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Inversion Methods (inversion + methods)

Distribution by Scientific Domains

Earth and Environmental Science	66%

Selected Abstracts

A Comparison of Tabular PDF Inversion Methods

COMPUTER GRAPHICS FORUM, Issue 1 2009
D. Cline
I.3.0 [Computer Graphics]: General Abstract The most common form of tabular inversion used in computer graphics is to compute the cumulative distribution table of a probability distribution (PDF) and then search within it to transform points, using an,O(log n),binary search. Besides the standard inversion method, however, several other discrete inversion algorithms exist that can perform the same transformation inO(1) time per point. In this paper, we examine the performance of three of these alternate methods, two of which are new. [source]

Mathematical Modeling of Bivariate Polymer Property Distributions Using 2D Probability Generating Functions, 1 , Numerical Inversion Methods

MACROMOLECULAR THEORY AND SIMULATIONS, Issue 6 2010
Mariano Asteasuain
Abstract This is the first of two papers presenting a new mathematical method for modeling bivariate distributions of polymer properties. It is based on the transformation of the infinite mass balances describing the evolution of a two-dimensional distribution using 2D probability generating functions (pgf). A key step of this method is the inversion of the transforms. In this work, two numerical inversion methods of 2D pgfs are developed and carefully validated. The accuracy obtained with both methods was very satisfactory. The inversion formulas of both methods are simple and easy to implement. A simple copolymerization example is used to show the complete procedure from the derivation of the pgf balances to the recovery of the bivariate molecular weight distribution. [source]

Full waveform inversion of seismic waves reflected in a stratified porous medium

GEOPHYSICAL JOURNAL INTERNATIONAL, Issue 3 2010
Louis De Barros
SUMMARY In reservoir geophysics applications, seismic imaging techniques are expected to provide as much information as possible on fluid-filled reservoir rocks. Since seismograms are, to some degree, sensitive to the mechanical parameters and fluid properties of porous media, inversion methods can be devised to directly estimate these quantities from the waveforms obtained in seismic reflection experiments. An inversion algorithm that uses a generalized least-squares, quasi-Newton approach is described to determine the porosity, permeability, interstitial fluid properties and mechanical parameters of porous media. The proposed algorithm proceeds by iteratively minimizing a misfit function between observed data and synthetic wavefields computed with the Biot theory. Simple models consisting of plane-layered, fluid-saturated and poro-elastic media are considered to demonstrate the concept and evaluate the performance of such a full waveform inversion scheme. Numerical experiments show that, when applied to synthetic data, the inversion procedure can accurately reconstruct the vertical distribution of a single model parameter, if all other parameters are perfectly known. However, the coupling between some of the model parameters does not permit the reconstruction of several model parameters at the same time. To get around this problem, we consider composite parameters defined from the original model properties and from a priori information, such as the fluid saturation rate or the lithology, to reduce the number of unknowns. Another possibility is to apply this inversion algorithm to time-lapse surveys carried out for fluid substitution problems, such as CO2 injection, since in this case only a few parameters may vary as a function of time. We define a two-step differential inversion approach which allows us to reconstruct the fluid saturation rate in reservoir layers, even though the medium properties are poorly known. [source]

Delineating the rupture planes of an earthquake doublet using Source-Scanning Algorithm: application to the 2005 March 3 Ilan Doublet, northeast Taiwan

GEOPHYSICAL JOURNAL INTERNATIONAL, Issue 2 2010
Chih-Wen Kan
SUMMARY Correct identification of the fault plane(s) associated with an earthquake doublet is a very challenging problem because the pair of events often occurs in close space and time with almost the same magnitude. Most long-period waveforms of an earthquake doublet are severely tangled and thus unsuitable for conventional waveform inversion methods. In this study, we try to resolve this issue by utilizing the recently developed Source-Scanning Algorithm (SSA). The SSA systematically searches the model space for seismic sources whose times and locations are most compatible with the observed arrivals of large amplitudes on seismograms. The identification of a seismic source is based on the brightness function, which is defined as the summation of the normalized waveform amplitudes at the predicted arrival times at all stations. By illuminating the spatiotemporal distribution of asperities during an earthquake's source process, we are able to constrain the orientation of the rupture propagation that, in turn, leads to the identification of the fault plane. A series of synthetic experiments are performed to test SSA's resolution under various scenarios including different directions of rupture propagation, imperfect station coverage and short origin time difference between the two events of a doublet. Because only short-period records are needed in the analysis, the proposed method is best suited for an earthquake doublet with a short time gap between the two events. Using the 2005 Ilan doublet (the origin time difference is only 70 s) that occurred in northeast Taiwan as an example, we show that the trace of the brightest spots moves towards the west and infer the E,W-striking plane to be the actual fault plane. [source]

Analytical and 3-D numerical modelling of Mt. Etna (Italy) volcano inflation

GEOPHYSICAL JOURNAL INTERNATIONAL, Issue 2 2005
A. Bonaccorso
SUMMARY Since 1993, geodetic data obtained by different techniques (GPS, EDM, SAR, levelling) have detected a consistent inflation of the Mt. Etna volcano. The inflation, culminating with the 1998,2001 strong explosive activity from summit craters and recent 2001 and 2002 flank eruptions, is interpreted in terms of magma ascent and refilling of the volcanic plumbing system and reservoirs. We have modelled the 1993,1997 EDM and GPS data by 3-D pressurized sources to infer the position and dimension of the magma reservoir. We have performed analytical inversions of the observed deformation using both spheroidal and ellipsoidal sources embedded in a homogeneous elastic half-space and by applying different inversion methods. Solutions for these types of sources show evidence of a vertically elongated magma reservoir located 6 km beneath the summit craters. The maximum elevation of topography is comparable to such depth and strong heterogeneities are inferred from seismic tomography; in order to assess their importance, further 3-D numerical models, employing source parameters extracted from analytical models, have been developed using the finite-element technique. The deformation predicted by all the models considered shows a general agreement with the 1993,1997 data, suggesting the primary role of a pressure source, while the complexities of the medium play a minor role under elastic conditions. However, major discrepancies between data and models are located in the SE sector, suggesting that sliding along potential detachment surfaces may contribute to amplify deformation during the inflation. For the first time realistic features of Mt. Etna are studied by a 3-D numerical model characterized by the topography and lateral variations of elastic structure, providing a framework for a deeper insight into the relationships between internal sources and tectonic structures. [source]

Addressing non-uniqueness in linearized multichannel surface wave inversion

GEOPHYSICAL PROSPECTING, Issue 1 2009
Michele Cercato
ABSTRACT The multichannel analysis of the surface waves method is based on the inversion of observed Rayleigh-wave phase-velocity dispersion curves to estimate the shear-wave velocity profile of the site under investigation. This inverse problem is nonlinear and it is often solved using ,local' or linearized inversion strategies. Among linearized inversion algorithms, least-squares methods are widely used in research and prevailing in commercial software; the main drawback of this class of methods is their limited capability to explore the model parameter space. The possibility for the estimated solution to be trapped in local minima of the objective function strongly depends on the degree of nonuniqueness of the problem, which can be reduced by an adequate model parameterization and/or imposing constraints on the solution. In this article, a linearized algorithm based on inequality constraints is introduced for the inversion of observed dispersion curves; this provides a flexible way to insert a priori information as well as physical constraints into the inversion process. As linearized inversion methods are strongly dependent on the choice of the initial model and on the accuracy of partial derivative calculations, these factors are carefully reviewed. Attention is also focused on the appraisal of the inverted solution, using resolution analysis and uncertainty estimation together with a posteriori effective-velocity modelling. Efficiency and stability of the proposed approach are demonstrated using both synthetic and real data; in the latter case, cross-hole S-wave velocity measurements are blind-compared with the results of the inversion process. [source]

Velocity analysis based on data correlation

GEOPHYSICAL PROSPECTING, Issue 6 2008
T. Van Leeuwen
ABSTRACT Several methods exist to automatically obtain a velocity model from seismic data via optimization. Migration velocity analysis relies on an imaging condition and seeks the velocity model that optimally focuses the migrated image. This approach has been proven to be very successful. However, most migration methods use simplified physics to make them computationally feasible and herein lies the restriction of migration velocity analysis. Waveform inversion methods use the full wave equation to model the observed data and more complicated physics can be incorporated. Unfortunately, due to the band-limited nature of the data, the resulting inverse problem is highly nonlinear. Simply fitting the data in a least-squares sense by using a gradient-based optimization method is sometimes problematic. In this paper, we propose a novel method that measures the amount of focusing in the data domain rather than the image domain. As a first test of the method, we include some examples for 1D velocity models and the convolutional model. [source]

Mathematical Modeling of Bivariate Polymer Property Distributions Using 2D Probability Generating Functions, 1 , Numerical Inversion Methods

Application of the self-potential method to archaeological prospection: some case histories

ARCHAEOLOGICAL PROSPECTION, Issue 2 2004
M. G. DrahorArticle first published online: 12 MAY 200
Abstract The self-potential (SP) method is very rarely used in archaeological prospection because related phenomena are not very well known. The aim of this study is to discuss the different SP phenomena that might be observed at archaeological sites, and therefore the SP method was applied at different archaeological sites in Anatolia (Turkey), such as Acemhöyük, Amorium, Burgaz and Ulucakhöyük archaeological areas and the Sinop amphorae workshop site. These studies indicated that SP anomalies existed over both burned or unburned materials at archaeological sites, such as walls, pits, kilns, etc. Furthermore, SP anomalies were also found over areas of complex soil distribution and visible physical changes on the surface. Other kinds of SP anomalies were also observed in those archaeological structures located very close to the coastline. These results were confirmed by archaeological excavations, which were carried out after geophysical surveys in the areas studied. All the studies supported that electrokinetic and electrochemical potentials might be the main cause of SP anomalies in the buried archaeological structures. The SP data collected with the gradient and total measurement techniques were processed by forward and inversion methods, and the main SP parameters (h, Q and x0) were determined. In addition, the SP results were compared with other applied geophysical methods such as resistivity and magnetic. Copyright © 2004 John Wiley & Sons, Ltd. [source]