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99
Tomographic inversion of local earthquake data from the Hengill–Grensdalur central volcano complex
, 1989
"... We have determined the threedimensional P wave velocity structure within the area of the HengillGrensdalur central volcano complex, southwest Iceland, from the tomographic inversion of 2409 P wave arrival times recorded by a local earthquake xperiment. The aperture of the 20element seismic networ ..."
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Cited by 35 (2 self)
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We have determined the threedimensional P wave velocity structure within the area of the HengillGrensdalur central volcano complex, southwest Iceland, from the tomographic inversion of 2409 P wave arrival times recorded by a local earthquake xperiment. The aperture of the 20element seismic network utilized in the inversion permitted imaging ofa 5kmthick rustal volume underlying a 15 x 14 km 2 area. Within this localized volume are located the underpinnings of the active Hengill volcano and fissure swarm, the extinct Grensdalur volcano, and an active hightemperature g othermal field. It was thus expected that the characteristic length scale of heterogeneity would be of the order of a kilometer. In order to image heterogeneous eismic velocity structure at this scale we paid particular attention to the fidelity of the assumed model parameterization, defined as the degree to which the parameterization can reproduce xpected structural heterogeneity. We also discuss the tradeoff between the resolution of model parameters and image fidelity, compare results obtained from different parameterizations t illustrate his tradeoff, and present: • synoptic means of assessing image resolution that utilizes the offdiagonal information contained within the resolution matrix. The final tomographic image presented here was determined for a parameterization with fidelity that closely matches the geologic heterogeneity observed on the surface. For this parameterization, the resolution of individual parameters i generally low; however, aquantitative analysis of resolution provides an unambiguous a sessment
Roecker The effect of Swave arrival times on the accuracy of hypocenter estimation
 Bull. Seismol. Soc. Am
, 1990
"... Wellconstrained hypocenters (latitude, longitude, depth, and origin time) are required for nearly all studies that use earthquake data. We have examined the theoretical basis behind some of the widely accepted "rules of thumb " for obtaining accurate hypocenter estimates that pertain to t ..."
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Cited by 27 (0 self)
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Wellconstrained hypocenters (latitude, longitude, depth, and origin time) are required for nearly all studies that use earthquake data. We have examined the theoretical basis behind some of the widely accepted "rules of thumb " for obtaining accurate hypocenter estimates that pertain to the use of S phases and illustrate, in a variety of ways, why and when these "rules " are applicable. Results of experiments done for this study show that epicentral estimates (latitude and longitude) are typically far more robust with respect to data inadequacies; therefore, only examples illustrating the relationship between S phase arrival time data and focal depth and origin time estimates are presented. Most methods used to determine earthquake hypocenters are based on iterative, linearized, leastsquares algorithms. Standard errors associated with hypocenter parameters are calculated assuming the data errors may be correctly described by a Gaussian distribution. We examine the influence of Sphase arrival time data on such algorithms by using the program HYPOINVERSE with synthetic datasets. Leastsquares hypocenter determination algorithms have several shortcomings: solutions may be highly dependent on starting hypocenters, linearization and the assumption that data errors follow a Gaussian distribution may not be appropriate, and depth/origin time tradeoffs are not readily apparent. These shortcomings can lead to biased hypocenter estimates and standard errors that do not always represent he true error. To illustrate the constraint provided by Sphase data on hypocenters determined without some of these potential problems, we also show examples of hypocenter estimates derived using a probabilistic approach that does not require linearization. We conclude that a correctly timed S phase recorded within about 1.4 focal depth's distance from the epicenter can be a powerful constraint on focal depth. Furthermore, we demonstrate that even a single incorrectly timed S phase can result in depth estimates and associated measures of uncertainty that are significantly incorrect.
The Somali plate and the East African rift system: presentday kinematics
 Geophysical Journal International
, 1994
"... The motion of the Somalia plate relative to the Nubia (Africa), Arabia and Antarctica platcs is reevaluated using a new inversion method based on a Monte Carlo technique and a least absolute value misfit criterion. A subset of the N U V E L 1 data set, with additional data along the Levant Fault an ..."
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Cited by 24 (1 self)
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The motion of the Somalia plate relative to the Nubia (Africa), Arabia and Antarctica platcs is reevaluated using a new inversion method based on a Monte Carlo technique and a least absolute value misfit criterion. A subset of the N U V E L 1 data set, with additional data along the Levant Fault and in the Red Sea is used. The results confirm that the motion of Arabia with respect to Africa is significantly different from the motion relative to Somalia. It is further shown that the data along the SW Indian Ridge are compatible with a pole of relative motion between Africa and Somalia located close to the hypothetical diffuse triple junction between the ridge and thc East African Rift. The resulting AfricaSomalia motion is then compatible with the geological structures and seismological data along the East African Rift system. Assuming a separate Somalia plate thus solves kinematic and geological problems around the Afar triple junction and along the East African Rift.
Comparison of various inversion techniques as applied to the determination of a geophysical deformation model for the 1983 Borah Peak earthquake., Bull. seism
 Soc. Am
, 1992
"... 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 leastsquares meth ..."
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Cited by 22 (0 self)
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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 leastsquares method (DLS), damped leastsquares 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 illposed inverse problem using a gradient technique (Ward and Barrientos, 1986), we have restored the wellposed 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
Nonlinear arrival time inversion— Constraining velocity anomalies by seeking smooth models in 3D
 Geophys J. Internat
, 1990
"... The problem of constraining 3D seismic anomalies using arrival times from a regional network is examined. The nonlinear dependence of arrival times on the hypocentral parameters of the earthquakes and the 3D velocity field leads to a multiparametertype nonlinear inverse problem, and the distrib ..."
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Cited by 20 (3 self)
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The problem of constraining 3D seismic anomalies using arrival times from a regional network is examined. The nonlinear dependence of arrival times on the hypocentral parameters of the earthquakes and the 3D velocity field leads to a multiparametertype nonlinear inverse problem, and the distribution of sources and receivers from a typical regional network results in an enormous 3D variation in data constraint. To ensure computational feasibility, authors have tended to neglect the nonlinearity of the problem by linearizing about some bestguess discretized earth model. One must be careful in interpreting 3D structure from linearized inversions because the inadequacy of the data window may combine with nonlinear effects to produce artificial or phantom ‘structure’. To avoid the generation of artificial velocity gradients we must determine only those velocity variations which are necessary to fit the data rather than merely estimating local velocities in different parts of the model, which is the more common practice. We present a series of inversion algorithms which seek to inhibit the generation of unnecessary structure while performing efficiently within the frame
Y.: The longer it has been since the last earthquake, the longer expected time till the next
 Bull. Seism. Soc. Am
, 1989
"... We adopt a Iognormal distribution for earthquake interval times, and we use a locally determined rather than a generic coefficient of variation, to estimate the probability of occurrence of characteristic earthquakes. We extend previous methods in two ways. First, we account for the aseismic period ..."
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Cited by 20 (0 self)
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We adopt a Iognormal distribution for earthquake interval times, and we use a locally determined rather than a generic coefficient of variation, to estimate the probability of occurrence of characteristic earthquakes. We extend previous methods in two ways. First, we account for the aseismic period since the last event (the "seismic drought") in updating the parameter estimates. Second, in calculating the earthquake probability we allow for uncertainties in the mean recurrence time and its variance by averaging over their likelihood. Both extensions can strongly influence the calculated earthquake probabilities, especially for long droughts in regions with few documented earthquakes. As time passes, the recurrence time and variance estimates increase if no additional events occur, leading eventually to an affirmative answer to the question in the title. The earthquake risk estimate begins to drop when the drought exceeds the estimated recurrence time. For the Parkfield area of California, the probability of a magnitude 6 event in the next 5 years is about 34 per cent, much lower than previous estimates. Furthermore, the estimated 5year probability will decrease with every uneventful year after 1988. For the Coachella Valley segment of the San Andreas Fault, the uncertainties are large, and we estimate the probability of a large event in the next 30 years to be 9 per cent, again much smaller than previous estimates. On the Mojave (Pallett Creek) segment the catalog includes 10 events, and the present drought is just approaching the recurrence interval, so the estimated risk is revised very little by our methods.
A New Look at the Entropy for Solving Linear Inverse Problems
 IEEE Transactions on Information Theory
, 1994
"... Entropybased methods are widely used for solving inverse problems, especially when the solution is known to be positive. We address here the linear illposed and noisy inverse problems y = Ax + n with a more general convex constraint x 2 C, where C is a convex set. Although projective methods ar ..."
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Cited by 17 (4 self)
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Entropybased methods are widely used for solving inverse problems, especially when the solution is known to be positive. We address here the linear illposed and noisy inverse problems y = Ax + n with a more general convex constraint x 2 C, where C is a convex set. Although projective methods are well adapted to this context, we study here alternative methods which rely highly on some "informationbased" criteria. Our goal is to enlight the role played by entropy in this frame, and to present a new and deeper point of view on the entropy, using general tools and results of convex analysis and large deviations theory. Then, we present a new and large scheme of entropicbased inversion of linearnoisy inverse problems. This scheme was introduced by Navaza in 1985 [48] in connection with a physical modeling for crystallographic applications, and further studied by DacunhaCastelle and Gamboa [13]. Important features of this paper are (i) a unified presentation of many well kno...
A reanalysis of the hypocentral location and related observations for the great 1906
 California earthquake, Bull. Seismol. Soc. Am. 95
, 2005
"... Abstract We determine probabilistic hypocentral locations for the foreshock and mainshock of the Great 1906 California earthquake through reanalysis of arrivaltime observations in conjunction with modern velocity models and advanced eventlocation techniques. We obtain two additional observations f ..."
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Cited by 16 (1 self)
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Abstract We determine probabilistic hypocentral locations for the foreshock and mainshock of the Great 1906 California earthquake through reanalysis of arrivaltime observations in conjunction with modern velocity models and advanced eventlocation techniques. We obtain two additional observations for the mainshock and one for the foreshock that were not used in previous location studies. Using a robust likelihood function for event location, we generate a usable subset of the predominantly unreliable teleseismic readings and determine new wavetype identifications for some of the local and teleseismic readings. Our locations are much better constrained than those of earlier studies, even though we do not assume that the epicenter lies on the San Andreas fault, as did previous authors. We confirm the conclusions of earlier studies that the local and teleseismic arrivaltime observations can be explained by a single foreshock focus and a single mainshock focus on the San Andreas fault, and that there is no single, unique hypocenter that satisfies all available local observations. The maximumlikelihood point (Latitude, 37.78 N; Longitude, 122.51 W) for our “preferred ” mainshock location indicates a hypocenter to the west of San Francisco, close to the San Andreas fault zone. This hypocenter has a 68 % confidence error of about 8 km parallel to the San Andreas fault and about 24 km perpendicular to the fault, and a depth in the midcrust of about 12 7 km. The closest point on the San Andreas fault to this hypocenter lies about 10 km to the northwest of the widely accepted mainshock epicenter of Bolt (1968). Our mainshock location is consistent with the association of initial rupture of the 1906 mainshock with a dilatational rightbend or stepover in the submerged San Andreas fault system offshore of the Golden Gate. Our foreshock location is less well constrained than our mainshock location but is consistent with the foreshock hypocenter being at the same location as the mainshock hypocenter. Online material: Visualization of 3D probabilistic hypocentral locations associated with the 1906 earthquake.
2002), An inquiry into the lunar interior: A nonlinear inversion of the Apollo lunar seismic data
 J. Geophys. Res
"... [1] This study discusses in detail the inversion of the Apollo lunar seismic data and the question of how to analyze the results. The wellknown problem of estimating structural parameters (seismic velocities) and other parameters crucial to an understanding of a planetary body from a set of arrival ..."
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Cited by 14 (2 self)
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[1] This study discusses in detail the inversion of the Apollo lunar seismic data and the question of how to analyze the results. The wellknown problem of estimating structural parameters (seismic velocities) and other parameters crucial to an understanding of a planetary body from a set of arrival times is strongly nonlinear. Here we consider this problem from the point of view of Bayesian statistics using a Markov chain Monte Carlo method. Generally, the results seem to indicate a somewhat thinner crust with a thickness around 45 km as well as a more detailed lunar velocity structure, especially in the middle mantle, than obtained in earlier studies. Concerning the moonquake locations, the shallow moonquakes are found in the depth range 50–220 km, and the majority of deep moonquakes are concentrated in the depth range 850–1000 km, with what seems to be an apparently rather sharp lower boundary. In wanting to further analyze the outcome of the inversion for specific features in a statistical fashion, we have used credible intervals, twodimensional marginals, and Bayesian hypothesis testing. Using this form of hypothesis testing, we are able to decide between the relative importance of any two hypotheses given data, prior information, and the physical laws that govern the relationship between model and data, such as having to decide between a thin crust of 45 km and a thick crust as implied by the generally assumed value of 60 km. We obtain a Bayes factor of 4.2, implying that a thinner crust is strongly favored. INDEX TERMS: 6250 Planetology: Solar
Use of fault striations and dislocation models to infer tectonic shear stress during the 1995 Hyogoken Nanbu (Kobe) earthquake
, 1998
"... derived by Yoshida et al. (1996) show substantial changes in direction of slip with time at specific points on the Nojima and Rokko fault systems, as do striations we observed on exposures of the Nojima fault surface on Awaji Island. Spudich (1992) showed that the initial stress, that is, the shear ..."
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Cited by 13 (2 self)
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derived by Yoshida et al. (1996) show substantial changes in direction of slip with time at specific points on the Nojima and Rokko fault systems, as do striations we observed on exposures of the Nojima fault surface on Awaji Island. Spudich (1992) showed that the initial stress, that is, the shear traction on the fault before the earthquake origin time, can be derived at points on the fault where the slip rake rotates with time if slip velocity and stress change are known at these points. From Yoshida's slip model, we calculated ynamic stress changes on the ruptured fault surfaces. To estimate rrors, we compared the slip velocities and dynamic stress changes of several published models of the earthquake. The differences between these models had an exponential distribution, not gaussian. We developed a Bayesian method to estimate the probability density function (PDF) of initial stress from the striations and from Yoshida's slip model. Striations near Toshima and Hirabayashi give initial stresses of about 13 and 7 MPa, respectively. We obtained initial stresses of about 7 to 17 MPa at depths of 2 to 10 km on a subset of points on the Nojima and Rokko fault systems. Our initial stresses and coseismic stress changes agree well with postearthquake stresses measured by hydrofracturing in deep boreholes near Hirabayashi and Ogura on Awaji Island. Our results indicate that the Nojima fault slipped at very low shear stress, and fractional stress drop was complete near the surface and about 32% below depths of 2 kin. Our results at depth depend on the accuracy of the rake rotations in Yoshida's model, which are probably correct on the Nojima fault but debatable on the Rokko fault. Our results imply that curved or crosscutting fault striations can be formed in a single earthquake, contradicting a common assumption of structural geology.