共查询到20条相似文献，搜索用时 62 毫秒
1.
为提高水平层状介质中三维电磁波散射和逆散射数值模拟的效率,在对角张量近似(DTA)的基础上根据不同回代方式得到了求解积分方程的DTA1和DTA2两种近似. 这两种近似可以作为计算积分方程稳定型双共轭梯度快速Fourier变换(BCGS-FFT)算法的初始猜测值和预条件因子，从而形成效率更高的混合DTA-BCGS算法. 散射实例说明了DTA2的高精度和混合DTA-BCGS算法尤其是混合DTA2-BCGS算法的高效率. 由于DTA2近似程度更高，将DTA2与变型Born迭代反演方法(DBIM)相结合形成了一种对三维异常体进行重构的快速电磁波逆散射技术. 文中的逆散射实例说明所开发的逆散射技术对重构水平层状介质中的任意三维异常体是非常有效的. 相似文献
2.
声波方程逆散射反演的近似方法 总被引：7，自引：0，他引：7
我们在文献[1]里研究了介质参考波速沿某个方向线性变化时的三维声散射理论,导出了声波方程逆散射反演问题解的解析表达式.考虑到应用时的实际条件,本文根据上述反演方法导出2.5维模型的声波方程逆散射反演的波速扰动计算公式,给出该方法在“高频”近似条件下的波速扰动反演计算公式,从而使我们提出的“参考波速线性变化时的声波方程逆散射反演”理论更接近实际应用条件.本文给出的这些反演公式仍然具有原方法的优点,即不但可以使Born近似的假定在大多数情况下能得以满足,而且可以利用快速Fourier变换来快速实现介质波速扰动的反演成象. 相似文献
3.
我们在文献[1]里研究了介质参考波速沿某个方向线性变化时的三维声散射理论,导出了声波方程逆散射反演问题解的解析表达式.考虑到应用时的实际条件,本文根据上述反演方法导出2.5维模型的声波方程逆散射反演的波速扰动计算公式,给出该方法在“高频”近似条件下的波速扰动反演计算公式,从而使我们提出的“参考波速线性变化时的声波方程逆散射反演”理论更接近实际应用条件.本文给出的这些反演公式仍然具有原方法的优点,即不但可以使Born近似的假定在大多数情况下能得以满足,而且可以利用快速Fourier变换来快速实现介质波速扰动的反演成象. 相似文献
4.
It is important to include the viscous effect in seismic numerical modelling and seismic migration due to the ubiquitous viscosity in an actual subsurface medium. Prestack reverse‐time migration (RTM) is currently one of the most accurate methods for seismic imaging. One of the key steps of RTM is wavefield forward and backward extrapolation and how to solve the wave equation fast and accurately is the essence of this process. In this paper, we apply the time‐space domain dispersion‐relation‐based finite‐difference (FD) method for visco‐acoustic wave numerical modelling. Dispersion analysis and numerical modelling results demonstrate that the time‐space domain FD method has great accuracy and can effectively suppress numerical dispersion. Also, we use the time‐space domain FD method to solve the visco‐acoustic wave equation in wavefield extrapolation of RTM and apply the source‐normalized cross‐correlation imaging condition in migration. Improved imaging has been obtained in both synthetic and real data tests. The migration result of the visco‐acoustic wave RTM is clearer and more accurate than that of acoustic wave RTM. In addition, in the process of wavefield forward and backward extrapolation, we adopt adaptive variable‐length spatial operators to compute spatial derivatives to significantly decrease computing costs without reducing the accuracy of the numerical solution. 相似文献
5.
6.
Extrapolating wavefields and imaging at each depth during three‐dimensional recursive wave‐equation migration is a time‐consuming endeavor. For efficiency, most commercial techniques extrapolate wavefields through thick slabs followed by wavefield interpolation within each thick slab. In this article, we develop this strategy by associating more efficient interpolators with a Fourier‐transform‐related wavefield extrapolation method. First, we formulate a three‐dimensional first‐order separation‐of‐variables screen propagator for large‐step wavefield extrapolation, which allows for wide‐angle propagations in highly contrasting media. This propagator significantly improves the performance of the split‐step Fourier method in dealing with significant lateral heterogeneities at the cost of only one more fast Fourier transform in each thick slab. We then extend the two‐dimensional Kirchhoff and Born–Kirchhoff local wavefield interpolators to three‐dimensional cases for each slab. The three‐dimensional Kirchhoff interpolator is based on the traditional Kirchhoff formula and applies to moderate lateral velocity variations, whereas the three‐dimensional Born–Kirchhoff interpolator is derived from the Lippmann–Schwinger integral equation under the Born approximation and is adapted to highly laterally varying media. Numerical examples on the three‐dimensional salt model of the Society of Exploration Geophysicists/European Association of Geoscientists demonstrate that three‐dimensional first‐order separation‐of‐variables screen propagator Born–Kirchhoff depth migration using thick‐slab wavefield extrapolation plus thin‐slab interpolation tolerates a considerable depth‐step size of up to 72 ms, eventually resulting in an efficiency improvement of nearly 80% without obvious loss of imaging accuracy. Although the proposed three‐dimensional interpolators are presented with one‐way Fourier extrapolation methods, they can be extended for applications to general migration methods. 相似文献
7.
A. J. Zhang E. R. G. Hill B. A. Hobbs 《Physics of the Earth and Planetary Interiors》1990,60(1-4):40-52
An important stage in two-dimensional magnetotelluric modelling is the calculation of the Earth's response functions for an assumed conductivity model and the calculation of the associated Jacobian relating those response functions to the model parameters. The efficiency of the calculation of the Jacobian will affect the efficiency of the inversion modelling. Rodi (1976) produced all the Jacobian elements by inverting a single matrix and using an approximate first-order algorithm. Since only one inverse matrix required calculation the procedure speeded up the inversion. An iterative scheme to improve the approximation to the Jacobian information is presented in this paper. While this scheme takes a little longer than Rodi's algorithm, it enables a more accurate determination of the Jacobian information. It is found that the Jacobian elements can be produced in 10% of the time required to calculate an inverse matrix or to calculate a 2D starting model. A modification of the algorithm can further be used to improve the accuracy of the original inverse matrix calculated in a 2D finite difference program and hence the solution this program produces. The convergence of the iteration scheme is found to be related both to the originally calculated inverse matrix and to the change in the newly formed matrix arising from perturbation of the model parameter. A ridge regression inverse algorithm is used in conjunction with the iterative scheme for forward modelling described in this paper to produce a 2D conductivity section from field data. 相似文献
8.
声波方程的逆散射反演乃是求解双曲型偏微分方程系数项反问题的一种解析方法,一般利用Born近似把这一非线性反问题线性化,并给出了恒参考波速介质中反问题解的解析表达式.由于Born近似假定波速扰动为一级无穷小,因此,在大多数情况下,恒参考波速介质模型的反问题的解无法得以应用.本文研究介质参考波速沿某个方向线性变化时的声散射理论,导出了声波方程逆散射问题解的解析表达式,从而既可使Born近似的假定在大多数情况下能得以满足,又可利用快速Fourier变换快速实现介质波速扰动的反演成象. 相似文献
9.
We present preserved‐amplitude downward continuation migration formulas in the aperture angle domain. Our approach is based on shot‐receiver wavefield continuation. Since source and receiver points are close to the image point, a local homogeneous reference velocity can be approximated after redatuming. We analyse this approach in the framework of linearized inversion of Kirchhoff and Born approximations. From our analysis, preserved‐amplitude Kirchhoff and Born inverse formulas can be derived for the 2D case. They involve slant stacks of filtered subsurface offset domain common image gathers followed by the application of the appropriate weighting factors. For the numerical implementation of these formulas, we develop an algorithm based on the true amplitude version of the one‐way paraxial approximation. Finally, we demonstrate the relevance of our approach with a set of applications on synthetic datasets and compare our results with those obtained on the Marmousi model by multi‐arrival ray‐based preserved‐amplitude migration. While results are similar, we observe that our results are less affected by artefacts. 相似文献
10.
Optimal implicit staggered‐grid finite‐difference schemes based on the sampling approximation method for seismic modelling 
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下载免费PDF全文 We propose new implicit staggered‐grid finite‐difference schemes with optimal coefficients based on the sampling approximation method to improve the numerical solution accuracy for seismic modelling. We first derive the optimized implicit staggered‐grid finite‐difference coefficients of arbitrary even‐order accuracy for the first‐order spatial derivatives using the plane‐wave theory and the direct sampling approximation method. Then, the implicit staggered‐grid finite‐difference coefficients based on sampling approximation, which can widen the range of wavenumber with great accuracy, are used to solve the first‐order spatial derivatives. By comparing the numerical dispersion of the implicit staggered‐grid finite‐difference schemes based on sampling approximation, Taylor series expansion, and least squares, we find that the optimal implicit staggered‐grid finite‐difference scheme based on sampling approximation achieves greater precision than that based on Taylor series expansion over a wider range of wavenumbers, although it has similar accuracy to that based on least squares. Finally, we apply the implicit staggered‐grid finite difference based on sampling approximation to numerical modelling. The modelling results demonstrate that the new optimal method can efficiently suppress numerical dispersion and lead to greater accuracy compared with the implicit staggered‐grid finite difference based on Taylor series expansion. In addition, the results also indicate the computational cost of the implicit staggered‐grid finite difference based on sampling approximation is almost the same as the implicit staggered‐grid finite difference based on Taylor series expansion. 相似文献
11.
用变分玻恩迭代方法重建二维非均匀介质结构 总被引：8，自引：1，他引：7
提出了用于二维轴对称非均匀介质结构的反演和成像的一种新的反演迭代方法──变分玻恩迭代方法（ＶＢＩＭ）．首先利用玻恩近似将非线性积分方程线性化,然后应用变分方法导出用于反演的电场积分方程．正演数据则利用高效的数值模式匹配方法获得．数值结果表明,ＶＢＩＭ与ＢＩＭ相比,其收敛速度、成像质量等均得到较大的改善。 相似文献
12.
Born正演是一种常用的地震波场正演模拟方法,也是线性化地震反演的理论基础.在实际应用时,Born正演通常结合常规的地震射线方法进行实现.为了克服常规地震射线方法的弊端,并且保证地震波场的模拟精度和计算效率,本文提出了一种基于高斯束的一阶散射波场Born正演方法.该方法分为两个环节:首先,我们利用高斯束的走时和振幅信息将地下散射点处的反射率映射为地表束中心位置处的局部平面波;然后,我们利用逆倾斜叠加将局部平面波转化为接收点处的时空域散射波场.在具体的实施过程中,我们提出一种以wavelet-bank方式实现的局部平面波合成方法,同现有的算法相比,可以在保持计算精度的同时,大大减少计算时间;此外,我们还利用最速下降法优化了高斯束的迭代循环过程,进一步提高了Born正演的计算效率.两个模型的应用效果证明,本文所提出的高斯束Born正演方法可以精确、高效的实现声波介质一次散射波场的正演模拟,为三维大规模地震波场的正演问题提供了一种切实可行的实现方案. 相似文献
13.
G.D. HUTTON 《Geophysical Prospecting》1987,35(6):681-699
The numerical modelling of seismic diffraction, e.g., at faults and other discontinuities, generally requires the use of fast approximate methods. The geophysicist responsible for the development of such numerical methods has a real need of exact solutions to certain ideal geometries to check the accuracy of his calculations. One such exact solution, which is available, is the acoustic wave solution to the perfectly reflecting wedge. The solution is three-dimensional and the source is an explosive point source. This model is ideal for seismic diffraction; the solution has the advantage of being exact, truly three-dimensional and of being in the convenient form of the temporal and spatial impulse response. More complicated sources which are extended in either space or time can, therefore, be modelled exactly by numerical integration. This paper presents some examples of the use of the perfectly reflecting wedge as a control model for an asymptotic high frequency diffraction modelling method. This control model has revealed that certain survey and wedge configurations can yield significant disagreement with, e.g., the Kirchhoff approximation. Such configurations could occur during VSP modelling when the survey lies in the near field or in the shadow zone of a high contrast fault. This control model has also been instructive in demonstrating why the high frequency, asymptotic, approximation is generally very good and has indicated a possible improvement to the Kirchhoff approximation for edge diffraction. 相似文献
14.
Morten Jakobsen 《Studia Geophysica et Geodaetica》2012,56(1):1-20
Forward seismic modelling in the acoustic approximation, for variable velocity but constant density, is dealt with. The wave
equation and the boundary conditions are represented by a volume integral equation of the Lippmann-Schwinger (LS) or Fredholm
type. A T-matrix (or transition operator) approach from quantum mechanical potential scattering theory is used to derive a
family of linear and nonlinear approximations (cluster expansions), as well as an exact numerical solution of the LS equation.
For models of 4D anomalies involving small or moderate contrasts, the Born approximation gives identical numerical results
as the first-order t-matrix approximation, but the predictions of an exact T-matrix solution can be quite different (depending
on spatial extention of the perturbations). For models of fluid-saturated cavities involving large or huge contrasts, the
first-order t-matrix approximation is much more accurate than the Born approximation, although it does not lead to significantly
more time-consuming computations. If the spatial extention of the perturbations is not too large, it is practical to use the
exact T-matrix solution which allows for arbitrary contrasts and includes all the effects of multiple scattering. 相似文献
15.
基于Born散射理论的二维黏声介质高斯波束正演 总被引：1，自引：0，他引：1
Born散射理论可以通过省略高阶项实现针对一次散射波场的模拟.在这一理论的基础上,本文提出了一种针对二维黏声介质的一次散射波场高斯束Born正演方法.在该方法中,格林函数通过一系列不同初射方向的高斯波束累加获得,可以计算多至走时波场,保证了正演算法的计算精度.同时为了提高计算效率,正演方法使用了wavelet-bank方式合成局部平面波.区别于针对声波介质正演的wavelet-bank使用方法,文中将介质黏滞性信息融入了局部平面波的wavelet-bank合成方法中,以此实现针对黏声介质的快速一次散射波场模拟.两个模型的计算结果表明:本文提出的黏声介质高斯波束正演方法具有良好的计算精度以及较高的计算效率. 相似文献
16.
This paper describes least‐squares reverse‐time migration. The method provides the exact adjoint operator pair for solving the linear inverse problem, thereby enhancing the convergence of gradient‐based iterative linear inversion methods. In this formulation, modified source wavelets are used to correct the source signature imprint in the predicted data. Moreover, a roughness constraint is applied to stabilise the inversion and reduce high‐wavenumber artefacts. It is also shown that least‐squares migration implicitly applies a deconvolution imaging condition. Three numerical experiments illustrate that this method is able to produce seismic reflectivity images with higher resolution, more accurate amplitudes, and fewer artefacts than conventional reverse‐time migration. The methodology is currently feasible in 2‐D and can naturally be extended to 3‐D when computational resources become more powerful. 相似文献
17.
复杂介质可控源电磁勘探数值模拟及反演算法的研究一直是国内外地球物理学者研究的热点。本文对复杂介质可控源电磁勘探快速正反演算法研究进行综述,重点对复杂介质快速正反演算法及应用进行分析,指出高效并行、特殊边界条件或将是其真正实用化的关键,当前仍然是极具挑战的研究方向。着重对未受关注的可控源电磁法复杂介质积分方程法正反演算法及其应用研究,如二维、2.5维快速正反演算法;地面、井筒电磁勘探实例、起伏地形异常场模拟等进行讨论。指出国内积分方程法的研究相对滞后,但应用前景较可观;特别是大尺度隐伏资源勘探领域,高精度、高效电磁勘探正反演需求较迫切。通过体积分方程法快速正反演算例分析,表明该方法可适用于大尺度勘探生产,具有较好实用性。复杂地形模拟,高效正反演算法等是积分方程法实用化的关键。 相似文献
18.
Numerical electromagnetic modeling by the finite-difference or finite-element methods leads to a large sparse system of linear algebraic equations. Fast direct methods, requiring an order of at most q log q arithmetic operations to solve a system of q equations, cannot easily be applied to such a system. This paper describes the iterative application of a fast method, namely cyclic reduction, to the numerical solution of the Helmholtz equation with a piecewise constant imaginary coefficient of the absolute term in a plane domain. By means of numerical tests the advantages and limitations of the method compared with classical direct methods are discussed. The iterative application of the cyclic reduction method is very efficient if one can exploit a known solution of a similar (e.g., simpler) problem as the initial approximation. This makes cyclic reduction a powerful tool in solving the inverse problem by trial-and-error. 相似文献
19.
Ahmed Salem Sheona Masterton Simon Campbell J. Derek Fairhead Jade Dickinson Colm Murphy 《Geophysical Prospecting》2013,61(5):1065-1076
Full Tensor Gravity Gradiometry (FTG) data are routinely used in exploration programmes to evaluate and explore geological complexities hosting hydrocarbon and mineral resources. FTG data are typically used to map a host structure and locate target responses of interest using a myriad of imaging techniques. Identified anomalies of interest are then examined using 2D and 3D forward and inverse modelling methods for depth estimation. However, such methods tend to be time consuming and reliant on an independent constraint for clarification. This paper presents a semi‐automatic method to interpret FTG data using an adaptive tilt angle approach. The present method uses only the three vertical tensor components of the FTG data (Tzx, Tzy and Tzz) with a scale value that is related to the nature of the source (point anomaly or linear anomaly). With this adaptation, it is possible to estimate the location and depth of simple buried gravity sources such as point masses, line masses and vertical and horizontal thin sheets, provided that these sources exist in isolation and that the FTG data have been sufficiently filtered to minimize the influence of noise. Computation times are fast, producing plausible results of single solution depth estimates t hat relate directly to anomalies. For thick sheets, the method can resolve the thickness of these layers assuming the depth to the top is known from drilling or other independent geophysical data. We demonstrate the practical utility of the method using examples of FTG data acquired over the Vinton Salt Dome, Louisiana, USA and basalt flows in the Faeroe‐Shetland Basin, UK. A major benefit of the method is the ability to quickly construct depth maps. Such results are used to produce best estimate initial depth to source maps that can act as initial models for any detailed quantitative modelling exercises using 2D/3D forward/inverse modelling techniques. 相似文献
20.
A parallel,scalable and memory efficient inversion code for very large‐scale airborne electromagnetics surveys 下载免费PDF全文
下载免费PDF全文 Esben Auken 《Geophysical Prospecting》2015,63(2):495-507
Over the past decade the typical size of airborne electromagnetic data sets has been growing rapidly, along with an emerging need for highly accurate modelling. One‐dimensional approximate inversions or data transform techniques have previously been employed for very large‐scale studies of quasi‐layered settings but these techniques fail to provide the consistent accuracy needed by many modern applications such as aquifer and geological mapping, uranium exploration, oil sands and integrated modelling. In these cases the use of more time‐consuming 1D forward and inverse modelling provide the only acceptable solution that is also computationally feasible. When target structures are known to be quasi layered and spatially coherent it is beneficial to incorporate this assumption directly into the inversion. This implies inverting multiple soundings at a time in larger constrained problems, which allows for resolving geological layers that are undetectable using simple independent inversions. Ideally, entire surveys should be inverted at a time in huge constrained problems but poor scaling properties of the underlying algorithms typically make this challenging. Here, we document how we optimized an inversion code for very large‐scale constrained airborne electromagnetic problems. Most importantly, we describe how we solve linear systems using an iterative method that scales linearly with the size of the data set in terms of both solution time and memory consumption. We also describe how we parallelized the core region of the code, in order to obtain almost ideal strong parallel scaling on current 4‐socket shared memory computers. We further show how model parameter uncertainty estimates can be efficiently obtained in linear time and we demonstrate the capabilities of the full implementation by inverting a 3327 line km SkyTEM survey overnight. Performance and scaling properties are discussed based on the timings of the field example and we describe the criteria that must be fulfilled in order to adapt our methodology for similar type problems. 相似文献