Coseismic Geodetic Data Research Articles

The 2015 Mw7.2 Sarez Strike‐Slip Earthquake in the Pamir Interior: Response to the Underthrusting of India's Western Promontory

The Pamir orogen, Central Asia, is the result of the ongoing northward advance of the Indian continent causing shortening inside Asia. Geodetic and seismic data place the most intense deformation along the northern rim of the Pamir, but the recent 7 December 2015, Mw7.2 Sarez earthquake occurred in the Pamir's interior. We present a distributed slip model of this earthquake using coseismic geodetic data and postseismic field observations. The earthquake ruptured an ∼80 km long, subvertical, sinistral fault consisting of three right‐stepping segments from the surface to ∼30 km depth with a maximum slip of three meters in the upper 10 km of the crust. The coseismic slip model agrees well with en échelon secondary surface breaks that are partly influenced by liquefaction‐induced mass movements. These structures reveal up to 2 m of sinistral offset along the northern, low‐offset segment of modeled rupture. The 2015 event initiated close to the presumed epicenter of the 1911 Mw∼7.3 Lake Sarez earthquake, which had a similar strike‐slip mechanism. These earthquakes highlight the importance of NE trending sinistral faults in the active tectonics of the Pamir. Strike‐slip deformation accommodates shear between the rapidly northward moving eastern Pamir and the Tajik basin in the west and is part of the westward (lateral) extrusion of thickened Pamir plateau crust into the Tajik basin. The Sarez‐Karakul fault system and the two large Sarez earthquakes likely are crustal expressions of the underthrusting of the northwestern leading edge of the Indian mantle lithosphere beneath the Pamir.

Significant lateral dip changes may have limited the scale of the 2015 Mw 7.8 Gorkha earthquake

AbstractThe 2015 Mw 7.8 Gorkha earthquake has drawn interest due to its complex fault geometry. Both geodetic and geologic studies have focused on the dip variations. In this study we invert the coseismic geodetic data for the 2‐D dip variations of the earthquake. The best fit model confirms that the dip varies with depth, and suggests that there is a significant lateral dip anomaly along strike. The depth‐dependent dip variation suggests that the earthquake ruptured a ramp‐flat fault. The shallow ramp may have prevented the rupture breaking through the surface. In addition, a lateral large‐dip anomaly is found in the northeastern corner of the slip area, which supports the previous findings of inferred interseismic fault coupling, coseismic high‐frequency radiations, and the aftershock mechanisms. This lateral dip anomaly is likely associated with local tearing within the Indian slab. It may have blocked the east‐southeastward rupture propagations of the Gorkha earthquake, implying important controls on the earthquake scale and the spatial limits of ruptures.

Evidence of large scale repeating slip during the 2011 Tohoku-Oki earthquake

[1] The repetition of slip during rupture process of earthquake is a debate issue which had never been confirmed clearly in the past big events due to the lack of dense near-field observations and limited resolution in time of source model. The 2011 M9.0 Tohoku-Oki earthquake generated a wealth seismic records which provided us an unprecedented opportunity to study the rupture evolution of giant earthquake at a high spatio-temporal resolution. Here we use teleseismic, local strong motion and near-field coseismic geodetic data to investigate the source rupture process of this event based on the parallel inversion technique. The results reveal a broad slip zone with remarkable large scale repeating slip during the earthquake. The inverted source model shows several time periods of energy release with three main peaks. These energy bursts and temporal rupture snapshots suggest repetition of a large scale slip on the biggest asperity. This rupture behavior resulted in >50 m slips on the slip zone and prolonged the entire rupture process for a long duration of ∼160 seconds. The proposed source model is in a good agreement with the aftershock distribution and can interpret the characteristics of local strong motions. Further investigations of repeating slip during this event are crucial which will deeply transform earthquake science from dynamic point of view.

Optimal fault resolution in geodetic inversion of coseismic data

SUMMARY With the continued growth in availability of differential interferometry from synthetic aperture radar and GPS data, space based geodesy has been widely applied to image the coseismic displacement field and to retrieve the static dislocation over the fault plane for almost all the significant earthquakes of the past two decades. This is performed by linear data inversion over a set of subfaults, generally characterized by a constant and predefined or manually adjusted dimensions. In this paper, we propose a new algorithm to automatically retrieve an optimized fault subdivision in the linear inversion of coseismic geodetic data. The code iteratively keeps the parameter resolution close to a predefined high value. We first discuss the rationale supporting ouralgorithmand,afteradetaileddescriptionofitsimplementation,weanalysetheadvantages of its introduction in the data inversion. The algorithm was tested against an exhaustive range of synthetic and real data sets and fault mechanisms. Among them, we present the results for theMw 6.2, 2009 L’Aquila (Central Italy) earthquake and compare the new and previously published slip distributions showing the disappearance of misleading slip pattern and the increased resolution for shallower zones.

Mechanical constraints on inversion of coseismic geodetic data for fault slip and geometry: Example from InSAR observation of the 6 October 2008Mw6.3 Dangxiong-Yangyi (Tibet) earthquake

[1] Modern geodetic techniques, such as the global positioning system (GPS) and Interferometric Synthetic Aperture Radar (InSAR), provide high-precision deformation measurements of earthquakes. Through elastic models and mathematical optimization methods, the observations can be related to a slip distribution model. The classic linear, kinematic, and static slip inversion problem requires specification of a smoothing norm of slip parameters and a residual norm of the data and a choice about the relative weight between the two norms. Inversions for unknown fault geometry are nonlinear and, therefore, the fault geometry is often assumed to be known for the slip inversion problem. We present a new method to invert simultaneously for fault slip and fault geometry assuming a uniform stress drop over the slipping area of the fault. The method uses a full Bayesian inference method as an engine to estimate the posterior probability distribution of stress drop, fault geometry parameters, and fault slip. We validate the method with a synthetic data set and apply the method to InSAR observations of a moderate-sized normal faulting event, the 6 October 2008 Mw 6.3 Dangxiong-Yangyi (Tibet) earthquake. The results show a 45.0 ± 0.2° west dipping fault with a maximum net slip of ∼1.13 m, and the static stress drop and rake angle are estimated as ∼5.43 MPa and ∼92.5°, respectively. The stress drop estimate falls within the typical range of earthquake stress drops known from previous studies.

Inversion of synthetic geodetic data for the 1997 Colfiorito events: clues on the effects of layering, assessment of model parameter PDFs, and model selection criteria

The 1997 September-October Umbria-Marche sequence has been extensively studied in the past by analyzing coseismic displacement data (GPS, leveling, SAR). Here we focus on synthetic data representative of the main event of the 1997 Umbria-Marche sequence and investigate the effects of a crustal layering proper to the Colfiorito area on surface displacements and inferred source features when inverting coseismic geodetic data without taking into account layering. We compare bootstrapping and NA-Bayes as tools for parameter uncertainty assessment and show how the Akaike Information Criterion can be used to select the model which is most likely to be correct. Since SAR images offer the most complete coverage of the study area, we use synthetic line-ofsight displacement data.

Effects of crustal layering on source parameter inversion from coseismic geodetic data

SUMMARY We study the effect of a superficial layer overlying a half-space on the surface displacements caused by uniform slipping of a dip-slip normal rectangular fault. We compute static coseismic displacements using a 3-D analytical code for different characteristics of the layered medium, different fault geometries and different configurations of bench marks to simulate different kinds of geodetic data (GPS, Synthetic Aperture Radar, and levellings). We perform both joint and separate inversions of the three components of synthetic displacement without constraining fault parameters, apart from strike and rake, and using a non-linear global inversion technique under the assumption of homogeneous half-space. Differences between synthetic displacements computed in the presence of the superficial soft layer and in a homogeneous half-space do not show a simple regular behaviour, even if a few features can be identified. Consequently, also retrieved parameters of the homogeneous equivalent fault obtained by unconstrained inversion of surface displacements do not show a simple regular behaviour. We point out that the presence of a superficial layer may lead to misestimating several fault parameters both using joint and separate inversions of the three components of synthetic displacement and that the effects of the presence of the superficial layer can change whether all fault parameters are left free in the inversions or not. In the inversion of any kind of coseismic geodetic data, fault size and slip can be largely misestimated, but the product (fault length) × (fault width) × slip, which is proportional to the seismic moment for a given rigidity modulus, is often well determined (within a few per cent). Because inversion of coseismic geodetic data assuming a layered medium is impracticable, we suggest that only a case-to-case study involving some kind of recursive determination of fault parameters through data correction seems to give the proper approach when layering is important.

Effects of superficial layers on coseismic displacements for a dip-slip fault and geophysical implications

We study the effect of a superficial layer overlying a half-space on the surface displacements created by a dip-slip dislocation on a planar rectangular fault using a 2-D finite element model. The effect of the density and Poisson’s ratio is negligible. On the other hand, the contrast in Young’s modulus between the top layer and the half-space below significantly affects the modelled coseismic displacements. The horizontal displacements are more sensitive than the vertical displacements to the existence of the top layer. Near the fault, a low-rigidity layer with a Young’s modulus of 10 GPa can increase the horizontal displacements by up to 40 per cent. An analytical 3-D half-space model is used to interpret this effect in terms of an ‘equivalent’ homogeneous model. The presence of a top layer can be partly simulated in a homogeneous half-space by perturbing the depth and the slip on the fault from their ‘real’ values to ‘equivalent’ values. For a given displacement field observed at the surface, the perturbations in fault depth and slip can reach 1km and 25 per cent respectively. The fault dip angle is not model-dependent. We conclude that for the accurate estimation of fault depth and slip from coseismic geodetic data, rigidity contrasts existing within the upper crust must be taken into account. Not taking into account the effect of an existing low-rigidity layer also leads to an underestimation of seismic moment release. This may in part be the cause of apparent discrepancies between seismic and geodetic moment releases in particular areas such as the Gulf of Corinth, Greece.

Geometry of the 1954 Fairview Peak‐Dixie Valley earthquake sequence from a joint inversion of leveling and triangulation data

In 1954, four earthquakes greater than Ms = 6.0 occurred within a 30‐km radius and in a period of 6 months. Elevation and angle changes calculated from repeated leveling and triangulation surveys which span the coseismic period provide constraints on the fault geometries and coseismic slip of the faults which were activated. The quality of the coseismic geodetic data is assessed. Corrections are applied to the leveling data for subsidence due to groundwater withdrawal in the Fallon area, and a rod miscalibration error of 150 ± 30 ppm is isolated in leveling surveys made in 1967. The leveling and triangulation observations are then simultaneously inverted using the single value decomposition (SVD) inversion method to determine fault geometries and coseismic slip. Using SVD, it is possible to determine on which faults slip is resolvable given the data distribution. The faults are found to dip between 50° and 80° and extend to depths of 5 to 14 km. The geodetically derived slip values are generally equal to, or greater than, the maximum observed displacement along the surface scarps. Where slip is resolvable the geodetic data indicates the 1954 sequence contained a significant component of right‐lateral slip. This is consistent with the N15°W trending shear zone which geodetic surveys have detected in western Nevada.

Surface deformation and energy release rates for constant stress drop slip zones in an elastic half‐space

Free surface displacements, stress intensity factors, and energy release rates are calculated for planar slip zones in an elastic half‐space subjected to a prescribed shear stress drop. Although the method can treat arbitrarily shaped planar zones and distributed stress drops, for simplicity, results are presented only for circular and elliptic zones and uniform stress drops. Calculations of the stress intensity factors and energy release rates for various geometries indicate that solutions for the half‐space differ by less than 10% from those in the full space if the distance from the slip zone center to the free surface is greater than the downdip width of the slip zone. In addition, the influence of the free surface is greater for decreasing dip angle. For slip zones that are near the free surface and, especially, those that break the surface there is a coupling between slip and normal relative displacement. That is, for a prescribed shear stress drop and zero normal stress change, slip induces relative normal displacement. As example applications, these solutions are used to reexamine the coseismic geodetic data from three earthquakes: 1966 Parkfield, 1983 Borah Peak, and 1987 Whittier Narrows. The geometries, moments, and stress drops are similar to those inferred in previous studies using dislocation methods. However, the stress drop inferred here may be more reliable because stress drop is one of the parameters adjusted to fit the observed surface deformations. In addition, the method makes it possible to estimate the critical energy release rate at the termination of rupture. Values for the Parkfield, Borah Peak, and Whittier Narrows earthquakes are 1.5.×106 J/m2, 1.2×106 J/m2, and 2×108 J/m2, respectively.

A maximum likelihood approach to nonlinear inversion under constraints

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

QUASI-STATIC DEFORMATIONS DUE TO AN INCLINED, RECTANGULAR FAULT IN A VISCOELASTIC HALF-SPACE

Analytical expressions of the quasi-static, surface deformations (displacement, strain and tilt) due to an inclined, rectangular fault in a viscoelastic half-space are obtained by applying a correspondence principle to the solutions of the associated elastic problem. The medium is assumed to be elastic dilatational and Maxwell deviatric, and the time dependence of a dislocation source is taken to be of a step function type.From the analytical expressions, it is directly found that the viscoelastic part of the deformation field vanishes exactly for both an arbitrary slip on a horizontal fault plane and a dip-slip faulting on a vertical plane. In other cases, the viscoelastic part has a time dependence prescribed by a factor, 1-exp(-t/τ), where τ denotes the relaxation time determined from the Lame's elastic constants and the viscosity of the medium.Patterns of the elastic and the viscoelastic parts of the deformation field are respectively shown for two representative fault models. As an example, postseismic vertical displacements associated with the Kanto earthquake of 1923 are computed by the fault model determined from the coseismic geodetic data, and compared with the observed crustal movements for the period of 1931-1950.