distribution was generally consistent with those estimated in the previous studies except for a large slip of 9 m along the western portion of the plate interface, up-dip near the Sagami trough. The east coast of the Izu Peninsula was inundated by the tsunami and surveyed after the tsunami to determine tsunami heights in the inundation areas. The tsunami inundation computed from the estimated slip distribution explained the tsunami heights, and the large slip played an important role in large inundation. These results indicate that the large slip west of the Sagami trough is essential for explaining the observed tsunami caused by the 1923 Kanto earthquake.

Continuous estimation of coseismic and early postseismic slip phenomena via the GNSS carrier phase to fault slip approach: a case study of the 2011 Tohoku-Oki sequence

The transition process from coseismic to early postseismic phenomena within a half-day remains a significant topic for understanding the slip budget and friction properties of the fault. However, the investigation of this phase has undergone limited advancement. This is mainly due to the lack of precision pertaining to the Global Navigation Satellite System (GNSS) analysis caused by difficulty of separation between fault slip and other unknown parameters such as tropospheric delay. Therefore, we propose an alternative approach (phase-to-slip; PTS) that detects fault slip directly from GNSS carrier phase variation without conventional positioning. Since the PTS simultaneously estimates fault slip and other unknowns, we can quantitatively evaluate their separation accuracy and contribution in the estimation. This study attempts to continuously estimate the coseismic and early postseismic slip of the 2011 Tohoku-Oki sequence using the PTS method. We analyzed 1-Hz carrier phase data for approximately 2 h before and after the mainshock origin (2011/03/11/05:46UTC). As a result, we successfully obtained the coseismic slip of the Mw9.0 mainshock and two major aftershocks in the off-Ibaraki (Mw7.8) and off Iwate (Mw7.4) regions. For all three events, the estimated slip distribution, equivalent moment magnitude, and calculated displacement field well agreed with those from the conventional positioning. Additionally, our results suggest postseismic slip mainly in the downdip area adjacent to the mainshock rupture. We obtained three major slip areas around the downdip region near Aomori, Iwate, and Miyagi. The estimated slip amount reaches approximately 0.1–0.2 m in 34 min immediately after the mainshock. The equivalent seismic moment of the slip areas near Iwate and Miyagi were approximately Mw7.4. This amount is similar or slightly greater than the estimations based on conventional positioning. Significant overlap is observed in the locations of the slip areas. In this manner, PTS continuously detected a series of coseismic and early postseismic slips with timescale ranging from a few minutes to an hour. Our results demonstrate the capability of the PTS method for broadband fault slip monitoring and its potential contribution to the investigation of early postseismic phenomena.

Bayesian Multi‐Model Estimation of Fault Slip Distribution for Slow Slip Events in Southwest Japan: Effects of Prior Constraints and Uncertain Underground Structure

AbstractWe consider a Bayesian multi‐model fault slip estimation (BMMFSE), which incorporates many candidates of the underground structure (Earth structure and plate boundary geometry) model characterized by a prior probability density function (PDF). The technique is used to study long‐term slow slip events (L‐SSEs) that occurred beneath the Bungo Channel, southwest Japan, in around 2010 and 2018. We here focus on the two advantages of BMMFSE: First, it allows for estimating slip distribution without introducing relatively strong prior information such as smoothing constraints, by combining a fully Bayesian inference and better consideration of model uncertainty to avoid overfitting. Second, the posterior PDF for the underground structure is also obtained during the fault slip estimation, which can be used as priors for the estimation of slip distribution for recurring events. The estimated slip distribution obtained using BMMFSE agreed better with the distribution of deep tectonic tremors at the down‐dip side of the main rupture area than those based on stronger prior constraints when the corresponding Coulomb failure stress changes are compared. This finding suggests a mechanical relationship between the L‐SSE and the synchronized tremors. The use of the posterior PDF of the underground structure estimated for the 2010 L‐SSE as prior PDF for the 2018 event resulted in more consistent estimation with the data, indicated by a smaller value of an information criterion.

Introduction of covariance components in slip inversion of geodetic data following a non-uniform spatial distribution and application to slip deficit rate estimation in the Nankai Trough subduction zone

SUMMARYInappropriate mathematical treatment of prediction errors associated with inaccurate forward modelling in an inversion scheme may result in significant unnatural short-wavelength components in the estimated slip distribution, which is a typical consequence of overfitting data. When geodetic data in observation stations following a non-uniform spatial distribution are used in a geodetic slip inversion, the spatial non-uniformity of the observation can possibly influence the distribution pattern of the short-wavelength components significantly, which may be confused with slip patterns that are geophysically meaningful. Such situations often occur when land and seafloor geodetic data are used in combination in slip inversions. To avoid overfitting, this study proposes a method that incorporates covariance components in the covariance matrix of the misfit vector, which originate from prediction errors. Because the proposed method retains the linearity of the inversion problem, widely known approaches that introduce prior constraints to a linear inversion problem are easily combined with the proposed method. This study demonstrates a combination of the newly introduced covariance components with a prior constraint on the smoothness of slip distribution, constructing a Bayesian model with unknown hyperparameters, which are objectively determined by minimizing Akaike’s Bayesian information criterion. In the synthetic tests, the proposed method estimated slip deficit rate (SDR) distributions that are closer to the true one, avoiding overfitting the geodetic data with spatial non-uniformity. By contrast, a conventional approach, which does not introduce covariance components, estimates unnaturally rough SDR distributions using the same synthetic data. The proposed method was applied to the estimation of SDR in the Nankai Trough subduction zone, using geodetic data of displacement rates provided by land GNSS stations and seafloor GNSS-Acoustic stations. This method estimates a reasonably smooth distribution of SDR, avoiding overfitting. The spatial distribution of residuals of the displacement rates suggests that the proposed method avoids overfitting some portions of the observed displacement rates that the forward model set for the analyses could not fundamentally explain.

Tsunami Source Inversion Using Tide Gauge and DART Tsunami Waveforms of the 2017 Mw8.2 Mexico Earthquake

On September 8, 2017 (UTC), a normal-fault earthquake occurred 87 km off the southeast coast of Mexico. This earthquake generated a tsunami that was recorded at coastal tide gauge and offshore buoy stations. First, we conducted a numerical tsunami simulation using a single-fault model to understand the tsunami characteristics near the rupture area, focusing on the nearby tide gauge stations. Second, the tsunami source of this event was estimated from inversion of tsunami waveforms recorded at six coastal stations and three buoys located in the deep ocean. Using the aftershock distribution within 1 day following the main shock, the fault plane orientation had a northeast dip direction (strike = 320^{circ }, dip = 77^{circ }, and rake =-92^{circ }). The results of the tsunami waveform inversion revealed that the fault area was 240 km × 90 km in size with most of the largest slip occurring on the middle and deepest segments of the fault. The maximum slip was 6.03 m from a 30 × 30 km2 segment that was 64.82 km deep at the center of the fault area. The estimated slip distribution showed that the main asperity was at the center of the fault area. The second asperity with an average slip of 5.5 m was found on the northwest-most segments. The estimated slip distribution yielded a seismic moment of 2.9 times 10^{21} Nm (Mw = 8.24), which was calculated assuming an average rigidity of 7times 10^{10} N/m2.

Resolving the Detailed Spatiotemporal Slip Evolution of Deep Tremor in Western Japan

AbstractWe study the detailed spatiotemporal behavior of deep tremor in western Japan through the development and application of a new slip inversion method. Although many studies now recognize tremor as shear slip along the plate interface manifested in low‐frequency earthquake (LFE) swarms, a conventional slip inversion analysis is not available for tremor due to insufficient knowledge of source locations and Green's functions. Here we introduce synthetic template waveforms, which are typical tremor waveforms obtained by stacking LFE seismograms at arranged points along the plate interface. Using these synthetic template waveforms as substitutes for Green's functions, we invert the continuous tremor waveforms using an iterative deconvolution approach with Bayesian constraints. We apply this method to two tremor burst episodes in western and central Shikoku, Japan. The estimated slip distribution from a 12 day tremor burst episode in western Shikoku is heterogeneous, with several patchy areas of slip along the plate interface where rapid moment releases with durations of <100 s regularly occur. We attribute these heterogeneous spatiotemporal slip patterns to heterogeneous material properties along the plate interface. For central Shikoku, where we focus on a tremor burst episode that occurred coincidentally with a very low frequency earthquake (VLF), we observe that the source size of the VLF is much larger than that estimated from tremor activity in western Shikoku. These differences in the size of the slip region may dictate the visibility of VLF signals in observed seismograms, which has implications for the mechanics of slow earthquakes and subduction zone processes.

Rupture process of the 1946 Nankai earthquake estimated using seismic waveforms and geodetic data

AbstractThe rupture process of the 1946 Nankai earthquake (MJMA 8.0) was estimated using seismic waveforms from teleseismic and strong motion stations together with geodetic data from leveling surveys and tide gauges. The results of joint inversion analysis showed that two areas with large slip are more confined than in previous studies. In our inversion, we assumed spatially varying strike and dip angles and depth of each subfault by fitting those to the actual complex shape of the upper surface of the Philippine Sea plate in the Nankai Trough region. As a result, we calculated the total seismic moment, M0 = 5.5 × 1021 Nm; the moment magnitude, Mw = 8.4; and a maximum slip of 5.1 m, occurring at a point south of Cape Muroto. The estimated slip distribution on the west side of the fault plane appears somewhat complicated, but it explains well the vertical deformations at Tosashimizu and in the vicinity of Inomisaki. Arguments have been made that the westernmost part slipped slowly after the earthquake over a period of days or months as an afterslip because the seismic waveforms can be largely explained without the slip in this part. However, in order to explain the displacement recorded by the tide gauge at Tosashimizu, we conclude that the westernmost part slipped simultaneously with the earthquake. Splay faulting, which was suggested in previous studies, is not required in our model to explain the seismic waveforms and geodetic data.

Teleseismic inversion of the 2004 Sumatra-Andaman earthquake rupture process using complete Green’s functions

Spatial and temporal variations in coseismic slip distribution are often obtained by rupture process analyses using teleseismic body waves. Many analyses using teleseismic body waves were based on the ray theory because of the very efficiently computable direct P-, S-, and major reflected waves near the source. The 2004 Sumatra-Andaman earthquake was one of the largest earthquakes recorded in history, and the data that are required for the entire rupture process analysis include later phases such as PP waves and a very long period phase called a W phase. However, calculating these later phases using the conventional ray theoretical method is difficult. Here we investigate the rupture process of the 2004 Sumatra-Andaman earthquake using complete Green’s functions, including all later phases such as PP waves and W phase. We use the direct solution method, which computes complete synthetic seismograms up to 2 Hz for transversely isotropic spherically symmetric media, to calculate the Green’s functions. The obtained synthetic seismograms generated fit the observed seismograms quite well from a short period to a long period. The estimated slip distribution consists of four large slip areas: the largest slip occurred in the shallow part off the Sumatra west coast with a maximum slip of approximately 29 m, the second and third largest slips occurred in the shallow and deep parts of the Nicobar region with maximum slips of approximately 8 m and 7 m, respectively, and the fourth slip occurred in the middle Andaman region with a maximum slip of approximately 6 m. The estimated average rupture velocity is 2.8 km/s, but the rupture may have slowed between the Sumatra and the shallow Nicobar slip areas, and between the Nicobar and the middle Andaman slip areas. The delayed initiation of the shallow slips in the Nicobar region may possibly have been triggered by the deeper slip in the Nicobar region. There were no distinct depth-varying properties for the shallow and deep slips in the Nicobar region, as were reported for the 2011 Tohoku-Oki and 2010 Chile earthquake.

Source rupture process of the 2011 Fukushima-ken Hamadori earthquake: how did the two subparallel faults rupture?

The 2011 Fukushima-ken Hamadori earthquake (MW 6.6) occurred about a month after the 2011 Great Tohoku earthquake (MW 9.0), and it is thought to have been induced by the 2011 Tohoku earthquake. After the 2011 Hamadori earthquake, two subparallel faults (the Itozawa and Yunodake faults) were identified by field surveys. The hypocenter was located nearby the Itozawa fault, and it is probable that the Itozawa fault ruptured before the Yunodake fault rupture. Here, we estimated the source rupture process of the 2011 Hamadori earthquake using a model with two subparallel faults based on strong motion data. The rupture starting point and rupture delay time of the Yunodake fault were determined based on Akaike’s Bayesian Information Criterion (ABIC). The results show that the Yunodake fault started to rupture from the northern deep point 4.5 s after the Itozawa fault started to rupture. The estimated slip distribution in the shallow part is consistent with the surface slip distribution identified by field surveys. Time-dependent Coulomb failure function changes (ΔCFF) were calculated using the stress change from the Itozawa fault rupture in order to evaluate the effect of the rupture on the Yunodake fault. The ΔCFF is positive at the rupture starting point of the Yunodake fault 4.5 s after the Itozawa fault started to rupture; therefore, it is concluded that during the 2011 Hamadori earthquake, the Yunodake fault rupture was triggered by the Itozawa fault rupture.

Using finite element and Okada models to invert coseismic slip of the 2008 Mw 7.2 Yutian earthquake, China, from InSAR data

We invert InSAR from ascending and descending passes of ENVISAT/ASAR data to estimate the distribution of coseismic slip for the 2008 Mw 7.2 Yutian earthquake by separately using uniform finite element models (FEMs), non-uniform FEMs, and analytical elastic half-space (Okada) models. We use the Steepest Descent method and Laplacian smoothing to regularize and estimate the slip distribution for each of these different models. Fault surface ruptures interpolated from Quickbird optical images constrain the strike of the fault. The uniform FEM and Okada models assume a fault embedded in a homogeneous and elastic finite domain or half-space, respectively, while the non-uniform FEM describes a domain with spatially variable elastic properties according to the geological structure of Tibet plateau and Tarim. We find that the estimated slip distribution of the non-uniform FEM is similar to that of the uniform FEM but has a slightly larger moment (~2 %). However, more noticeable discrepancies occur between the slip distributions of the uniform FEM and Okada model, where the slip pattern estimated with the FEM looks more scattered and locates at a lower depth. We conclude that, for the case of the Yutian earthquake, the improvement brought by simulating the distribution of geologic material properties is insignificant. This suggests that the uniform geologic structure of Okada models may be sufficient for simulating large intra-continental earthquakes.

Source model of the great 2011 Tohoku earthquake estimated from tsunami waveforms and crustal deformation data

The slip distribution of the 11 March 2011 Tohoku earthquake is inferred from tsunami waveforms, GPS data, and seafloor crustal deformation data. The major slip region extends all the way to the trench, and the large slip area extends 300km long and 160km wide. The largest slip of 44m is located up-dip of the hypocenter. The large slip amount, about 41m, ruptured the plate interface near the trench. The seismic moment calculated from the estimated slip distribution is 5.5×1022Nm (Mw 9.1). The large tsunami due to the 2011 Tohoku earthquake is generated from those large slip areas near the trench. The additional uplift at the sedimentary wedge as suggested for the 1896 Sanriku earthquake may have occurred during the 2011 Tohoku earthquake, too.

Coseismic slip distribution of the 2011 off the Pacific Coast of Tohoku Earthquake (M9.0) refined by means of seafloor geodetic data

On 11 March 2011, the devastating M9.0 Tohoku Earthquake occurred on the interface of the subducting Pacific plate, and was followed by a huge tsunami that killed about 20,000 people. Several geophysical studies have already suggested that the very shallow portion of the plate interface might have played an important role in producing such a large earthquake and tsunami. However, the sparsity of seafloor observations leads to insufficient spatial resolution of the fault slip on such a shallow plate interface. For this reason, the location and degree of the slip has not yet been estimated accurately enough to assess future seismic risks. Thus, we estimated the coseismic slip distribution based on terrestrial GPS observations and all available seafloor geodetic data that significantly improve the spatial resolution at the shallow portion of the plate interface. The results reveal that an extremely large (greater than 50 m) slip occurred in a small (about 40 km in width and 120 km in length) area near the Japan Trench and generated the huge tsunami. The estimated slip distribution and a comparison of it with the coupling coefficient distribution deduced from the analysis of the small repeating earthquakes suggest that the 2011 Tohoku Earthquake released strain energy that had accumulated over the past 1000 years, probably since the Jogan Earthquake in 869. The accurate assessments of seismic risks on very shallow plate interfaces in subduction zones throughout the world can be obtained by improving the quality and quantity of seafloor geodetic observations.

Coseismic slip distribution of the 2011 off the Pacific coast of Tohoku Earthquake (M 9.0) estimated based on GPS data— Was the asperity in Miyagi-oki ruptured?

We investigated the crustal deformation associated with the 2011 off the Pacific coast of Tohoku Earthquake (M 9.0) that occurred on March 11, 2011, along the plate boundary off Tohoku district, northeastern Japan, based on dense GPS observation. Coseismic displacements due to this event were applied to estimate the causal interplate slip by means of a geodetic inversion analysis. The major slip area is located around the asperities of the 1981 Miyagi-oki (M 7.2) and 2003 Fukushima-oki (M 6.8) earthquakes and the maximum slip is estimated as being up to 35 m. The estimated slip distribution suggests that the asperities of the Miyagi-oki earthquake in 1978 (M 7.4) that had not been ruptured during the Miyagi-oki earthquake in 2005 were ruptured as a part of the main shock fault of the 2011 off the Pacific coast of Tohoku Earthquake.

Slip distribution of the 1973 Nemuro-oki earthquake estimated from the re-examined geodetic data

AbstractGeodetic data, including leveling, tide-gauge, triangulation/trilateration, and repeated EDM data, from eastern Hokkaido, Japan, were re-examined to clarify the crustal deformation associated with the 1973 Nemuro-oki earthquake. We inverted the geodetic data to estimate the slip distribution on the interface of the subducting Pacific plate. The estimated coseismic slip, potentially including afterslip, showed a patch of large slip (i.e., an asperity) near the epicenter of the mainshock. The moment magnitude of the Nemuro-oki earthquake was estimated to be 8.0 from the geodetic data, which is comparable to the 2003Mw= 8.0 Tokachi-oki earthquake. The estimated slip distribution suggests a 50 km-long gap in the coseismic slip between the 1973 Nemuro-oki and the 2003 Tokachi-oki earthquakes. The slip area of the 2004Mw= 7.0 Kushiro-oki earthquake, estimated from GPS data, was located at the northwestern edge of the Nemuro-oki earthquake, which implies that the area may have acted as a barrier during the Nemuro-oki earthquake. The postseismic deformation observed by leveling and tide-gauge measurements suggests that the afterslip of the Nemuro-oki earthquake occurred at least in a western and northern (i.e., deeper) extension of the asperity on the plate interface.

A Fully Bayesian Inversion for Spatial Distribution of Fault Slip with Objective Smoothing

Abstract In inversion of geodetic data for spatial distribution of fault slip under smoothing and positivity constraints, subjective or incorrect techniques are often employed to select a smoothing parameter that determines the relative weight placed on fitting the data versus smoothing the slip distribution. A popular objective method based on Akaike’s Bayesian information criterion (ABIC) is incorrect if positivity constraints are employed. We introduce a fully probabilistic inversion method to simultaneously estimate the slip distribution and smoothing parameter objectively and correctly in a Bayesian framework. The complete solution to the inverse problem, the joint posterior probability density function of slip and smoothing parameter, is formulated using Bayes’ theorem and sampled with a Markov chain Monte Carlo method. We apply the new method to coseismic displacement data from the 1999 Chi-Chi, Taiwan, earthquake and compare the results of our method with conventional methods. The slip distribution estimated with our method is significantly smoother than that estimated by the ABIC-based method, demonstrating that the ABIC-based method may in general generate significantly undersmoothed or oversmoothed slip distributions under positivity constraints. On the other hand, the estimated slip distribution is similar to that estimated using another conventional method based on cross validation. Multiple trade-off curve plots between slip roughness and data misfit show that trade-off curves provide no basis for selecting a single smoothing parameter. The new method is easily generalized to slip inversions of multiple data sets with unknown relative weighting and to slip inversions with unknown fault geometry parameters.

Re-estimation of tsunami source of the 1952 Tokachi-oki earthquake

Abstract Previous studies indicate that the source area of the 2003 Tokachi-oki earthquake (M 8.0) was smaller than the comparable 1952 Tokachi-oki earthquake (M 8.2) source. We reinverted the 1952 tsunami waveforms, by adopting higher-resolution tsunami simulation method, and estimating and correcting for clock errors of tide gauges from comparison of the 1952 and 2003 tsunami waveforms. The estimated slip distribution indicates that the 1952 tsunami source area was indeed larger than the 2003 source. The distributions of measured and computed coastal tsunami heights also support this conclusion.

Coseismic deformation of the 2002 Denali Fault earthquake: Insights from GPS measurements

We estimate coseismic displacements from the 2002 Mw7.9 Denali Fault earthquake at 232 GPS sites in Alaska and Canada. Displacements along a N‐S profile crossing the fault indicate right‐lateral slip on a near‐vertical fault with a significant component of vertical motion, north‐side up. We invert both GPS displacements and geologic surface offsets for slip on a three‐dimensional (3‐D) fault model in an elastic half‐space. We restrict the motion to right‐lateral slip and north‐side‐up dip slip. Allowing for oblique slip along the Denali and Totschunda faults improves the model fit to the GPS data by about 30%. We see mostly right‐lateral strike‐slip motion on the Denali and Totschunda faults, but in a few areas we see a significant component of dip slip. The slip model shows increasing slip from west to east along the Denali Fault, with four localized higher‐slip patches, three near the Trans‐Alaska pipeline crossing and a large slip patch corresponding to a Mw7.5 subevent about 40 km west of the Denali‐Totschunda junction. Slip of 1–3 m was estimated along the Totschunda Fault with the majority of slip being at shallower than 9 km depth. We have limited resolution on the Susitna Glacier Fault, but the estimated slip along the fault is consistent with a Mw7.2 thrust subevent. Total estimated moment in the Denali Fault earthquake is equivalent to Mw7.89. The estimated slip distribution along the surface is in very good agreement with geological surface offsets, but we find that surface offsets measured on glaciers are biased toward lower values.

Elastic stress relaxation: A mechanism for opposite sense of secondary faulting with respect to a major fault

The motion along a major fault perturbs the local stress field and produces numerous secondary fractures. Among these, the secondary fractures that have the opposite sense of motion with respect to the main fault are particularly intriguing. For example, the right-lateral/reverse motion of the M s 7.1 Loma Prieta earthquake of 18 October 1989 produced a series of left-lateral/normal fractures, located in a narrow zone about 1 km in widt subparallel to the trace of the San Andreas fault. Through a rigorous inversion of geodetic data associated with the earthquake that allowed the slip to vary on the rupture surface, we studied the origin of the left-lateral/normal fractures by comparing the location, orientation and slip sense of the observed fractures with the perturbed elastic stress field calculated from the estimated slip distribution of the earthquake. The perturbed state of stress at the Earth's surface is complex, and the greatest principal stress changes from horizontal to vertical. The area of left-lateral/tensile state of stress coincides with that of the observed left-lateral/normal fractures. The magnitudes of the induced fault-normal tensile stresses of 60–120 bars and left-lateral fault-parallel shear stresses of 0–4 bars in the area are large enough to produce the ground failures. Thus, the observed left-lateral/normal fractures adjacent to the San Andreas fault are interpreted to be related to coseismic elastic stress relaxation. The same mechanism can also be used to explain the normal faulting in the upthrown blocks of the thrust faults which produced the 1980 El Asnam, Algeria and the 1968 Tokachi-Oki, Japan earthquakes.

Rupture directivity and slip distribution for the Ms 6.8 earthquake of 6 April 1992, Offshore British Columbia: An application of the empirical Green's function method using surface waves

Abstract On 6 April 1992 at 13:55 UT, an earthquake of Ms = 6.8 occurred along the Revere-Dellwood-Wilson (RDW) fault, in the triple-junction region at the northern end of the Cascadia subduction zone. This was the first significant event in this region recorded by modern digital broadband seismic networks, thus providing the first opportunity to examine the rupture process of a major earthquake along this young oceanic transform fault. In this article, an empirical Green's Function technique is applied to regional and teleseismic surface waves to estimate the rupture directivity, the extent of rupture, and the slip distribution along the Revere-Dellwood-Wilson fault associated with this earthquake. The 20-sec low-pass-filtered relative source time functions (RSTF's) are single pulses with an azimuthal variation in the pulse width. This suggests that the rupture propagated to the NW (315° ± 20°), along the Revere-Dellwood-Wilson fault (striking 326°). Higher frequency RSTF's reveal two discrete subevents. The clear azimuthal variation in the time separation of these subevents requires that relative to the first subevent, the second is located 13 to 20 km in the direction 345° ± 20°. Using the RSTF at HRV (perpendicular to the rupture direction), a total rupture length of 35 km is estimated, with the bulk of the slip concentrated in a 20-km-long segment of the RDW fault to the northwest of the epicenter. Two peaks are observed in the estimated slip distribution, with maximum values of 1.8 and 1.1 m, respectively. The rupture model derived from this analysis is similar to that obtained from the analysis of body waves and is consistent with the results of aftershock studies. The latter indicate a paucity of aftershock activity (and low moment release) in the 20-km-long segment of the RDW fault to the NW of the epicenter. A distinct peak in aftershock activity 30 to 40 km to the NW of the epicenter likely represents the termination of rupture. The good agreement between the results of this study, the rupture model estimated from body-wave analysis, and the aftershock distribution bode well for the application of the empirical Green's function method using surface waves. It suggests that this method could be applied to large, historic earthquakes in this region, for which regional and teleseismic surface waves are often the most reliable data set.

Comparison of various inversion techniques as applied to the determination of a geophysical deformation model for the 1983 Borah Peak earthquake

Abstract A number of techniques are employed to overcome nonuniqueness and instability inherent in linear inverse problems. To test the factors that enter into the selection of an inversion technique for fault slip distribution, we used a penalty function with smoothness (PF + S), a damped least-squares method (DLS), damped least-squares method with a positivity constraint (DLS + P), and a penalty function with smoothness and a positivity constraint (PF + S + P) for inverting the elevation changes for slip associated with the 1983 Borah Peak earthquake. Unlike solving an ill-posed inverse problem using a gradient technique (Ward and Barrientos, 1986), we have restored the well-posed character between the elevation changes and normal slip distribution. Studies showed that the constraints based on sound understanding of the physical nature of the problem are crucial in the derivation of a meaningful solution and dictates primarily the selection of a particular inversion technique. All available geological and geophysical information were used to determine a geophysical deformation model for the earthquake. It is suggested that the PF + S + P solution for a fault length of 75 km is the preferred model. The long wavelength features in the estimated slip distribution are similar to those obtained by Ward and Barrientos (1986), whereas the shorter wavelength features differ between two solutions. The fault dips 49° to the southwest. The slipped zones deepen from the surface at the northwest to about 20-km downdip depth at the southeast. The fault extends to the southeast beyond the epicenter of the mainshock. It is also shown that only the long wavelength features of the slip distribution are well resolved. The resolution is better at shallower levels than at deeper levels. The resolution deteriorates when the deformation sources are away from the leveling lines. Smoothness constraints provide better resolution than damping does at depth. The addition of a positivity constraint significantly improves the model resolution.