共查询到20条相似文献，搜索用时 15 毫秒
1.
Summary. For the determination of lateral velocity or absorption inhomogeneities, methods such as the generalized matrix inversion and its damped versions, for example the stochastic inverse, are usually applied in seismology to travel-time or amplitude anomalies. These methods are not appropriate for the solution of very extensive systems of equations. Reconstruction techniques as developed for computer tomography are suitable for operations with extremely large numbers of equations and unknown parameters. In this paper solutions obtained with the BPT (Back Projection Technique), ART (Algebraic Reconstruction Technique) and SIRT (Simultaneous Iterative Reconstruction Technique) are compared with those obtained from a damped version of the generalized inverse method. Data of 2-D model-seismic experiments are presented for demonstration. 相似文献
2.
A global particle swarm optimization (GPSO) technique is developed and applied to the inversion of residual gravity anomalies caused by buried bodies with simple geometry (spheres, horizontal, and vertical cylinders). Inversion parameters, such as density contrast of geometries, radius of body, depth of body, location of anomaly, and shape factor, were optimized. The GPSO algorithm was tested on noise-free synthetic data, synthetic data with 10% Gaussian noise, and five field examples from different parts of the world. The present study shows that the GPSO method is able to determine all the model parameters accurately even when shape factor is allowed to change in the optimization problem. However, the shape was fixed a priori in order to obtain the most consistent appraisal of various model parameters. For synthetic data without noise or with 10% Gaussian noise, estimates of different parameters were very close to the actual model parameters. For the field examples, the inversion results showed excellent agreement with results from previous studies that used other inverse techniques. The computation time for the GPSO procedure is very short (less than 1 s) for a swarm size of less than 50. The advantage of the GPSO method is that it is extremely fast and does not require assumptions about the shape of the source of the residual gravity anomaly. 相似文献
3.
An iterative solution to the non-linear 3-D electromagnetic inverse problem is obtained by successive linearized model updates using the method of conjugate gradients. Full wave equation modelling for controlled sources is employed to compute model sensitivities and predicted data in the frequency domain with an efficient 3-D finite-difference algorithm. Necessity dictates that the inverse be underdetermined, since realistic reconstructions require the solution for tens of thousands of parameters. In addition, large-scale 3-D forward modelling is required and this can easily involve the solution of over several million electric field unknowns per solve. A massively parallel computing platform has therefore been utilized to obtain reasonable execution times, and results are given for the 1840-node Intel Paragon. The solution is demonstrated with a synthetic example with added Gaussian noise, where the data were produced from an integral equation forward-modelling code, and is different from the finite difference code embedded in the inversion algorithm 相似文献
4.
Choice of norm for the density distribution of the Earth 总被引：1，自引：0，他引：1
Summary. The determination of the density distribution of the Earth from gravity data is called the inverse gravimetric problem. A unique solution to this problem may be obtained by introducing a priori data concerning the covariance of density anomalies. This is equivalent to requiring the density to fulfil a minimum norm condition. The generally used norm is the one equal to the integral of the square of the density distribution ( L2 -norm), the use of which implies that blocks of constant density are uncorrelated. It is shown that for harmonic anomalous density distributions this leads to an external gravity field with a power spectrum (degree-variances) which tends too slowly to zero, i.e. implying gravity anomalies much less correlated than actually observed. It is proposed to use a stronger norm, equal to the integral of the square sum of the derivatives of the density distribution. As a consequence of this, base functions which are constant within blocks, are no longer a natural choice when solving the inverse gravimetric problem. Instead a block with a linearly varying density may be used. A formula for the potential of such a block is derived. 相似文献
5.
Stable Iterative Methods for the Inversion of Geophysical Data 总被引：6，自引：0，他引：6
《Geophysical Journal International》1975,42(3):957-976
Summary. Interpretation of earth electrical measurements can often be assisted by inversion, which is a non-linear model-fitting problem in these cases. Iterative methods are normally used, and the solution is defined by' best fit'in the sense of generalized least-squares.
The inverse problems we describe are ill-posed. That is, small changes in the data can lead to large changes in both the solution and in the iterative process that finds the solution. Through an analysis of the problem, based on local linearization, we define a class of methods that stabilize the iteration, and provide a robust solution. These methods are seen as generalizations of the well-known Singular Value Truncation and Marquardt Methods of iterative inversion.
Here, and in a companion paper, we give examples illustrating the successful application of the method to ill-posed problems relating to the resistivity of the Earth. 相似文献
The inverse problems we describe are ill-posed. That is, small changes in the data can lead to large changes in both the solution and in the iterative process that finds the solution. Through an analysis of the problem, based on local linearization, we define a class of methods that stabilize the iteration, and provide a robust solution. These methods are seen as generalizations of the well-known Singular Value Truncation and Marquardt Methods of iterative inversion.
Here, and in a companion paper, we give examples illustrating the successful application of the method to ill-posed problems relating to the resistivity of the Earth. 相似文献
6.
Non-linear altimetric geoid inversion for lithospheric elastic thickness and crustal density 总被引：1，自引：0，他引：1
The inversion of high-resolution geoid anomaly maps derived from satellite altimetry should allow one to retrieve the lithospheric elastic thickness, T e , and crustal density, c . Indeed, the bending of a lithospheric plate under the load of a seamount depends on both parameters, and the associated geoid anomaly is correspondingly dependent on the two parameters. The difference between the observed and modelled geoid signatures is estimated by a cost function, J , of the two variables, T e and c . We show that this cost function forms a valley structure along which many local minima appear, the global minimum of J corresponding to the true values of the lithospheric parameters. Classical gradient methods fail to find this global minimum because they converge to the first local minimum of J encountered, so that the final parameter estimate strongly depends on the starting pair of values ( T e , c ). We here implement a non-linear optimization algorithm to recover these two parameters from altimetry data. We demonstrate from the inversion of synthetic data that this approach ensures robust estimates of T e and c by activating two search phases alternately: a gradient phase to find a local minimum of J , and a tunnelling phase through high values of the cost function. The accuracy of the solution can be improved by a search in an iteratively restricted parameter subspace. Applying our non-linear inversion to the Great Meteor Seamount geoid data, we further show that the inverse problem is intrinsically ill-posed. As a consequence, minute geoid (or gravity) data errors can induce large changes in any recovery of lithospheric elastic thickness and crustal density. 相似文献
7.
8.
Summary . Born inverse methods give accurate and stable results when the source wavelet is impulsive. However, in many practical applications (reflection seismology) an impulsive source cannot be realized and the inversion needs to be generalized to include an arbitrary source function. In this paper, we present a Born solution to the seismic inverse problem which can accommodate an arbitrary source function and give accurate and stable results. It is shown that the form of the generalized inversion algorithm reduces to a Wiener shaping ***filter, which is solved efficiently using a Levinson recursion algorithm. Numerical examples of synthetic and real field data illustrate the validity of our method. 相似文献
9.
In advanced exploration projects or operating mines, the process of allocating capital for infill drilling programs is a significant and recurrent challenge. Within a large company, the different mine sites and projects compete for the available funds for drilling. To maximize a project’s value to its company, a drillhole location optimizer can be used as an objective tool to compare drilling campaigns. The fast semi-greedy optimizer presented here can allow for the obtention of close to optimal solutions to the coverage problem with up to three orders of magnitude less computing time needed than with integer programming. The heuristic approach is flexible as it allows dynamic updating of block values once new drillholes are selected in the solution, as opposed to existing methods based on static block values. The block values used for optimization incorporate kriging estimate and variance, estimate of indicator at cutoff grade and distances to existing or newly selected drillholes. The heuristic approach tends to locate new drillholes within the maximum risk areas, i.e., within less informed zones predicted as being ore zones. Applied to different deposits, it enables, after suitable normalization, comparison of different drilling campaigns and allocation of budgets accordingly.
相似文献10.
We investigate the use of general, non- l 2 measures of data misfit and model structure in the solution of the non-linear inverse problem. Of particular interest are robust measures of data misfit, and measures of model structure which enable piecewise-constant models to be constructed. General measures can be incorporated into traditional linearized, iterative solutions to the non-linear problem through the use of an iteratively reweighted least-squares (IRLS) algorithm. We show how such an algorithm can be used to solve the linear inverse problem when general measures of misfit and structure are considered. The magnetic stripe example of Parker (1994 ) is used as an illustration. This example also emphasizes the benefits of using a robust measure of misfit when outliers are present in the data. We then show how the IRLS algorithm can be used within a linearized, iterative solution to the non-linear problem. The relevant procedure contains two iterative loops which can be combined in a number of ways. We present two possibilities. The first involves a line search to determine the most appropriate value of the trade-off parameter and the complete solution, via the IRLS algorithm, of the linearized inverse problem for each value of the trade-off parameter. In the second approach, a schedule of prescribed values for the trade-off parameter is used and the iterations required by the IRLS algorithm are combined with those for the linearized, iterative inversion procedure. These two variations are then applied to the 1-D inversion of both synthetic and field time-domain electromagnetic data. 相似文献
11.
The presence of anisotropy requires that tomographic methods be generalized to account for anisotropy. This generalization allows geological structure to be correctly imaged and allows the anisotropic parameters to be estimated. Use of isotropic inversion for imaging anisotropic structures gives systematic trends in the traveltime and polarization residuals. However, due to the limited directional coverage, the traveltimes along may not be sufficient to study the anisotropic properties of the structure. Polarizations can provide independent information on the structure. Traveltime and polarization inversion are applied to synthetic examples simulating VSP experiments. Transverse isotropy and 1-D structure are assumed. Plots of traveltime and polarization residuals are an important tool to detect the anomalies due to the presence of anisotropy. For receivers located in anisotropic layers, polarization residuals display consistent anomalies of several degrees. The synthetic examples show that even the simple 1-D problem is difficult, when using direct arrivals only. Large a posteriori errors in anisotropic parameters are obtained by traveltime inversion in layers where available incidence angles are less than 45°. Resolution of the tomographic image of VSP data is greatly improved by a combination of traveltime and polarization information. In order to obtain accurate inversion results, the measurement error of polarization data should be kept to within a few degrees. 相似文献
12.
Inversion of time domain three-dimensional electromagnetic data 总被引：7，自引：0，他引：7
Eldad Haber Douglas W. Oldenburg R. Shekhtman 《Geophysical Journal International》2007,171(2):550-564
We present a general formulation for inverting time domain electromagnetic data to recover a 3-D distribution of electrical conductivity. The forward problem is solved using finite volume methods in the spatial domain and an implicit method (Backward Euler) in the time domain. A modified Gauss–Newton strategy is employed to solve the inverse problem. The modifications include the use of a quasi-Newton method to generate a pre-conditioner for the perturbed system, and implementing an iterative Tikhonov approach in the solution to the inverse problem. In addition, we show how the size of the inverse problem can be reduced through a corrective source procedure. The same procedure can correct for discretization errors that inevidably arise. We also show how the inverse problem can be efficiently carried out even when the decay time for the conductor is significantly larger than the repetition time of the transmitter wave form. This requires a second processor to carry an additional forward modelling. Our inversion algorithm is general and is applicable for any electromagnetic field ( E , H , d B / dt ) measured in the air, on the ground, or in boreholes, and from an arbitrary grounded or ungrounded source. Three synthetic examples illustrate the basic functionality of the algorithm, and a result from a field example shows applicability in a larger-scale field example. 相似文献
13.
Geological structures introduce heterogeneity along deformed strata, which in turn exert a strong control on regional groundwater occurrences and water flow. We developed and applied procedures of structural, borehole and direct current resistivity (DCR) data to (1) figure out a reliable structural model of a fault-related dome, (2) visualize the relationship between structural complexity and aquifers geometry and (3) characterize the fault damage zones and its related sealing potentialities. The present approach was applied at the northern Eastern Desert, Egypt, considering its complex deformation history. To alleviate the uncertainties and artifacts in solving the DCR inverse problem, advanced and non-conventional inversion schemes were applied. Moreover, fault seal potentialities were assessed by applying the shale gouge ratio (SGR) estimation to predict the groundwater pathway flow. The main findings include: (a) The DCR measurements can be considered as a complementary tool to visualize the relationship between subsurface structures and aquifers geometry at highly deformed areas; (b) detailed surface structural data analysis combined with sophisticated inversion algorithms application can increase the reliability of the constructed geo-electrical cross sections for deep and large-scale geological surveys; and (c) the structural modeling of geological units and faults distribution contributes to clarify hydrogeological settings and aquifers connectivity. The approach can be readily applied elsewhere, as long as detailed structural analysis, geometric parameters and high-resolution DCR resistivity data are available.
相似文献14.
We have formulated a 3-D inverse solution for the magnetotelluric (MT) problem using the non-linear conjugate gradient method. Finite difference methods are used to compute predicted data efficiently and objective functional gradients. Only six forward modelling applications per frequency are typically required to produce the model update at each iteration. This efficiency is achieved by incorporating a simple line search procedure that calls for a sufficient reduction in the objective functional, instead of an exact determination of its minimum along a given descent direction. Additional efficiencies in the scheme are sought by incorporating preconditioning to accelerate solution convergence. Even with these efficiencies, the solution's realism and complexity are still limited by the speed and memory of serial processors. To overcome this barrier, the scheme has been implemented on a parallel computing platform where tens to thousands of processors operate on the problem simultaneously. The inversion scheme is tested by inverting data produced with a forward modelling code algorithmically different from that employed in the inversion algorithm. This check provides independent verification of the scheme since the two forward modelling algorithms are prone to different types of numerical error. 相似文献
15.
Spatial optimization for regionalization problems with spatial interaction: a heuristic approach 总被引：2，自引：0，他引：2
Kamyoung Kim Denis J. Dean Hyun Kim 《International journal of geographical information science》2016,30(3):451-473
Spatial optimization techniques are commonly used for regionalization problems, often represented as p-regions problems. Although various spatial optimization approaches have been proposed for finding exact solutions to p-regions problems, these approaches are not practical when applied to large-size problems. Alternatively, various heuristics provide effective ways to find near-optimal solutions for p-regions problem. However, most heuristic approaches are specifically designed for particular geographic settings. This paper proposes a new heuristic approach named Automated Zoning Procedure-Center Interchange (AZP-CI) to solve the p-functional regions problem (PFRP), which constructs regions by combining small areas that share common characteristics with predefined functional centers and have tight connections among themselves through spatial interaction. The AZP-CI consists of two subprocesses. First, the dissolving/splitting process enhances diversification and thereby produces an extensive exploration of the solution space. Second, the standard AZP locally improves the objective value. The AZP-CI was tested using randomly simulated datasets and two empirical datasets with different sizes. These evaluations indicate that AZP-CI outperforms two established heuristic algorithms: the AZP and simulated annealing, in terms of both solution quality and consistency of producing reliable solutions regardless of initial conditions. It is also noted that AZP-CI, as a general heuristic method, can be easily extended to other regionalization problems. Furthermore, the AZP-CI could be a more scalable algorithm to solve computational intensive spatial optimization problems when it is combined with cyberinfrastructure. 相似文献
16.
Z.-M. Yin 《Geophysical Journal International》1996,125(3):841-849
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. 相似文献
17.
Two-dimensional magnetotelluric inversion 总被引：2，自引：0，他引：2
Summary. When complex structure is encountered in magnetotelluric surveys, interpretation by locally fitted layered models is of questionable validity. However, when the processed data show two-dimensional structure, numerical inversion schemes for two-dimensional models may be constructed as an aid to regional data interpretation.
The two-dimensional magnetotellurics inversion problem is here formulated in a way that may be applied to many problems. A resulting computer program is analysed carefully in terms of its cost relative to that of simpler layered modelling.
As an example, the method is applied to some field data where the interpretive advantages of the program become evident. 相似文献
The two-dimensional magnetotellurics inversion problem is here formulated in a way that may be applied to many problems. A resulting computer program is analysed carefully in terms of its cost relative to that of simpler layered modelling.
As an example, the method is applied to some field data where the interpretive advantages of the program become evident. 相似文献
18.
Observations and origin of Rayleigh-wave amplitude anomalies 总被引：1，自引：0，他引：1
S. van der Lee 《Geophysical Journal International》1998,135(2):691-699
This is a report of observations of amplitude anomalies of fundamental-mode Rayleigh waves ( R 1) between periods of 17 and 100 s. The anomalies are with respect to amplitudes predicted by Rayleigh-wave excitation for a reference earth model and catalogued centroid earthquake source parameters, such as are used in large-scale waveform inversions. The observations indicate that the amplitude anomalies are consistent for nearby recordings of the same event, while there is no obvious relation between the observed anomalies and the paths travelled by the waves. This is in contrast to Rayleigh-wave phase anomalies, which are consistent for similar propagation paths, and hence form the input in many inversions for along-path structure. The observations in this paper show that a similar inversion of intermediate-period amplitude anomalies for along- and near-path structure is not warranted without eliminating source effects, since the amplitude anomalies are dominated by scattering off near-source earth structure and by possible uncertainties in the source parameters. Sensitivity kernels that take the coupling between the moment tensor and displacement field into account demonstrate that Rayleigh-wave amplitude sensitivity is largest near the source. This report argues that the interaction between source-radiated Rayleigh waves and near-source earth structure may not be ignored in amplitude inversion procedures. 相似文献
19.
Summary. A new closed-form solution is obtained analytically for a B- polarization induction problem of geophysical interest, in which a local region of the Earth is represented by a generalized thin sheet at the surface of and in electrical contact with a uniformly conducting half-space. The generalized sheet, first introduced by Ranganayaki & Madden, is a mathematical idealization of a double layer which consists, in this problem, of two adjacent half-planes with distinct conductances representing a surface conductivity discontinuity such as an ocean—coast boundary, underlain by a uniform sheet of finite integrated resistivity representing the lower crust. The resistive sheet exerts a considerable mathematical influence on the solution causing, under certain conditions, an additional pole to appear in one of the forms of contour integral by which the solution can be expressed; it also weakens or eliminates field singularities that would otherwise occur at the conductance discontinuity. A numerical calculation is made for model parameters typifying an ocean—coast boundary underlain by a highly resistive crust. It is found that the residue of the pole associated with the resistive sheet dominates the solution for this example, the main consequence of which is a huge increase in the horizontal range over which the induced currents adjust themselves between the different 'skin-effect' distributions at infinity on either side of the model. Moreover the solution shows that this 'adjustment distance' has a more complicated dependence on the conductance and integrated resistivity of the sheet than that given simply by the square root of their product which was the length parameter proposed by Ranganayaki & Madden. 相似文献
20.
Numerical scheme for the inversion of acoustical impedance profile based on the Gelfand-Levitan method 总被引：1，自引：0，他引：1
Fadil Santosa 《Geophysical Journal International》1982,70(1):229-243
Summary. An exact method for the solution of the inverse problem in plane wave propagation modelled after the Gelfand-Levitan technique is reviewed and refined. A numerical scheme for the solution of the integral equation that arises in the method is proposed. A discussion on the stability and an error analysis of the numerical approximation are presented. The applicability of the inversion algorithm is demonstrated in a numerical experiment. 相似文献