共查询到20条相似文献，搜索用时 46 毫秒
1.
Recovering magnetic susceptibility from electromagnetic data over a one-dimensional earth 总被引：1，自引：0，他引：1
While the inversion of electromagnetic data to recover electrical conductivity has received much attention, the inversion of those data to recover magnetic susceptibility has not been fully studied. In this paper we invert frequency-domain electromagnetic (EM) data from a horizontal coplanar system to recover a 1-D distribution of magnetic susceptibility under the assumption that the electrical conductivity is known. The inversion is carried out by dividing the earth into layers of constant susceptibility and minimizing an objective function of the susceptibility subject to fitting the data. An adjoint Green's function solution is used in the calculation of sensitivities, and it is apparent that the sensitivity problem is driven by three sources. One of the sources is the scaled electric field in the layer of interest, and the other two, related to effective magnetic charges, are located at the upper and lower boundaries of the layer. These charges give rise to a frequency-independent term in the sensitivities. Because different frequencies penetrate to different depths in the earth, the EM data contain inherent information about the depth distribution of susceptibility. This contrasts with static field measurements, which can be reproduced by a surface layer of magnetization. We illustrate the effectiveness of the inversion algorithm on synthetic and field data and show also the importance of knowing the background conductivity. In practical circumstances, where there is no a priori information about conductivity distribution, a simultaneous inversion of EM data to recover both electrical conductivity and susceptibility will be required. 相似文献
2.
Summary Magnetotelluric measurements at periods from 30 to 1000s were made at eight locations in the Market Weighton (MW) area, along an east—west profile across gravity and magnetic anomalies. Dimensional parameters were developed for assessing the structural dimensionality of the electrical conductivity of the Earth from the data. One-dimensional inversion modelling techniques were employed to interpret the data at each site, and four-layer models were obtained to explain the main structure of the crust in the area studied. If it is assumed that all strata are unmagnetized then the results show that there is a highly resistive layer in the crust, the thickness of the highly resistive layer ranges from 12 km in the east to 44 km in the west with a large change in the middle near the MW site. A structural boundary lying north—south near MW was also indicated by the principal directions of rotated apparent resistivities and transfer functions. Both electrical conductivity and magnetic permeability contrast in the ground were considered in an attempt to interpret the observed variations in apparent resistivity at different periods. 相似文献
3.
快速、无损监测农田土壤水分含量,是智慧农业的重要研究内容。以新疆南疆阿拉尔国家农业科技园区膜下滴灌棉田为研究对象,运用EM38-MK2大地电导率仪快速、高效的获取了4组不同时期的棉田土壤表观电导率数据,并同步采集表层土壤(0~20 cm)样品,通过构建表观电导率数据与室内测定含水量数据间的反演模型获取了测点的含水量数据,并按照土壤水分干旱分级标准对研究区土壤水分进行划分,综合利用GIS软件和地统计方法对土壤水分的时空变异性进行研究。结果表明:4个时期的土壤水分反演模型决定系数均大于0.80且均方根误差(RMSE)和平均绝对百分误差(MAPE)均较小,表明反演模型精度较高,土壤表观电导率与表层土壤水分相关性较好;不同时期土壤含水量数据表明土壤水分具有很强的时间变异性,变异性由中等变异转变为弱变异再转变为中等变异;受人为灌溉等因素的影响,变异函数模型也存在差异;半方差分析中4个时期的土壤水分块金值与基台值之比均大于75%,表明土壤水分在空间上趋近于弱空间相关;高程反距离权重(IDW)插值图及水分克里格插值图表明微地形是影响土壤水分分布的重要因素。本研究可为干旱区膜下滴灌棉田土壤水分动态监测提供重要的方法支撑,从而更好地指导农业灌溉。 相似文献
4.
Robert L. Parker 《Geophysical Journal International》1982,68(1):165-170
Summary. The exponential attenuation of fluctuating electromagnetic fields suggests that practical magneto telluric measurements may be uninformative about the electrical conductivity at sufficiently great depths. This notion can be made precise for one-dimensional systems. Below a critical depth the conductivity function may be chosen freely without affecting the consistency of the model with the data. This depth is readily computable with quadratic or linear programming techniques and does not rely upon linearization of the equations. 相似文献
5.
Summary. The problem of determination of the electrical conductivity of the Earth from the geomagnetic induction data is formulated as that of finding the coefficients of the continued fraction expansion of a certain rational fraction representation of the total response (or impedance) of the medium at the surface when this quantity is given for N frequencies. The coefficients of expansion are related to the conductivities of N layers of constant attenuation, where, within each layer the conductivity is assumed to be constant. Thus in this approach the conductivity profile resulting from the inversion of the response function is given as a series of step functions. 相似文献
6.
Alan G. Jones 《Geophysical Journal International》1982,68(2):371-388
Summary. An interpretation of the geomagnetic inductive response function, C (ω, 0), observed at Kiruna in northern Sweden, is herein undertaken. The bounds of acceptable solutions are initially discovered by a Monte-Carlo random search procedure, and the best-fitting solutions are examined by the application of linear theory to the problem. The data are shown to have a higher degree of internal consistency than that described by the estimated variances of each datum. A further Monte-Carlo inversion of the variance- reduced data set gives solutions with well defined model parameters.
The two major features of the models are: (1) a small, or non-existent, electrical conductivity variation across the seismic Moho boundary, and (2) the unequivocal existence of an electrical asthenosphere, under the Fenno- scandian shield, beginning at a depth of between 155–185 km, and of 60km minimum thickness. Both of these observations have seismic counterparts.
Finally, possible mantle temperature profiles are deduced which depend on the assumptions and laboratory data employed. 相似文献
The two major features of the models are: (1) a small, or non-existent, electrical conductivity variation across the seismic Moho boundary, and (2) the unequivocal existence of an electrical asthenosphere, under the Fenno- scandian shield, beginning at a depth of between 155–185 km, and of 60km minimum thickness. Both of these observations have seismic counterparts.
Finally, possible mantle temperature profiles are deduced which depend on the assumptions and laboratory data employed. 相似文献
7.
D. W. Vasco 《Geophysical Journal International》2000,142(3):970-990
Many geophysical inverse problems derive from governing partial differential equations with unknown coefficients. Alternatively, inverse problems often arise from integral equations associated with a Green's function solution to a governing differential equation. In their discrete form such equations reduce to systems of polynomial equations, known as algebraic equations. Using techniques from computational algebra one can address questions of the existence of solutions to such equations as well as the uniqueness of the solutions. The techniques are enumerative and exhaustive, requiring a finite number of computer operations. For example, calculating a bound to the total number of solutions reduces to computing the dimension of a linear vector space. The solution set itself may be constructed through the solution of an eigenvalue problem. The techniques are applied to a set of synthetic magnetotelluric values generated by conductivity variations within a layer. We find that the estimation of the conductivity and the electric field in the subsurface, based upon single-frequency magnetotelluric field values, is equivalent to a linear inverse problem. The techniques are also illustrated by an application to a magnetotelluric data set gathered at Battle Mountain, Nevada. Surface observations of the electric ( E y ) and magnetic ( H x ) fields are used to construct a model of subsurface electrical structure. Using techniques for algebraic equations it is shown that solutions exist, and that the set of solutions is finite. The total number of solutions is bounded above at 134 217 728. A numerical solution of the algebraic equations generates a conductivity structure in accordance with the current geological model for the area. 相似文献
8.
Magnetotelluric image of the crust and upper mantle in the backarc of the northwestern Argentinean Andes 总被引：2，自引：0，他引：2
Magnetotelluric data from the backarc of the Central Andes in NW Argentinawere re-examined by employing impedance tensor decomposition and 2-D inversion and modelling techniques. The data in the period range of 50–15 000 s were collected on a profile of 220 km length reaching from the Eastern Cordillera across the Santa Barbara System to the Andean foreland of the Argentinean Chaco.
After a dimensionality analysis, data from most sites were treated as regional 2-D. The exception was the eastern section of the profile, where the magnetotelluric transfer functions for periods ≤ 1000 s reflect a 3-D earth. Application of two tensor decomposition schemes yielded a regional strike direction of N–S, which is the azimuth of the Central Andean mountain chains. Several 2-D models were obtained by pseudo- and full 2-D Occam inversion schemes. Special emphasis was placed on the inversion of phase data to reduce the influence of static shifts in the apparent resistivity data. The smooth inversion models all show a good conductor at depth. A final model was then calculated using a finite element forward algorithm.
The most prominent feature of the resulting model is a conductor which rises from depths of 180 km below the Chaco region to 80 km beneath the Santa Barbara System and the Eastern Cordillera. Its interpretation as a rise of the electrical asthenosphere is supported by seismic attenuation studies. Magnetotelluric results, surface heat-flow distribution in the area, and the electrical properties of crustal and mantle rocks suggest that the upper mantle is predominantly ductile beneath the Eastern Cordillera and the western Santa Barbara System. This generally agrees with anelastic seismic attenuation models of the area and is useful in discriminating between models of Q quality factor distribution. 相似文献
After a dimensionality analysis, data from most sites were treated as regional 2-D. The exception was the eastern section of the profile, where the magnetotelluric transfer functions for periods ≤ 1000 s reflect a 3-D earth. Application of two tensor decomposition schemes yielded a regional strike direction of N–S, which is the azimuth of the Central Andean mountain chains. Several 2-D models were obtained by pseudo- and full 2-D Occam inversion schemes. Special emphasis was placed on the inversion of phase data to reduce the influence of static shifts in the apparent resistivity data. The smooth inversion models all show a good conductor at depth. A final model was then calculated using a finite element forward algorithm.
The most prominent feature of the resulting model is a conductor which rises from depths of 180 km below the Chaco region to 80 km beneath the Santa Barbara System and the Eastern Cordillera. Its interpretation as a rise of the electrical asthenosphere is supported by seismic attenuation studies. Magnetotelluric results, surface heat-flow distribution in the area, and the electrical properties of crustal and mantle rocks suggest that the upper mantle is predominantly ductile beneath the Eastern Cordillera and the western Santa Barbara System. This generally agrees with anelastic seismic attenuation models of the area and is useful in discriminating between models of Q quality factor distribution. 相似文献
9.
New techniques for improving both the computational and imaging performance of the three-dimensional (3-D) electromagnetic inverse problem are presented. A non-linear conjugate gradient algorithm is the framework of the inversion scheme. Full wave equation modelling for controlled sources is utilized for data simulation along with an efficient gradient computation approach for the model update. Improving the modelling efficiency of the 3-D finite difference (FD) method involves the separation of the potentially large modelling mesh, defining the set of model parameters, from the computational FD meshes used for field simulation. Grid spacings and thus overall grid sizes can be reduced and optimized according to source frequencies and source–receiver offsets of a given input data set. Further computational efficiency is obtained by combining different levels of parallelization. While the parallel scheme allows for an arbitrarily large number of parallel tasks, the relative amount of message passing is kept constant. Image enhancement is achieved by model parameter transformation functions, which enforce bounded conductivity parameters and thus prevent parameter overshoots. Further, a remedy for treating distorted data within the inversion process is presented. Data distortions simulated here include positioning errors and a highly conductive overburden, hiding the desired target signal. The methods are demonstrated using both synthetic and field data. 相似文献
10.
Long-period geomagnetic data can resolve large-scale 3-D mantle electrical conductivity heterogeneities which are indicators of physiochemical variations found in the Earth's dynamic mantle. A prerequisite for mapping such heterogeneity is the ability to model accurately electromagnetic induction in a heterogeneous sphere. A previously developed finite element method solution to the geomagnetic induction problem is validated against an analytic solution for a fully 3-D geometry: an off-axis spherical inclusion embedded in a uniform sphere. Geomagnetic induction is then modelled in a uniform spherical mantle overlain by a realistic distribution of oceanic and continental conductances. Our results indicate that the contrast in electrical conductivity between oceans and continents is not primarily responsible for the observed geographic variability of long-period geomagnetic data. In the absence of persistent high-wavenumber magnetospheric disturbances, this argues strongly for the existence of large-scale, high-contrast electrical conductivity heterogeneities in the mid-mantle. Lastly, for several periods the geomagnetic anomaly associated with a mid-mantle spherical inclusion is calculated. A high-contrast inclusion can be readily detected beneath the outer shell of oceans and continents. A comparison between observed and computed c responses suggests that the mid-mantle contains more than one order of magnitude of lateral variability in electrical conductivity, while the upper mantle contains at least two orders of magnitude of lateral variability in electrical conductivity. 相似文献
11.
Regularization is usually necessary in solving seismic tomographic inversion problems. In general the equation system of seismic tomography is very large, often making a suitable choice of the regularization parameter difficult. In this paper, we propose an algorithm for the practical choice of the regularization parameter in linear tomographic inversion. The algorithm is based on the types of statistical assumptions most commonly used in seismic tomography. We first transfer the system of equations into a Krylov subspace by using Lanczos bidiagonalization. In the transformed subspace, the system of equations is then changed into the form of a standard damped least squares normal equation. The solution to this normal equation can be written as an explicit function of the regularization parameter, which makes the choice of the regularization computationally convenient. Two criteria for the choice of the regularization parameter are investigated with the numerical simulations. If the dimensions of the transformed space are much less than that of the original model space, the algorithm can be very computationally efficient, which is practically useful in large seismic tomography problems. 相似文献
12.
A tomographic inversion technique that inverts traveltimes to obtain a model of the subsurface in terms of velocities and interfaces is presented. It uses a combination of refraction, wide-angle reflection and normal-incidence data, it simultaneously inverts for velocities and interface depths, and it is able to quantify the errors and trade-offs in the final model. The technique uses an iterative linearized approach to the non-linear traveltime inversion problem. The subsurface is represented as a set of layers separated by interfaces, across which the velocity may be discontinuous. Within each layer the velocity varies in two dimensions and has a continuous first derivative. Rays are traced in this medium using a technique based on ray perturbation theory, and two-point ray tracing is avoided by interpolating the traveltimes to the receivers from a roughly equidistant fan of rays. The calculated traveltimes are inverted by simultaneously minimizing the misfit between the data and calculated traveltimes, and the roughness of the model. This 'smoothing regularization' stabilizes the solution of the inverse problem. In practice, the first iterations are performed with a high level of smoothing. As the inversion proceeds, the level of smoothing is gradually reduced until the traveltime residual is at the estimated level of noise in the data. At this point, a minimum-feature solution is obtained, which should contain only those features discernible over the noise.
The technique is tested on a synthetic data set, demonstrating its accuracy and stability and also illustrating the desirability of including a large number of different ray types in an inversion. 相似文献
The technique is tested on a synthetic data set, demonstrating its accuracy and stability and also illustrating the desirability of including a large number of different ray types in an inversion. 相似文献
13.
R. S. Anderssen 《Geophysical Journal International》1979,57(1):67-71
Summary . Using a variational formulation for the response function V ( r ), commonly used in the inversion of electromagnetic induction data for a spherically symmetric earth, a number of independent expressions for the total variation of this response function with respect to perturbations in the (electrical) conductivity S o have been derived. These results have been used to indicate:
(1) How the boundary constraints contained in the expressions for the total variation of V ( r ) affect any computational implementation.
(2) How refinement modelling for the inversion of electromagnetic induction data can be implemented iteratively without the use of linearization.
In addition, these results have been used to examine the validity of Parker's linearization proposal by showing that his results depend heavily on the exclusion of certain boundary constraints, and the choice of the L2 norm as the norm to use. 相似文献
(1) How the boundary constraints contained in the expressions for the total variation of V ( r ) affect any computational implementation.
(2) How refinement modelling for the inversion of electromagnetic induction data can be implemented iteratively without the use of linearization.
In addition, these results have been used to examine the validity of Parker's linearization proposal by showing that his results depend heavily on the exclusion of certain boundary constraints, and the choice of the L
14.
《Geophysical Journal International》1982,71(1):247-260
Summary. Compressional and shear wave velocities and electrical conductivity have been measured simultaneously on three saturated samples of granite up to 0.4 GPa effective pressure and one of chalk up to 0.04 GPa effective pressure. The velocity–pressure data have been inverted using the non-interactive theory of Kuster & Toksöz to produce pore aspect ratio spectra. Archie's Law, and a model devised by Hoening have been used to calculate a theoretical electrical conductivity from the derived pore spectra. In general there is good agreement between the observed conductivity and the conductivity calculated using Hoening's equation applied to 'cigar-shaped' cracks. Predicted conductivities obtained via Archie's Law are in approximate agreement using a power of two and are much less than the observed values using a power of one. The results suggest that simultaneous electrical conductivity measurements might provide an important constraint in interpreting velocity—pressure data in terms of pore spectra. 相似文献
15.
海冰作为冰雪圈的重要组成部分,对气候变化十分敏感,海冰物理过程研究需要得到精确的海冰厚度。本文介绍一种能够高效探测海冰厚度的电磁感应方法及其在波罗的海(Baltic Sea)的成功应用。该技术方法针对海冰和海水的电特性,利用电磁感应原理精确探测仪器至冰水交界面的距离,以实现海冰厚度的测定。通过电磁感应(EM)仪直接观测的视电导率与同点位钻孔测量数据对比分析,获得视电导率与海冰厚度的转换关系式,并对通过该关系式计算出的海冰厚度进行验证,表明电磁感应技术能够获得可靠的海冰厚度数据,平均相对误差仅为12%。对波西尼亚海湾(Bothnian Bay)海冰厚度探测剖面的统计结果表明,2007年春季该区域平整冰厚度范围在0.4-0.6m之间。 相似文献
16.
Investigation of a Tertiary maar structure using three-dimensional resistivity imaging 总被引：1，自引：0，他引：1
Ingolf Brunner Sven Friedel Franz Jacobs & Erik Danckwardt 《Geophysical Journal International》1999,136(3):771-780
This paper presents the application of the electrical resistivity tomography (ERT) method to the investigation of the Tertiary maar structure of Baruth (Germany) known from previous gravimetric surveys. ERT was applied to support the optimum location for a palaeoclimatological drill hole.
Special modifications of data acquisition, signal processing and inversion are introduced to adapt the method of ERT to the special requirements for the 3-D investigation of structures with horizontal extensions of 1 km or more. More than 5000 dipole–dipole combinations were recorded at three concentric circular electrode arrangements using stand-alone transient data acquisition systems (RefTek).
We present a fast approximate imaging technique based on the simultaneous iterative reconstruction technique (SIRT). As the complete calculation of the inverse Frechét matrix is avoided, the algorithm is especially suitable for large data and model spaces, where complete inversion is beyond the limits of available computing hardware. The single-step method is applicable to arbitrary irregular electrode layouts. Synthetic tests show that the imaging procedure reconstructs the main features of the subsurface.
A low-resistivity body could be interpreted as limnic sediments filling the interior of the Tertiary maar crater. Considering the horizontal resistivity gradient, estimates for the lateral and depth extents of the structure were made. An optimum position for a palaeoclimatological borehole was found, and was in good agreement with the gravimetric minimum. 相似文献
Special modifications of data acquisition, signal processing and inversion are introduced to adapt the method of ERT to the special requirements for the 3-D investigation of structures with horizontal extensions of 1 km or more. More than 5000 dipole–dipole combinations were recorded at three concentric circular electrode arrangements using stand-alone transient data acquisition systems (RefTek).
We present a fast approximate imaging technique based on the simultaneous iterative reconstruction technique (SIRT). As the complete calculation of the inverse Frechét matrix is avoided, the algorithm is especially suitable for large data and model spaces, where complete inversion is beyond the limits of available computing hardware. The single-step method is applicable to arbitrary irregular electrode layouts. Synthetic tests show that the imaging procedure reconstructs the main features of the subsurface.
A low-resistivity body could be interpreted as limnic sediments filling the interior of the Tertiary maar crater. Considering the horizontal resistivity gradient, estimates for the lateral and depth extents of the structure were made. An optimum position for a palaeoclimatological borehole was found, and was in good agreement with the gravimetric minimum. 相似文献
17.
Remote Sensing Inversion for Simulation of Soil Salinization Based on Hyperspectral Data and Ground Analysis in Yinchuan,China 总被引：2，自引：0，他引：2
Wu Dan Jia Keli Zhang Xiaodong Zhang Junhua Abd El-Hamid Hazem T. 《Natural Resources Research》2021,30(6):4641-4656
The Pingluo area, as an experimental study area in Yinchuan, has been subjected to major environmental degradation due to soil salinization problems. Soil salinization is one of the main problems of land degradation in arid and semiarid regions. In the present study, remote sensing was integrated with mathematical modeling to evaluate soil salinization adequately. To detect soil salinization, soil water content and electrical conductivity of soil samples were analyzed. The reflectance of soil samples was measured using a spectrometer (SR-3500) with 1024 bands. Indices of soil salinity, vegetation and drought were analyzed using Landsat images over the study area. Based on Landsat images, physicochemical analysis, reflectance of sensitive bands for soil salinization and environmental indices, canopy response salinity index (CRSI), perpendicular drought index (PDI) and enhanced normalized difference vegetation index (ENDVI), a new model was established for simulation and prediction of soil salinization in the study area. Correlation analyses and multiple regression methods were used to construct an accurate model. The results showed that green, blue and near-infrared light was significantly correlated with soil salinity and that the spectral parameters improved this correlation significantly. Therefore, the model was more effective when combining spectral parameters with sensitive bands with modeling. After mathematical transformation of soil reflectance, the correlations of bands sensitive to soil salinization were 0.739 and 0.7 for electrical conductivity and water content, respectively. After transformation of vegetation reflectance, the correlation coefficient of soil salinity became 0.577. After inversion of the model based on soil hyperspectral and water content, the significance became 0.871 and 0.726, respectively, which can be used to predict soil salinity and water content. The spectral soil salinity model had a coefficient of 0.739 for soil salinity prediction. Among the salinity indices, the CRSI was selected as the most significant, with R2 of 0.571, whereas the R2 for PDI reached only 0.484. Among the vegetation indices, the ENDVI had the highest response to soil salinity, with R2 of 0.577. After scale conversion, the correlation percentages between CRSI and measured soil salinity and between ENDVI and measured soil salinity increased to 16.2% and 8.5%, respectively. Following the correlation between PDI and soil water content, the percentage of correlation increased to 11.6%. The integration of hyperspectral remote sensing, ground methods and an inversion method for salinity is a very important and effective technique for rapid and nondestructive monitoring of soil salinization.
相似文献18.
E. Gomez-Treviño 《Geophysical Journal International》1996,127(3):762-772
This paper presents a simple non-linear method of magnetotelluric inversion that accounts for the computation of depth averages of the electrical conductivity profile of the Earth. The method is not exact but it still preserves the non-linear character of the magnetotelluric inverse problem. The basic formula for the averages is derived from the well-known conductance equation, but instead of following the tradition of solving directly for conductivity, a solution is sought in terras of spatial averages of the conductivity distribution. Formulas for the variance and the resolution are then readily derived. In terms of Backus-Gilbert theory for linear appraisal, it is possible to inspect the classical trade-off curves between variance and resolution, but instead of resorting to linearized iterative methods the curves can be computed analytically. The stability of the averages naturally depends on their variance but this can be controlled at will. In general, the better the resolution the worse the variance. For the case of optimal resolution and worst variance, the formula for the averages reduces to the well-known Niblett-Bostick transformation. This explains why the transformation is unstable for noisy data. In this respect, the computation of averages leads naturally to a stable version of the Niblett-Bostick transformation. The performance of the method is illustrated with numerical experiments and applications to field data. These validate the formula as an approximate but useful tool for making inferences about the deep conductivity profile of the Earth, using no information or assumption other than the surface geophysical measurements. 相似文献
19.
As an important component of the cryosphere,sea ice is very sensitive to the climate change.The study of the sea ice physics needs accurate sea ice thickness.This paper presents an electromagnetic-induction(EM) technique which can be used to measure the sea ice thickness distribution efficiently,and the successful application in Bothnian Bay.Based on the electromagnetic field theory and the electrical properties of sea ice and seawater,EM technique can detect the distance between the instrument and the ice/water interface accurately,than the sea ice thickness is obtained.Contrastive analysis of the apparent conductivity data obtained by EM and the value of drill-hole at same positions allows a construction of a transformable formula of the apparent conductivity to sea ice thickness.The verification of the sea ice thickness calculated by this formula indicates that EM technique is able to get reliable sea ice thickness with average relative error of only 12%.The statistic of all ice thickness profiles shows that the level ice distribution in Bothnian Bay was 0.4-0.6 m. 相似文献
20.
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