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Earth Models (earth + models)
Selected AbstractsA one-way wave equation for modelling seismic waveform variations due to elastic heterogeneityGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 3 2005D. A. Angus SUMMARY The application of a new one-way narrow-angle elastic wave equation to isotropic heterogeneous media is described. This narrow-angle finite-difference propagator should provide an efficient and accurate method of simulating primary body wave(s) passing through smoothly varying heterogeneous media. Although computationally slower than ray theory, the narrow-angle propagator can model frequency-dependent forward diffraction and scattering as well as the averaging effects due to smooth variations in medium parameters that vary on the sub-Fresnel zone level. Example waveforms are presented for the propagation of body waves in deterministic as well as stochastic heterogeneous 3-D Earth models. Extrapolation within deterministic media will highlight various familiar wave-diffraction and pulse-distortion effects associated with large-scale inhomogeneities, such as geometrical spreading, wavefront folding and creeping-wave diffraction by a compact object. Simulation within stochastic media will examine the effects of varying the correlation lengths of random heterogeneities on wave propagation. In particular, wave phenomena such as frequency-dependent forward scattering, the appearance of random caustics and the generation of seismic coda will be shown. [source] First evidence of post-seismic deformation in the central Mediterranean: Crustal viscoelastic relaxation in the area of the 1980 Irpinia earthquake (Southern Italy)GEOPHYSICAL JOURNAL INTERNATIONAL, Issue 3 2003G. Dalla Via SUMMARY Comparison between measured vertical displacements obtained from two levelling campaigns performed in 1981 and 1985 in the epicentral area of the 1980 Irpinia earthquake (MS= 6.9) and predictions from viscoelastic Earth models reveal the occurrence of post-seismic deformation due to stress relaxation in the ductile part of the crust. Two regions of broad uplift and subsidence, accumulated during the time interval, characterize the deformation pattern in the footwall and hangingwall of the major fault. The spatial wavelength of the deformation pattern favours relaxation occurring in the lower crust rather than in a weak upper-mantle: the uplift in the footwall explains the 30 mm of upwarping of the crust measured along the levelling line crossing the area where the fault pierces the Earth's surface. [source] Spectral-element simulations of global seismic wave propagation,II.GEOPHYSICAL JOURNAL INTERNATIONAL, Issue 1 2002Three-dimensional models, oceans, rotation, self-gravitation Summary We simulate global seismic wave propagation based upon a spectral-element method. We include the full complexity of 3-D Earth models, i.e. lateral variations in compressional-wave velocity, shear-wave velocity and density, a 3-D crustal model, ellipticity, as well as topography and bathymetry. We also include the effects of the oceans, rotation and self-gravitation in the context of the Cowling approximation. For the oceans we introduce a formulation based upon an equivalent load in which the oceans do not need to be meshed explicitly. Some of these effects, which are often considered negligible in global seismology, can in fact play a significant role for certain source,receiver configurations. Anisotropy and attenuation, which were introduced and validated in a previous paper, are also incorporated in this study. The complex phenomena that are taken into account are introduced in such a way that we preserve the main advantages of the spectral-element method, which are an exactly diagonal mass matrix and very high computational efficiency on parallel computers. For self-gravitation and the oceans we benchmark spectral-element synthetic seismograms against normal-mode synthetics for the spherically symmetric reference model PREM. The two methods are in excellent agreement for all body- and surface-wave arrivals with periods greater than about 20 s in the case of self-gravitation and 25 s in the case of the oceans. At long periods the effect of gravity on multiorbit surface waves up to R4 is correctly reproduced. We subsequently present results of simulations for two real earthquakes in fully 3-D Earth models for which the fit to the data is significantly improved compared with classical normal-mode calculations based upon PREM. For example, we show that for trans-Pacific paths the Rayleigh wave can arrive more than a minute earlier than in PREM, and that the Love wave is much shorter in duration. [source] Migration velocity analysis and waveform inversionGEOPHYSICAL PROSPECTING, Issue 6 2008William W. Symes ABSTRACT Least-squares inversion of seismic reflection waveform data can reconstruct remarkably detailed models of subsurface structure and take into account essentially any physics of seismic wave propagation that can be modelled. However, the waveform inversion objective has many spurious local minima, hence convergence of descent methods (mandatory because of problem size) to useful Earth models requires accurate initial estimates of long-scale velocity structure. Migration velocity analysis, on the other hand, is capable of correcting substantially erroneous initial estimates of velocity at long scales. Migration velocity analysis is based on prestack depth migration, which is in turn based on linearized acoustic modelling (Born or single-scattering approximation). Two major variants of prestack depth migration, using binning of surface data and Claerbout's survey-sinking concept respectively, are in widespread use. Each type of prestack migration produces an image volume depending on redundant parameters and supplies a condition on the image volume, which expresses consistency between data and velocity model and is hence a basis for velocity analysis. The survey-sinking (depth-oriented) approach to prestack migration is less subject to kinematic artefacts than is the binning-based (surface-oriented) approach. Because kinematic artefacts strongly violate the consistency or semblance conditions, this observation suggests that velocity analysis based on depth-oriented prestack migration may be more appropriate in kinematically complex areas. Appropriate choice of objective (differential semblance) turns either form of migration velocity analysis into an optimization problem, for which Newton-like methods exhibit little tendency to stagnate at nonglobal minima. The extended modelling concept links migration velocity analysis to the apparently unrelated waveform inversion approach to estimation of Earth structure: from this point of view, migration velocity analysis is a solution method for the linearized waveform inversion problem. Extended modelling also provides a basis for a nonlinear generalization of migration velocity analysis. Preliminary numerical evidence suggests a new approach to nonlinear waveform inversion, which may combine the global convergence of velocity analysis with the physical fidelity of model-based data fitting. [source] A 2-D spectral-element method for computing spherical-earth seismograms,II.GEOPHYSICAL JOURNAL INTERNATIONAL, Issue 3 2008Waves in solid, fluid media SUMMARY We portray a dedicated spectral-element method to solve the elastodynamic wave equation upon spherically symmetric earth models at the expense of a 2-D domain. Using this method, 3-D wavefields of arbitrary resolution may be computed to obtain Fréchet sensitivity kernels, especially for diffracted arrivals. The meshing process is presented for varying frequencies in terms of its efficiency as measured by the total number of elements, their spacing variations and stability criteria. We assess the mesh quantitatively by defining these numerical parameters in a general non-dimensionalized form such that comparisons to other grid-based methods are straightforward. Efficient-mesh generation for the PREM example and a minimum-messaging domain decomposition and parallelization strategy lay foundations for waveforms up to frequencies of 1 Hz on moderate PC clusters. The discretization of fluid, solid and respective boundary regions is similar to previous spectral-element implementations, save for a fluid potential formulation that incorporates the density, thereby yielding identical boundary terms on fluid and solid sides. We compare the second-order Newmark time extrapolation scheme with a newly implemented fourth-order symplectic scheme and argue in favour of the latter in cases of propagation over many wavelengths due to drastic accuracy improvements. Various validation examples such as full moment-tensor seismograms, wavefield snapshots, and energy conservation illustrate the favourable behaviour and potential of the method. [source] Time-domain approach to linearized rotational response of a three-dimensional viscoelastic earth model induced by glacial-isostatic adjustment: I. Inertia-tensor perturbationsGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 2 2005k Martinec SUMMARY For a spherically symmetric viscoelastic earth model, the movement of the rotation vector due to surface and internal mass redistribution during the Pleistocene glaciation cycle has conventionally been computed in the Laplace-transform domain. The method involves multiplication of the Laplace transforms of the second-degree surface-load and tidal-load Love numbers with the time evolution of the surface load followed by inverse Laplace transformation into the time domain. The recently developed spectral finite-element method solves the field equations governing glacial-isostatic adjustment (GIA) directly in the time domain and, thus, eliminates the need of applying the Laplace-domain method. The new method offers the possibility to model the GIA-induced rotational response of the Earth by time integration of the linearized Liouville equation. The theory presented here derives the temporal perturbation of the inertia tensor, required to be specified in the Liouville equation, from time variations of the second-degree gravitational-potential coefficients by the MacCullagh's formulae. This extends the conventional approach based on the second-degree load Love numbers to general 3-D viscoelastic earth models. The verification of the theory of the GIA-induced rotational response of the Earth is performed by using two alternative approaches of computing the perturbation of the inertia tensor: a direct numerical integration and the Laplace-domain method. The time-domain solution of both the GIA and the induced rotational response of the Earth is readily combined with a time-domain solution of the sea level equation with a time-varying shoreline geometry. In a follow-up paper, we derive the theory for the case when GIA-induced perturbations in the centrifugal force affect not only the distribution of sea water, but also deformations and gravitational-potential perturbations of the Earth. [source] Artificial neural networks for parameter estimation in geophysicsGEOPHYSICAL PROSPECTING, Issue 1 2000Carlos Calderón-Macías Artificial neural systems have been used in a variety of problems in the fields of science and engineering. Here we describe a study of the applicability of neural networks to solving some geophysical inverse problems. In particular, we study the problem of obtaining formation resistivities and layer thicknesses from vertical electrical sounding (VES) data and that of obtaining 1D velocity models from seismic waveform data. We use a two-layer feedforward neural network (FNN) that is trained to predict earth models from measured data. Part of the interest in using FNNs for geophysical inversion is that they are adaptive systems that perform a non-linear mapping between two sets of data from a given domain. In both of our applications, we train FNNs using synthetic data as input to the networks and a layer parametrization of the models as the network output. The earth models used for network training are drawn from an ensemble of random models within some prespecified parameter limits. For network training we use the back-propagation algorithm and a hybrid back-propagation,simulated-annealing method for the VES and seismic inverse problems, respectively. Other fundamental issues for obtaining accurate model parameter estimates using trained FNNs are the size of the training data, the network configuration, the description of the data and the model parametrization. Our simulations indicate that FNNs, if adequately trained, produce reasonably accurate earth models when observed data are input to the FNNs. [source] | ||||||||||