Centroid moment tensor inversion of low-frequency seismic spectra using Green's functions for aspherical earth models

We present a new method for centroid moment tensor (CMT) inversion, in which we employ the Green's function computed for aspherical earth models using the Direct Solution Method. We apply this method to CMT inversion of low-frequency seismic spectra for the 1994 Bolivia and 1996 Flores Sea deep earthquakes. The estimated centroid locations agree well with those obtained by multiple-shock analyses using body-wave data. This shows that it is possible to obtain reliable CMT solutions by analyses of low-frequency seismic spectra using accurate Green's functions computed for present 3-D earth models.     

A Bayesian approach to estimating tectonic stress from seismological data

Earthquakes are conspicuous manifestations of tectonic stress, but the non-linear relationships between the stresses acting on a fault plane, its frictional slip, and the ensuing seismic radiation are such that a single earthquake by itself provides little information about the ambient state of stress. Moreover, observational uncertainties and inherent ambiguities in the nodal planes of earthquake focal mechanisms preclude straightforward inferences about stress being drawn on the basis of individual focal mechanism observations. However, by assuming that each earthquake in a small volume of the crust represents a single, uniform state of stress, the combined constraints imposed on that stress by a suite of focal mechanism observations can be estimated. Here, we outline a probabilistic (Bayesian) technique for estimating tectonic stress directions from primary seismological observations. The Bayesian formulation combines a geologically motivated prior model of the state of stress with an observation model that implements the physical relationship between the stresses acting on a fault and the resultant seismological observation. We show our Bayesian formulation to be equivalent to a well-known analytical solution for a single, errorless focal mechanism observation. The new approach has the distinct advantage, however, of including (1) multiple earthquakes, (2) fault plane ambiguities, (3) observational errors and (4) any prior knowledge of the stress field. Our approach, while computationally demanding in some cases, is intended to yield reliable tectonic stress estimates that can be confidently compared with other tectonic parameters, such as seismic anisotropy and geodetic strain rate observations, and used to investigate spatial and temporal variations in stress associated with major faults and coseismic stress perturbations.     

Post-seismic reloading and temporal clustering on a single fault

Geological studies show evidence for temporal clustering of large earthquakes on individual fault systems. Since post-seismic deformation due to the inelastic rheology of the lithosphere may result in a variable loading rate on a fault throughout the interseismic period, it is reasonable to expect that the rheology of the non-seismogenic lower crust and mantle lithosphere may play a role in controlling earthquake recurrence times. We study this phenomenon using a 2-D, finite element method continuum model of the lithosphere containing a single strike-slip fault. This model builds on a previous study using a 1-D spring-dashpot-slider analogue of a single fault system to study the role of Maxwell viscoelastic relaxation in producing non-periodic earthquakes. In our 2-D model, the seismogenic portion of the fault slips when a predetermined yield stress is exceeded; stress accumulated on the seismogenic fault is shed to the viscoelastic layers below and recycled back to the seismogenic fault through viscoelastic relaxation. We find that random variation of the fault yield stress from one earthquake to the next can cause the earthquake sequence to be clustered; the amount of clustering depends on a non-dimensional number, W , called the Wallace number defined as the standard deviation of the randomly varied fault yield stress divided by the effective viscosity of the system times the tectonic loading rate. A new clustering metric based on the bimodal distribution of interseismic intervals allows us to investigate clustering behaviour of systems over a wide range of model parameters and those with multiple viscoelastic layers. For models with   W ≥ 1  clustering increases with increasing W , while those with   W ≤ 1  are unclustered, or quasi-periodic.     

Geodetic inversion for space–time distribution of fault slip with time-varying smoothing regularization

We have developed a new geodetic inversion method for space–time distribution of fault slip velocity with time-varying smoothing regularization in order to reconstruct accurate time histories of aseismic fault slip transients. We introduce a temporal smoothing regularization on slip and slip velocity through a Bayesian state space approach in which the strength of regularization (temporal smoothness of slip velocity) is controlled by a hyperparameter. The time-varying smoothing regularization is realized by treating the hyperparameter as a time-dependent stochastic variable and adopting a hierarchical Bayesian state space model, in which a prior distribution on the hyperparameter is introduced in addition to a conventional Bayesian state space model. We have tested this inversion method on two synthetic data sets generated by simulated aseismic slip transients. Results show that our method reproduces well both rapid changes of slip velocity and steady-state velocity without significant oversmoothing and undersmoothing, which has been hard to overcome by the conventional Bayesian approach with time-independent smoothing regularization. Application of this method to transient deformation in 2002 caused by a silent earthquake off the Boso peninsula, Japan, also shows similar advantages of this method over the conventional approach.     

Local and regional components of western Aegean deformation extracted from 100 years of geodetic displacement measurements

Our objectives are as follows. First, we wish to develop a methodology to recover the long-term component of deformation from any set of distributed, time-averaged geodetic strain measurements that were subject to seismic disturbance, given a catalogue of local seismicity that occurred during the measurement period. Second, using seismic and geodetic data sets that span approximately 100 years, we apply this technique in the western Aegean to assess the role of local seismicity in regional deformation. The methodology is developed using a model for crustal deformation constructed from a long-term, smooth regional strain field combined with instantaneous, local perturbations from upper-crustal earthquakes approximated by static elastic dislocations. By inverting geodetic displacements for the smooth field while simultaneously floating influential but uncertain earthquake source parameters, an estimate of the regional component of deformation that is approximately independent of the seismicity can be made. In the western Aegean we find that the horizontal component of regional deformation can be described with minor inaccuracy by a quadratic relative displacement field. The principal horizontal extensional axes calculated from the regionally smooth displacement field agree in orientation with the T-axes of earthquakes in the region. These observations indicate that the instantaneous elastic strain of the 10 km thick seismogenic layer is driven by a stress field that is smooth on the scale of the geodetic network as a whole, 200-300 km.     

Joint two-dimensional cross-gradient imaging of magnetotelluric and seismic traveltime data for structural and lithological classification

Collocated magnetotelluric (MT) and seismic profiling is emerging as a necessary combined approach for deep and near-surface imaging but the resulting experimental data are typically interpreted separately since no production programs exist for multidimensional joint inversion of MT and seismic data. We present a joint 2-D inversion approach for imaging collocated MT and seismic refraction data with cross-gradient structural constraints. We describe the main features of the algorithm and first apply it to synthetic data generated for a hypothetical complex geological model. For the synthetic data, we find that the scheme leads to models with remarkable structural resemblance and improved estimates of electrical resistivity and seismic velocity. We apply the scheme to near-surface field data to test the consistency of a previously suggested resistivity–velocity interrelationship and its potential use for subsurface lithofacies discrimination or structural classification. The MT-seismic relationship is found to be in excellent accord with that derived previously for DC resistivity and seismic data set at the test site. Our results suggest that joint MT-seismic cross-gradient imaging leads to improved characterization of heterogeneous geological targets at near-surface to mantle depths.     

An improved method for the determination of the tectonic stress field from focal mechanism data

All conventional stress inversion methods, when applied to earthquake focal mechanism data, suffer from uncertainty as to which plane is the true fault plane. This paper deals with several problems in stress inversion brought about by this uncertainty. Our analysis shows that the direction of shear stress on the auxiliary plane does not coincide with the hypothetical slip direction unless the B -axis is parallel to one of the three principal stress directions. Based on this simple fact, we propose a new algorithm dealing with the ambiguity in fault/auxiliary plane identification. We also propose a method to handle the inhomogeneity problem of data quality, which is common and unique for focal mechanism data. Different inversion methods and algorithms are applied to two sets of 'focal mechanism' data simulated from field fault-slip measurement data. The inversion results show that, among the four stress parameters inverted, the stress ratio suffers the most from the ambiguity in fault/auxiliary plane identity, whereas the solutions for the principal stress directions are surprisingly good. The errors in inversion solutions resulting from the fault/auxiliary plane ambiguity can be significantly reduced by controlling subjectively the sample variance of the measurement errors. Our results also suggest that the fault plane cannot be distinguished correctly from the auxiliary plane with a high probability on the basis of the stress inversion alone.     

Crosshole seismic waveform tomography – II. Resolution analysis

In an accompanying paper, we used waveform tomography to obtain a velocity model between two boreholes from a real crosshole seismic experiment. As for all inversions of geophysical data, it is important to make an assessment of the final model, to determine which parts of the model are well-resolved and can confidently be used for geological interpretation. In this paper we use checkerboard tests to provide a quantitative estimate of the performance of the inversion and the reliability of the final velocity model. We use the output from the checkerboard tests to determine resolvability across the velocity model. Such tests can act as good guides for designing appropriate inversion strategies. Here we discovered that, by including both reference-model and smoothing constraints in initial inversions, and then relaxing the smoothing constraint for later inversions, an optimum velocity image was obtained. Additionally, we noticed that the performance of the inversion was dependent on a relationship between velocity perturbation and checkerboard grid-size: larger velocity perturbations were better-resolved when the grid-size was also increased. Our results suggest that model assessment is an essential step prior to interpreting features in waveform tomographic images.     

The 2003 Mw 7.2 Fiordland subduction earthquake, New Zealand: aftershock distribution, main shock fault plane and static stress changes on the overlying Alpine Fault

The 2003 August 21 Fiordland earthquake ( M _L7.0, M _W7.2) was the largest earthquake to occur in New Zealand for 35 yr and the fifth of M6+ associated with shallow subduction in Fiordland in the last 15 yr. The aftershocks are diffuse and do not distinguish between the two possible main shock fault planes implied by the Harvard CMT solution, one corresponding to subduction interface thrusting and the other corresponding to steeply seaward dipping thrusting. The distinction is important for calculating the induced stress changes on the overlying Alpine Fault which has a history of very large earthquakes, the last possibly in 1717. We have relocated the aftershocks, using data from temporary seismographs in the epicentral region and the double difference technique. We then use the correlation between aftershock hypocentres and regions of positive changes in Coulomb Failure Stress (CFS) due to various candidate main shock fault planes to argue for concentrated slip on the shallow landward dipping subduction interface. Average changes in CFS on the offshore segments of the Alpine Fault are then negative, retarding any future large events. In our models the change in CFS is evaluated on faults of optimal orientation in the regional stress field as determined by inversion of P -wave polarities.     

Viscoelastic relaxation and long-lasting after-slip following the 1997 Umbria-Marche (Central Italy) earthquakes

We combine Global Positioning System (GPS) measurements with forward modelling of viscoelastic relaxation and after-slip to study the post-seismic deformation of the 1997 Umbria-Marche (Central Apennines) moderate shallow earthquake sequence. Campaign GPS measurements spanning the time period 1999–2003 are depicting a clear post-seismic deformation signal. Our results favour a normal faulting rupture model where most of the slip is located in the lower part of the seismogenic upper crust, consistent with the rupture models obtained from the inversion of strong motion data. The preferred rheological model, obtained from viscoelastic relaxation modelling, consists of an elastic upper crust, underlain by a transition zone with a viscosity of 10¹⁸ Pa s, while the rheology of deeper layers is not relevant for the observed time-span. Shallow fault creep and after-slip at the base of the seismogenic upper crust are the first order processes behind the observed post-seismic deformation. The deep after-slip, below the fault zone at about 8 km depth, acting as a basal shear through localized time-dependent deformation, identifies a rheological discontinuity decoupling the seismogenic upper crust from the low-viscosity transition zone.     

Tectonic inversion assessed by integration of geological and geophysical data: The intracontinental Rio do Peixe Basin,NE Brazil

Common basin models assume that the post‐rift tectonic evolution of most basins is usually associated with tectonic quiescence. However, tectonic inversion during the post‐rift phase has been proposed for several sedimentary basins worldwide, but how and why it happens is still a matter of debate, especially in intracontinental settings where the lithosphere is old and thick. Here, we use geological and geophysical data from the Rio do Peixe Basin in NE Brazil to show evidence that intracontinental sedimentary basins can be tectonically inverted by far‐field compressive stresses acting on pre‐existing weakness zones of lithospheric‐scale where stresses can concentrate and inversion can occur. Geomorphological and field data combined with seismic reflection, gravimetric and borehole data show that: (a) inversion occurred along two main Precambrian lithospheric‐scale shear zones, the Patos (E‐W trending) and Portalegre (NE‐SW trending), which had already been reactivated as basin‐bounding faults during the earlier rift stage; (b) post‐rift reactivation affected (mostly) the original master normal faults with the largest rift displacements, and locally produced new reverse faults; (c) during contraction, deformation was partitioned between fault reactivation and buckling of the incompetent sediment pushed against the hard basement; (d) all these signs of inversion have been observed in the field and can be demonstrated on seismic reflection profiles; and (e) combined gravimetric and seismic data show that the main structures of the basin were followed by an inversion. These data are consistent with the operation of WSW‐ENE horizontal maximum compressive stress as a result of combined pushes of the Mid‐Atlantic Ridge (towards the W) and the Andes (towards the E), responsible for the post‐rift oblique inversion of normal faults inherited from the rift phase and formed with vertical maximum compressive stress.     

中国地震发生频率与烈度的空间分布

考虑不同区域地震记录具有时间长度不等的特点,对“震中分布分震级网格点密集值”算法进行改进,结合 GIS 的空间分析方法将地震目录中的点数据空间化为能反映地震发生频率的栅格数据;依据地震震级和烈度的关 系以及地震烈度在空间上的椭圆衰减模型,选择逼近和近似的计算手段,并结合空间插值方法得到中国地震烈度 分布的栅格图。从地震频率分布结果上看,大致以宁夏、甘肃、四川和云南为界,中国西部地区3 级以上的地震发生 频率要高于东部地区;从地震烈度分布结果看,中国甘肃、陕西、宁夏、山西、河北、四川、云南等位于地震带内的区 域在发生地震时产生的烈度较高。     

Sequential integrated inversion of refraction and wide-angle reflection traveltimes and gravity data for two-dimensional velocity structures

A new algorithm is presented for the integrated 2-D inversion of seismic traveltime and gravity data. The algorithm adopts the 'maximum likelihood' regularization scheme. We construct a 'probability density function' which includes three kinds of information: information derived from gravity measurements; information derived from the seismic traveltime inversion procedure applied to the model; and information on the physical correlation among the density and the velocity parameters. We assume a linear relation between density and velocity, which can be node-dependent; that is, we can choose different relationships for different parts of the velocity–density grid. In addition, our procedure allows us to consider a covariance matrix related to the error propagation in linking density to velocity. We use seismic data to estimate starting velocity values and the position of boundary nodes. Subsequently, the sequential integrated inversion (SII) optimizes the layer velocities and densities for our models. The procedure is applicable, as an additional step, to any type of seismic tomographic inversion.
We illustrate the method by comparing the velocity models recovered from a standard seismic traveltime inversion with those retrieved using our algorithm. The inversion of synthetic data calculated for a 2-D isotropic, laterally inhomogeneous model shows the stability and accuracy of this procedure, demonstrates the improvements to the recovery of true velocity anomalies, and proves that this technique can efficiently overcome some of the limitations of both gravity and seismic traveltime inversions, when they are used independently.
An interpretation of field data from the 1994 Vesuvius test experiment is also presented. At depths down to 4.5 km, the model retrieved after a SII shows a more detailed structure than the model obtained from an interpretation of seismic traveltime only, and yields additional information for a further study of the area.     

Likelihood analysis of earthquake catalogues

We apply several classes of stochastic multidimensional models to statistical analysis of earthquake catalogues using likelihood methods. We investigate the importance of including different earthquake parameters in the model: epicentral coordinates, hypocentral depth, time limits for interearthquake interaction, and especially spatial distribution of earthquakes as well as spatial aftershock patterns. Results of this study combined with other investigations, suggest that most distributions controlling earthquake interaction have a fractal or scale-invariant form. Developed models are used for statistical analysis of several earthquake catalogues to evaluate parameters of earthquake occurrence. These parameters are shown to be similar for shallow earthquakes of different magnitude ranges and seismogenic regions, confirming self-similarity of the earthquake process. Whereas intermediate earthquakes seem to emulate the pattern of shallow earthquake occurrence, albeit at a much smaller aftershock rate, deep earthquakes differ significantly in their properties. Predictability of standard shallow earthquake catalogues has been analysed; we present evidence that for the best available catalogues the predictability is close to 10 bits per earthquake. Several synthetic earthquake catalogues have been created and processed through the likelihood inversion scheme. The results from likelihood analysis of these catalogues confirm our approach.     

Estimate of the stress field in Kilauea's South Flank, Hawaii

We estimated stress and seismic strain tensors for the Kilauea volcano's south flank. the stress orientation inversion and the seismic strain calculation were performed using fault-plane solutions. the principal stress and seismic strain directions are approximately uniformly distributed in space and time during the interval covered by the data. However, the σ1, σ3 plane is approximately orthogonal to the 1, 3 plane. Therefore, a weak layer may exist beneath the south flank. σ1 has a plunge of 59° and an azimuth of 152°, with a 10° 95 per cent confidence range. We also developed a stress magnitude inversion to estimate magnitudes of boundary and interior stresses. In this inversion, the principal stress directions were taken as constraints in the seismic volume, and surface geodetic observations were used as data. the maximum magmatic pressure in Kilauea's rift zone is about 160 MPa. the direction of σ1 can be interpreted as the superposition of hydrostatic stress ( pgh ) and magmatic pressure. Without the constraint imposed by the direction of σ1, the estimated pressure is only 60MPa, the distribution of magmatic pressure may be similar to that of pgh . In contrast, the upper rift zone may be in tension. the shear stress in the rift zone is about one order of magnitude smaller than the maximum compressive stress, supporting the interpretation of magmatic flow as fluid in dikes or channels. the combination of stress orientation inversion, seismic strain calculation, and stress magnitude inversion performed in this study provides a means by which to estimate the stress state in seismic areas.     

Accurate hypocentre determination in the seismogenic zone of the subducting Nazca Plate in northern Chile using a combined on-/offshore network

The coupled plate interface of subduction zones—commonly called the seismogenic zone—has been recognized as the origin of fatal earthquakes. A subset of the after-shock series of the great Antofagasta thrust-type event (1995 July 30; M _w = 8.0) has been used to study the extent of the seismogenic zone in northern Chile. To achieve reliable and precise hypocentre locations we applied the concept of the minimum 1-D model, which incorporates iterative simultaneous inversion of velocity and hypocentre parameters. The minimum 1-D model is complemented by station corrections which are influenced by near-surface velocity heterogeneity and by the individual station elevations. By relocating mine blasts, which were not included in the inversion, we obtain absolute location errors of 1  km in epicentre and 2  km in focal depth. A study of the resolution parameters ALE and DSPR documents the importance of offshore stations on location accuracy for offshore events. Based on precisely determined hypo-centres we calculate a depth of 46  km for the lower limit of the seismogenic zone, which is in good agreement with previous studies for this area. For the upper limit we found a depth of 20  km. Our results of an aseismic zone between the upper limit of the seismogenic zone and the surface correlates with a detachment zone proposed by other studies; the results are also in agreement with thermal studies for the Antofagasta forearc region.     

Inversion of seismic attributes for velocity and attenuation structure

We have developed an inversion formuialion for velocity and attenuation structure using seismic attributes, including envelope amplitude, instantaneous frequency and arrival times of selected seismic phases. We refer to this approach as AFT inversion for amplitude, (instantaneous) frequency and time. Complex trace analysis is used to extract the different seismic attributes. The instantaneous frequency data are converted to t * using a matching procedure that approximately removes the effects of the source spectra. To invert for structure, ray-perturbation methods are used to compute the sensitivity of the seismic attributes to variations in the model. An iterative inversion procedure is then performed from smooth to less smooth models that progressively incorporates the shorter-wavelength components of the model. To illustrate the method, seismic attributes are extracted from seismic-refraction data of the Ouachita PASSCAL experiment and used to invert for shallow crustal velocity and attenuation structure. Although amplitude data are sensitive to model roughness, the inverted velocity and attenuation models were required by the data to maintain a relatively smooth character. The amplitude and t * data were needed, along with the traveltimes, at each step of the inversion in order to fit all the seismic attributes at the final iteration.     

Source history of the 1905 great Mongolian earthquakes (Tsetserleg, Bolnay)

Two great Mongolian earthquakes, Tsetserleg and Bolnay, occurred on 1905 July 9 and 23. We determined the source history of these events using body waveform inversion. The Tsetserleg rupture (azimuth N60°) correspond to a N60° oriented branch of the long EW oriented Bolnay fault.
Historical seismograms recorded by Wiechert instruments are digitized and corrected for the geometrical deformation due to the recording system. We use predictive filters to recover the signals lost at the minute marks.
The total rupture length for the Tsetserleg earthquake may reach up to 190 km, in order to explain the width of the recorded body waves. This implies adding 60 km to the previously mapped fault. The rupture propagation is mainly eastward. It starts at the southwest of the central subsegment, showing a left lateral strike-slip with a reverse component. The total duration of the modelled source function is 65 s. The seismic moment deduced from the inversion is 10²¹ N m, giving a magnitude   M _w = 8  .
The nucleation of the Bolnay earthquake was at the intersection between the main fault (375 km left lateral strike-slip) and the Teregtiin fault (N160°, 80 km long right lateral strike-slip with a vertical component near the main fault). The rupture was bilateral along the main fault: 100 km to the west and 275 km to east. It also propagated 80 km to the southeast along the Teregtiin fault. The source duration was 115 s. The moment magnitude Mw varies between 8.3 and 8.5.
The nucleation and rupture depths remain uncertain. We tested three cases: (1) nucleation and rupture depth limited to the seismogenic zone; (2) nucleation in the seismogenic zone and rupture propagation going to the base of the crust and (3) nucleation within the crust–upper mantle interface and rupture propagation within the upper mantle.     

A method of obtaining a velocity-depth envelope from wide-angle seismic data

Summary. Due to the non-uniqueness of traveltime inversion of seismic data, it is more appropriate to determine a velocity-depth ( v-z ) envelope, rather than just a v-z function. Several methods of obtaining a v-z envelope by extremal inversion have been proposed, all of which invert the data primarily from either x-p , or T-p , or both domains. These extremal inversion methods may be divided into two groups: linear extremal and non-linear extremal. There is some debate whether the linearized perturbation techniques should be applied to the inherently non-linear problem of traveltime inversion. We have obtained a v-z envelope by extremal inversion in T-p with the constraint that the inversion paths also satisfy x-p observations. Thus we use data jointly in r-p and x-p , and yet avoid the linearity assumptions.
This joint, non-linear extremal inversion method has been applied to obtain a v-z envelope down to a depth of about 30 km in the Baltimore Canyon trough using x-t data from an Expanding Spread Profile acquired during the LASE project. We have found that the area enclosed by the v-z envelope is reduced by about 15 per cent using x-p control on the T-p inversion paths, compared to the inversion without x-p control.     

New seismogenic source and deep structures revealed by the 1999 Chia-yi earthquake sequence in southwestern Taiwan

In a tectonically active setting large earthquakes are always threats; however, they may also be useful in elucidating the subsurface geology. Instrumentally recorded seismicity is, therefore, widely utilized to extend our knowledge into the deeper crust, especially where basement is involved. It is because the earthquakes are triggered by underground stress changes that usually corresponding to the framework of geological structures. Hidden faults, therefore, can be recognized and their extension as well as orientation can be estimated. Both above are of relevance for assessment on seismic hazard of a region, since the active faults are supposed to be re-activated and cause large earthquakes. In this study, we analysed the 1999 October 22 earthquake sequence that occurred in southwestern Taiwan. Two major seismicity clusters were identified with spatial distribution between depths of 10 and 16 km. One cluster is nearly vertical and striking 032°, corresponding to the strike-slip Meishan fault (MSF) that generated the 1906 surface rupture. Another cluster strikes 190° and dips 64° to the west, which is interpreted as west-vergent reverse fault, in contrast to previous expectation of east vergence. Our analysis of the focal solutions of all the larger earthquakes in the 1999 sequence with the 3-D distribution of all the earthquakes over the period 1990–2004 allows us reinterpret the structural framework and suggest previously unreognized seismogenic sources in this area. We accordingly suggest: (1) multiple detachment faults are present in southwestern Taiwan coastal plain and (2) additional seismogenic sources consist of tear faults and backthrust faults in addition to sources associated with west-vergent fold-and-thrust belt.