共查询到20条相似文献，搜索用时 843 毫秒
1.
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
2.
P. S. Martyshko E. N. Akimova V. E. Misilov 《Izvestiya Physics of the Solid Earth》2016,52(5):704-708
New methods for solving the three-dimensional inverse gravity problem in the class of contact surfaces are described. Based on the approach previously suggested by the authors, new algorithms are developed. Application of these algorithms significantly reduces the number of the iterations and computing time compared to the previous ones. The algorithms have been numerically implemented on the multicore processor. The example of solving the structural inverse gravity problem for a model of four-layer medium (with the use of gravity field measurements) is constructed. 相似文献
3.
I. E. Stepanova I. A. Kerimov D. N. Raevskiy A. V. Shchepetilov 《Izvestiya Physics of the Solid Earth》2018,54(1):91-105
The interrelation between different modifications of the method of linear integral representation is studied. Combined approximations of the topography and geopotential fields enable more refined tuning of the method in solving inverse problems of geophysics and geomorphology and provide a more complete allowance for the a priori information about the surface elevation data and elements of anomalous fields. A technique for finding the numerical solution for the inverse problem for determining the mass distributions equivalent in terms of the external field is presented. The results of the mathematical experiment are discussed. 相似文献
4.
A novel algorithm called Isometric Method (IM) for solving smooth real-valued non-linear inverse problems has been developed.
Model and data spaces are represented by using m + 1 corresponding vectors at a time (m is the dimension of model space).
Relations among vectors in the data space are set up and then transferred into the model space thus generating a new model.
If the problem is truly linear, this new model is the exact solution of the inverse problem. If the problem is non-linear,
the whole procedure has to be repeated iteratively. The basic underlying idea of IM is to postulate the distance in the model
space in such a way that the model and data spaces are isometric, i.e. distances in both spaces have the same measure. As
all model-data vector pairs are used many times in successive iterations, the number of the forward problem computations is
minimized. There is no necessity to deal with derivatives. The requirement for the computer memory is low. IM is suitable
especially for solving smooth medium non-linear problems when forward modelling is time-consuming and minimizing the number
of function evaluations is topical. Applications of IM on synthetic and real geophysical problems are also presented.
malek@irsm.cas.cz 相似文献
5.
T.V. Hromadka 《Advances in water resources》1984,7(3):141-143
A simple numerical model for estimating a phreatic surface in an earthen dam is presented. The numerical approach is based upon the Complex Variable Boundary Element Method (CVBEM). By expanding the CVBEM approximation geometric functions into a first order Taylor series, the unknown phreatic surface location geometrics can be approximated without iteration by solving a single matrix system. The developed technique provides for the numerical solution of the inverse problem of locating the phreatic surface coordinates. A comparison of results produced from this simple approach to results produced from a finite element analog and an iterative CVBEM analog for an example problem is presented. 相似文献
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I. E. Stepanova I. A. Kerimov D. N. Raevskiy A. V. Shchepetilov 《Izvestiya Physics of the Solid Earth》2018,54(6):933-948
The interrelation between different variants of the method of linear integral representations in the spaces of an arbitrary dimension is considered. The combined approximations of the topography and geopotential fields allows the selection of the optimal parameters of the method in solving a wide range of inverse problems in geophysics and geomorphology, as well as a most thorough use of the a priori information about the elevations and elements of anomalous fields. A method for numerically solving an inverse problem on finding the equivalent, in terms of the external field, mass distributions in the ordinary three-dimensional (3D) space and in the four-dimensional (4D) space is described. 相似文献
9.
P. HUBRAL 《Geophysical Prospecting》1978,26(3):627-630
A horizontally layered non-absorptive system of homogeneous layers may be specified by giving the reflection coefficients at each interface. Provided the layers have equal vertical travel time and a perfect reflector as a free surface, the reflection coefficients are generally reconstructed from the reflected pulses by way of solving simultaneous equations of the Toeplitz matrix form with the Levinson recursion method. There exists an alternative approach to solving this problem which by simple reasoning immediately turns out the (Levinson) recursion scheme. The method is based on formulas that relate to solving the forward problem. It resembles Kunetz's (1962) original inverse solution in as much as the computation of the reflection coefficients is based on the idea of separating the contribution of a primary from the sum of all multiples. 相似文献
10.
Spatial distribution of principal stresses in a layered elastic medium is considered in the paper. Transformations of the principal stresses across an interface between the layers are analyzed. A method for reconstructing the spatial stress distributions in layered medium from several spot measurements is proposed. The introduced approach is capable of obtaining the stable solution of the stress reconstruction problem with respect to the noise in input data. A typical layered medium is considered for which the stresses are reconstructed from few independent spot measurements of the stress state. The proposed approach may be used for solving an inverse problem of tectonic stresses reconstruction from the borehole logging data. 相似文献
11.
The work develops the approximation approach to solving the inverse MTS problem with the use of neural networks. The inverse
problem is considered in model classes of parametrized geoelectric structures, whose electric conductivity is controlled by
a few hundreds of macroparameters (N ∼ 300). An approximate inverse operator of the problem is constructed for each model class as a neural network, whose coefficients
are determined in the process of training on a representative sample of standard examples of forward problem solutions. The
problem of determination of the model class of geolectric structures corresponding to the presented input MT data is solved
with the use of the neural network classifier constructed for the available set of model classes of structures. Regularizing
factors and errors of the neural network method are analyzed. The operation of the algorithm is illustrated by examples of
the 2-D inversion of synthetic MT data. 相似文献
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Shimelevich M. I. Rodionov E. A. Obornev I. E. Obornev E. A. 《Izvestiya Physics of the Solid Earth》2022,58(5):605-614
Izvestiya, Physics of the Solid Earth - Abstract—The approximation neural network (ANN) method for solving the inverse geoelectric problem in the piecewise constant classes of media with the... 相似文献
14.
Summary Methods of solving the inverse magnetotelluric problem are compared. Basic relations for Newton's method, the least-squares method and Marquardt's method are presented and the convergence properties of these methods are studied. The high effectiveness of Marquardt's method is demonstrated and its application to practical magnetotelluric data is discussed. 相似文献
15.
The root cause of the instability problem of the least-squares (LS) solution of the resistivity inverse problem is the ill-conditioning of the sensitivity matrix. To circumvent this problem a new LS approach has been investigated in this paper. At each iteration, the sensitivity matrix is weighted in multiple ways generating a set of systems of linear equations. By solving each system, several candidate models are obtained. As a consequence, the space of models is explored in a more extensive and effective way resulting in a more robust and stable LS approach to solving the resistivity inverse problem. This new approach is called the multiple reweighted LS method (MRLS). The problems encountered when using the L 1 - or L 2 -norm are discussed and the advantages of working with the MRLS method are highlighted. A five-layer earth model which generates an ill-conditioned matrix due to equivalence is used to generate a synthetic data set for the Schlumberger configuration. The data are randomly corrupted by noise and then inverted by using L 2 , L 1 and the MRLS algorithm. The stabilized solutions, even though blurred, could only be obtained by using a heavy ridge regression parameter in L 2 - and L 1 -norms. On the other hand, the MRLS solution is stable without regression factors and is superior and clearer. For a better appraisal the same initial model was used in all cases. The MRLS algorithm is also demonstrated for a field data set: a stable solution is obtained. 相似文献
16.
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17.
A Fourier transform approach is applied to the transient analysis of dynamic soil–structure interaction under SH-motion. The governing equations are formulated in the frequency domain using a Finite Element–Boundary Element (FE–BE) coupling method. After solving the transformed problem, the transient solution is obtained using the discrete inverse Fourier transform with a fast Fourier transform algorithm. Two examples are presented in order to show the numerical performance of the proposed technique. 相似文献
18.
A procedure is suggested of a more effective and faster computation of the impedance, the transfer function and amplitudes of the induced field in a spherically symmetric model of the electrical conductivity. The existing induction data have been supplemented by about 80 new values derived from the analysis of daily means. The fit of the existing 1-D models of the electrical conductivity of the mantle to the set of induction data is investigated. The characteristic equation for the free electromagnetic oscillations of a radially inhomogeneous Earth is derived and its possible importance in solving the inverse problem of electric conductivity is pointed out. 相似文献
19.
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
20.
Juan C. Carvajal Víctor M. Taboada-Urtuzustegui Miguel P. Romo 《Soil Dynamics and Earthquake Engineering》2002,22(4)
The installation of vertical downhole arrays in the field that record the soil behavior during earthquakes, has opened the opportunity of exploring another alternate method for assessing the soil dynamic properties by solving the inverse problem. This article proposes a methodology for solving this problem using spectral analysis of downhole arrays records. The one-dimensional shear wave propagation model was used, considering a homogeneous-viscoelastic medium. This methodology was applied at the site known as Central de Abasto Oficinas (CAO), which is located in the lake zone of the Mexico City. The results indicate that even relatively low frequencies have a noticeable effect on dynamic soil properties. Shear modulus increases and damping ratio lessens when the frequency rises. 相似文献