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1.
A new class of algorithms for solving the inverse problems of gravity prospecting is considered. The best interpretation is selected from the set Q of the admissible versions by the optimality criteria that are borrowed from the solution-making theory and adapted for the geophysical problems. The concept of retrieving the information about the sources of gravity anomalies, which treats the result of the interpretation as a set of locally optimal solutions of the inverse problem but not as a single globally optimal solution is discussed. The locally optimal solutions of the inverse problem are sort of singularity points of set Q. They are preferable to the other admissible solutions by a certain criterion formulated in terms of the geologically important information about the anomalous bodies. The admissible versions of the interpretation of the gravimetry data that meet the criteria of the decision-making theory are the primary candidates for the singularity points. The results of the numerical calculations are presented. The set of the admissible solutions from which the locally optimal versions of interpretation are selected is formed by the modifications of the assembly method developed by V.N. Strakhov. 相似文献
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P. S. Martyshko I. V. Ladovskii A. G. Tsidaev 《Izvestiya Physics of the Solid Earth》2010,46(11):931-942
The technique of solving the inverse structural gravity problem based on the joint interpretation of gravity and seismic data
is described in this paper. The method of solving is based on the method of local corrections, but involves some modifications
described in the paper. An area of the northeastern part of the Urals and West Siberia (60°-65°N, 54°-72°E) was studied with
the use of this technology and the spatial position of the boundaries of the crystalline crust of the Earth (its roof K0 and base M) were determined from seismic and gravity data. 相似文献
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Ilya Prutkin Peter VajdaRobert Tenzer Miroslav Bielik 《Journal of Applied Geophysics》2011,75(3):472-478
We present a novel methodology for 3D gravity/magnetic data inversion. It combines two algorithms for preliminary separation of sources and an original approach to 3D inverse problem solution. The first algorithm is designed to separate sources in depth and to remove the shallow ones. It is based on subsequent upward and downward data continuation. For separation in the lateral sense, we approximate the given observed data by the field of several 3D line segments. For potential field data inversion we apply a new method of local corrections. The method is efficient and does not require trial-and-error forward modeling. It allows retrieving unknown 3D geometry of anomalous objects in terms of restricted bodies of arbitrary shape and contact surfaces. For restricted objects, we apply new integral equations of gravity and magnetic inverse problems. All steps of our methodology are demonstrated on the Kolarovo gravity anomaly in the Danube Basin of Slovakia. 相似文献
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Z. Z. Arsanukaev 《Izvestiya Physics of the Solid Earth》2017,53(1):140-146
The results of the studies within the new approach to solving the inverse problem of gravimetry are considered. This approach consists in direct (analytical) continuation of the anomalous gravitational field specified on the Earth’s surface into the lower half-space with the use of the method of discrete approximations. The solution of the problem of analytical continuation is demonstrated by the model example. In the solution of the problem of analytical continuation, the developed algorithms and computer programs were implemented in two program packages which are used both in the model computations and in practice. 相似文献
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Parameters of the gravity field harmonics outside the geoid are sought in solving the Stokes boundary-value problem while
harmonics outside the Earth in solving the Molodensky boundary-value problem. The gravitational field generated by the atmosphere
is subtracted from the Earth’s gravity field in solving either the Stokes or Molodensky problem. The computation of the atmospheric
effect on the ground gravity anomaly is of a particular interest in this study. In this paper in particular the effect of
atmospheric masses is discussed for the Stokes problem. In this case the effect comprises two components, specifically the
direct and secondary indirect atmospheric effects. The numerical investigation is conducted at the territory of Canada. Numerical
results reveal that the complete effect of atmosphere on the ground gravity anomaly varies between 1.75 and 1.81 mGal. The
error propagation indicates that precise determination of the atmospheric effect on the gravity anomaly depends mainly on
the accuracy of the atmospheric mass density distribution model used for the computation. 相似文献
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高层建筑结构质量动力评定技术研究 总被引：1，自引：0，他引：1
李杰 《地震工程与工程振动》2001,21(4):125-131
结构质量评价对我国住宅产业的发展具有重要意义.本文提出一种基于复合反演算以别高层建筑刚度和阻尼的型动力评定技术.给出了两种解决混合反演问题的时域方法,并通过实例诠释了该方法在局部振动和环境激励下应用的可行性,将此技术结合传统的材料强度测试及静态无损捡测技术,可建立一种包含动力检测方法的新型工程质量评定体系. 相似文献
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Miroslav Kocifaj 《Studia Geophysica et Geodaetica》1994,38(4):416-422
Summary A methodical approach is presented of solving the inverse problem of atmospheric optics for the vertical profile of ozone
concentration. Observations of spectral sky radiance and direct solar radiation are taken as input data. A gradient method
is suggested for solving the inverse problem.
on leave from the Astronomical Institute, Slovak Academy of Sciences 相似文献
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Penenko Vladimir Baklanov Alexander Tsvetova Elena Mahura Alexander 《Pure and Applied Geophysics》2012,169(3):447-465
A concept of environmental forecasting based on a variational approach is discussed. The basic idea is to augment the existing
technology of modeling by a combination of direct and inverse methods. By this means, the scope of environmental studies can
be substantially enlarged. In the concept, mathematical models of processes and observation data subject to some uncertainties
are considered. The modeling system is derived from a specially formulated weak-constraint variational principle. A set of
algorithms for implementing the concept is presented. These are: algorithms for the solution of direct, adjoint, and inverse
problems; adjoint sensitivity algorithms; data assimilation procedures; etc. Methods of quantitative estimations of uncertainty
are of particular interest since uncertainty functions play a fundamental role for data assimilation, assessment of model
quality, and inverse problem solving. A scenario approach is an essential part of the concept. Some methods of orthogonal
decomposition of multi-dimensional phase spaces are used to reconstruct the hydrodynamic background fields from available
data and to include climatic data into long-term prognostic scenarios. Subspaces with informative bases are constructed to
use in deterministic or stochastic-deterministic scenarios for forecasting air quality and risk assessment. The results of
implementing example scenarios for the Siberian regions are presented. 相似文献
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Mohammad Bagherbandi Robert Tenzer Lars E. Sjöberg 《Studia Geophysica et Geodaetica》2014,58(2):227-248
We formulate an error propagation model based on solving the Vening Meinesz-Moritz (VMM) inverse problem of isostasy. The system of observation equations in the VMM model defines the relation between the isostatic gravity data and the Moho depth by means of a second-order Fredholm integral equation of the first kind. The corresponding error model (derived in a spectral domain) functionally relates the Moho depth errors with the commission errors of used gravity and topographic/bathymetric models. The error model also incorporates the non-isostatic bias which describes the disagreement, mainly of systematic nature, between the isostatic and seismic models. The error analysis is conducted at the study area of the Tibetan Plateau and Himalayas with the world largest crustal thickness. The Moho depth uncertainties due to errors of the currently available global gravity and topographic models are estimated to be typically up to 1–2 km, provided that the GOCE gravity gradient observables improved the medium-wavelength gravity spectra. The errors due to disregarding sedimentary basins can locally exceed ～2 km. The largest errors (which cause a systematic bias between isostatic and seismic models) are attributed to unmodeled mantle heterogeneities (including the core-mantle boundary) and other geophysical processes. These errors are mostly less than 2 km under significant orogens (Himalayas, Ural), but can reach up to ～10 km under the oceanic crust. 相似文献
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The forward gravity problem is solved with the use of the subdivision of each body of a deposit into a set of adjoining vertical bars, and in the inverse problem each body of a deposit is modeled by a uniform spheroid. Well-known formulas for the gravitational potential and the gravity field components of oblate and prolate spheroids are reduced to a convenient form. Parameters of a spheroid are determined via the minimization of the Tikhonov smoothing functional with the use of constraints on the parameters. This makes the ill-posed inverse problem single-valued and stable. The Bulakh algorithm for estimating the depth and mass of a deposit is elaborated. This method is illustrated by a numerical example of a deposit consisting of two bodies. 相似文献
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In global studies investigating the Earth’s lithospheric structure, the spectral expressions for the gravimetric forward and inverse modeling of the global gravitational and crustal structure models are preferably used, because of their numerical efficiency. In regional studies, the applied numerical schemes typically utilize the expressions in spatial form. Since the gravity-gradient observations have a more localized support than the gravity measurements, the gravity-gradient data (such as products from the Gravity field and steady-state Ocean Circulation Explorer - GOCE - gravity-gradiometry satellite mission) could preferably be used in regional studies, because of reducing significantly the spatial data-coverage required for a regional inversion or interpretation. In this study, we investigate this aspect in context of a regional Moho recovery. In particular, we compare the numerical performance of solving the Vening Meinesz-Moritz’s (VMM) inverse problem of isostasy in spectral and spatial domains from the gravity and (vertical) gravity-gradient data. We demonstrate that the VMM spectral solutions from the gravity and gravity-gradient data are (almost) the same, while the VMM spatial solutions differ from the corresponding spectral solutions, especially when using the gravity-gradient data. The validation of the VMM solutions, however, reveals that the VMM spatial solution from the gravity-gradient data has a slightly better agreement with seismic models. A more detailed numerical analysis shows that the VMM spatial solution formulated for the gravity gradient is very sensitive to horizontal spatial variations of the vertical gravity gradient, especially in vicinity of the computation point. Consequently, this solution provides better results in regions with a relatively well-known crustal structure, while suppressing errors caused by crustal model uncertainties from distant zones. Based on these findings we argue that the gravity-gradient data are more suitable than the gravity data for a regional Moho recovery. 相似文献
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An algorithm to calculate the gravity anomaly of sedimentary basins with exponential density-depth relationships 总被引：2，自引：0，他引：2
We derive wavenumber domain expressions to calculate the gravity anomaly of a body with irregular bounding surfaces and an exponential density‐depth relationship. We apply the method to sedimentary basins, which commonly have this type of geometry and density distribution. The mathematical formulation also allows the exponential density‐depth relationship to be measured from an arbitrary irregular surface rather than the top surface. Using this arrangement, the gravity anomaly of exhumed sedimentary basins can be predicted if the amount of eroded section can be estimated. The corresponding inverse algorithms are also derived. Examples of the use of the forward algorithms, from the Galicia Interior Basin and the Central Irish Sea Basin, are used to illustrate these methods. 相似文献
15.
Summary
A solution of the direct gravity problem for a finite body with variable density is given. The method is based on Green's formula and is applicable when a particular solution of Poisson's equation is known. The attraction due to the body is expressed by integrals over its surface
The exact solution of the direct gravity problem, as known from the theory of two-dimensional fields [1–3], is closely connected with the problem of the analytic continuation of the exterior field of the attracting mass system into its interior. In the first place, this is a problem of determining the singularities of the exterior field, their distribution within the system and their nature. This approach to the solution of the direct problem is also meaningful from the point of view of determining the characteristics of the attracting system and, therefore, also of solving the inverse problem. In the case of two-dimensional fields the methods of analytical continuation were widely developed in a series of well-known papers by V. N. Strakhov, and they are mainly based on the methods of the theory of the functions of the complex variable. These methods were also successfully applied by Tsirulskii and Golizdra [1, 2] in treating the homogeneous and inhomogeneous, two-dimensional direct problem by means of Cauchy's integrals. However, as regards three-dimensional fields a number of fundamental problems has not been solved in this respect.Dedicated to 90th Birthday of Professor Frantiek Fiala 相似文献
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Robert Tenzer Pavel Novák Ilya Prutkin Artu Ellmann Peter Vajda 《Studia Geophysica et Geodaetica》2009,53(2):157-167
To reduce the numerical complexity of inverse solutions to large systems of discretised integral equations in gravimetric
geoid/quasigeoid modelling, the surface domain of Green’s integrals is subdivided into the near-zone and far-zone integration
sub-domains. The inversion is performed for the near zone using regional detailed gravity data. The farzone contributions
to the gravity field quantities are estimated from an available global geopotential model using techniques for a spherical
harmonic analysis of the gravity field. For computing the far-zone contributions by means of Green’s integrals, truncation
coefficients are applied. Different forms of truncation coefficients have been derived depending on a type of integrals in
solving various geodetic boundary-value problems. In this study, we utilise Molodensky’s truncation coefficients to Green’s
integrals for computing the far-zone contributions to the disturbing potential, the gravity disturbance, and the gravity anomaly.
We also demonstrate that Molodensky’s truncation coefficients can be uniformly applied to all types of Green’s integrals used
in solving the boundaryvalue problems. The numerical example of the far-zone contributions to the gravity field quantities
is given over the area of study which comprises the Canadian Rocky Mountains. The coefficients of a global geopotential model
and a detailed digital terrain model are used as input data. 相似文献
17.
Non‐linear stochastic inversion of gravity data via quantum‐behaved particle swarm optimisation: application to Eurasia–Arabia collision zone (Zagros,Iran) 
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下载免费PDF全文 Potential field data such as geoid and gravity anomalies are globally available and offer valuable information about the Earth's lithosphere especially in areas where seismic data coverage is sparse. For instance, non‐linear inversion of Bouguer anomalies could be used to estimate the crustal structures including variations of the crustal density and of the depth of the crust–mantle boundary, that is, Moho. However, due to non‐linearity of this inverse problem, classical inversion methods would fail whenever there is no reliable initial model. Swarm intelligence algorithms, such as particle swarm optimisation, are a promising alternative to classical inversion methods because the quality of their solutions does not depend on the initial model; they do not use the derivatives of the objective function, hence allowing the use of L1 norm; and finally, they are global search methods, meaning, the problem could be non‐convex. In this paper, quantum‐behaved particle swarm, a probabilistic swarm intelligence‐like algorithm, is used to solve the non‐linear gravity inverse problem. The method is first successfully tested on a realistic synthetic crustal model with a linear vertical density gradient and lateral density and depth variations at the base of crust in the presence of white Gaussian noise. Then, it is applied to the EIGEN 6c4, a combined global gravity model, to estimate the depth to the base of the crust and the mean density contrast between the crust and the upper‐mantle lithosphere in the Eurasia–Arabia continental collision zone along a 400 km profile crossing the Zagros Mountains (Iran). The results agree well with previously published works including both seismic and potential field studies. 相似文献
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The inversion gravity problem formulated as follows is solved. The excess density in each layer of a fixed horizontal stratified model is a function of horizontal coordinates (σ(ξ, η)) approximated by a specially constructed function. The problem is to reconstruct the function σ = σ(ξ, η) from the external gravity field. If the geological model includes more than one layer, the problem is solved with the use of a set of reference points at which the sought function is given. Variations in a gravity anomaly with respect to the field at a fixed point are used in solving this problem. 相似文献
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N. I. Berezina V. I. Dmitriev N. A. Merschikova 《Izvestiya Physics of the Solid Earth》2013,49(3):350-355
We consider the iterative numerical method for solving two-dimensional (2D) inverse problems of magnetotelluric sounding, which significantly reduces the computational burden of the inverse problem solution in the class of quasi-layered models. The idea of the method is to replace the operator of the direct 2D problem of calculating the low-frequency electromagnetic field in a quasi-layered medium by a quasi-one dimensional operator at each observation point. The method is applicable for solving the inverse problems of magnetotellurics with either the E- and H-polarized fields and in the case when the inverse problem is simultaneously solved using the impedance values for the fields with both polarizations. We describe the numerical method and present the examples of its application to the numerical solution of a number of model inverse problems of magnetotelluric sounding. 相似文献