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1.
2.5-D modeling and inversion techniques are much closer to reality than the simple and traditional 2-D seismic wave modeling
and inversion. The sensitivity kernels required in full waveform seismic tomographic inversion are the Fréchet derivatives
of the displacement vector with respect to the independent anisotropic model parameters of the subsurface. They give the sensitivity
of the seismograms to changes in the model parameters. This paper applies two methods, called ‘the perturbation method’ and
‘the matrix method’, to derive the sensitivity kernels for 2.5-D seismic waveform inversion. We show that the two methods
yield the same explicit expressions for the Fréchet derivatives using a constant-block model parameterization, and are available
for both the line-source (2-D) and the point-source (2.5-D) cases. The method involves two Green’s function vectors and their
gradients, as well as the derivatives of the elastic modulus tensor with respect to the independent model parameters. The
two Green’s function vectors are the responses of the displacement vector to the two directed unit vectors located at the
source and geophone positions, respectively; they can be generally obtained by numerical methods. The gradients of the Green’s
function vectors may be approximated in the same manner as the differential computations in the forward modeling. The derivatives
of the elastic modulus tensor with respect to the independent model parameters can be obtained analytically, dependent on
the class of medium anisotropy. Explicit expressions are given for two special cases—isotropic and tilted transversely isotropic
(TTI) media. Numerical examples are given for the latter case, which involves five independent elastic moduli (or Thomsen
parameters) plus one angle defining the symmetry axis. 相似文献
2.
In order to perform resistivity imaging, seismic waveform tomography or sensitivity analysis of geophysical data, the Fréchet derivatives, and even the second derivatives of the data with respect to the model parameters, may be required. We develop a practical method to compute the relevant derivatives for 2.5D resistivity and 2.5D frequency-domain acoustic velocity inversion. Both geophysical inversions entail the solution of a 2.5D Helmholtz equation. First, using differential calculus and the Green's functions of the 2.5D Helmholtz equation, we strictly formulate the explicit expressions for the Fréchet and second derivatives, then apply the finite-element method to approximate the Green's functions of an arbitrary medium. Finally, we calculate the derivatives using the expressions and the numerical solutions of the Green's functions. Two model parametrization approaches, constant-point and constant-block, are suggested and the computational efficiencies are compared. Numerical examples of the derivatives for various electrode arrays in cross-hole resistivity imaging and for cross-hole seismic surveying are demonstrated. Two synthetic experiments of resistivity and acoustic velocity imaging are used to illustrate the method. 相似文献
3.
Doug Oldenburg 《Surveys in Geophysics》1990,11(2-3):231-270
This paper explores some of the newer techniques for acquiring and inverting electromagnetic data. Attention is confined primarily to the 2d magnetotelluric (MT) problem but the inverse methods are applicable to all areas of EM induction. The basis of the EMAP technique of Bostick is presented along with examples to illustrate the efficacy of that method in structural imaging and in overcoming the deleterious effects of near-surface distortions of the electric field. Reflectivity imaging methods and the application of seismic migration techniques to EM problems are also explored as imaging tools. Two new approaches to the solution of the inverse problem are presented. The AIM (Approximate Inverse Mapping) inversion of Oldenburg and Ellis uses a new way to estimate a perturbation in an iterative solution which does not involve linearization of the equations. The RRI (Rapid Relaxation Inverse) of Smith and Booker shows how approximate Fréchet derivatives and sequences of 1d inversions can be used to develop a practical inversion algorithm. The overview is structured to provide insight about the latest inversion techniques and also to touch upon most areas of the inverse problem that must be considered to carry out a practical inversion. These include model parameterization, methods of calculating first order sensitivities, and methods for setting up a linearized inversion. 相似文献
4.
低频成分缺失和地下速度强烈变化会导致严重的周期跳现象,是地震数据全波形反演的难题.通过对地震数据加时间阻尼和时间积分降主频处理,提出了一种可有效去除周期跳现象的多主频波场时间阻尼全波形反演方法.由浅到深的速度不准确会造成波形走时失配和走时失配的累积.浅部速度的准确反演可有效地减小深部波形走时失配与周期跳现象.对地震数据施加时间阻尼得到时间阻尼数据,利用不同阻尼值的时间阻尼地震数据实现由浅到深的全波形反演.低主频波场的周期跳现象相对高主频波场的要弱.对地震波场进行不同阶的时间积分以得到不同主频的波场,把低主频波场的全波形反演结果作为高主频波场全波形反演的初始模型.应用缺失4 Hz以下频谱成分的二维盐丘模型合成数据验证所提出的全波形反演方法的正确性和有效性,数值试验结果显示多主频波场的时间阻尼全波形反演方法对缺失低频成分地震数据和地下速度强烈变化具有很好的适应性. 相似文献
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Sufficient low‐frequency information is essential for full‐waveform inversion to get the global optimal solution. Multi‐scale envelope inversion was proposed using a new Fréchet derivative to invert the long‐wavelength component of the model by directly using the low‐frequency components contained in an envelope of seismic data. Although the new method can recover the main structure of the model, the inversion quality of the model bottom still needs to be improved. Reflection waveform inversion reduces the dependence of inversion on low‐frequency and long‐offset data by using travel‐time information in reflected waves. However, when the underground medium contains strong contrast or the initial model is far away from the true model, it is hard to get reliable reference reflectors for the generation of reflected waves. Here, we propose a combination inversion algorithm, i.e., reflection multi‐scale envelope inversion, to overcome the limitations of multi‐scale envelope inversion and reflection waveform inversion. First, wavefield decomposition was introduced into the multi‐scale envelope inversion to improve the inversion quality of the long‐wavelength components of the model. Then, after the initial model had been established to be accurate enough, migration and de‐migration were introduced to achieve multi‐scale reflection waveform inversion. The numerical results of the salt‐layer model and the SEG/EAGE salt model verified the validity of the proposed approach and its potential. 相似文献
7.
使用阻尼最小二乘法进行震源参数和地壳三维速度结构的走时联合反演．所用资料为Ｓ波和Ｐ波到时差,并用人工地震资料的二维解释结果作为三维速度模型的特定约束条件．为建立初始模型,又利用天然地震构成了准二维剖面．在走时反演基础上,利用遗传算法进行了几个地震事件的波形反演尝试,并对走时反演获得的地壳速度结构模型的局部进行了修正．以３４°～４２°Ｎ,９４°～１１２°Ｅ作为研究区域,在该区域中收集了１９８６年以来大量地震的Ｓ波和Ｐ波到时差资料,７条人工地震二维速度剖面资料和２个数字化地震台的几个地震的三分向记录资料．对这些资料进行了处理,最后得出了０～２５ｋｍ深度不同截面的速度分布,并对所得结果进行了分析． 相似文献
8.
波动方程深度偏移是解决复杂地质体成像的关键技术,基于波动方程的速度建模为其提供更为精确的速度模型.频率域波形反演是目前研究最为广泛的波动方程速度建模方法之一,它推动了波形反演在勘探尺度下的应用.本文通过对频率域波形反演的实现,分析对比了其有效执行过程中与频率相关的影响因素.介绍了时间域的多尺度反演方法在频率域的一种实现方式,对比分析了输入数据的频点带宽和应用的子波频带范围不同时对反演结果的影响.本文通过设计的山地地质模型对频率域波形反演进行了测试和对比,得到的结论为频率域波形反演的有效计算提供了依据和参考. 相似文献
9.
We propose an optimized method to compute travel times for seismic inversion problems. It is a hybrid method combining several approaches to deal with travel time computation accuracy in unstructured meshes based on tetrahedral elementary cells. As in the linear travel time interpolation method, the proposed approach computes travel times using seismic ray paths. The method operates in two sequential steps: At a first stage, travel times are computed for all nodes of the mesh using a modified version of the shortest path method. The difference with the standard version is that additional secondary nodes (called tertiary nodes) are added temporarily around seismic sources in order to improve accuracy with a reasonable increase in computational cost. During the second step, the steepest travel time gradient method is used to trace back ray paths for each source–receiver pair. Travel times at each receiver are then recomputed using slowness values at the intersection points between the ray path and the traversed cells. A number of numerical tests with an array of different velocity models, mesh resolutions and mesh topologies have been carried out. These tests showed that an average relative error in the order of 0.1% can be achieved at a computational cost that is suitable for travel time inversion. 相似文献
10.
WTW(Wave equation traveltime+Waveform inversion)反演是基于波动方程的走时反演（WT反演）和波形反演的联合反演方法.WT反演利用波动方程计算走时和走时关于速度的导数，和传统以射线为基础的走时反演相比，具有不必射线追踪、不必拾取初至、不必高频假设以及初始模型和实际模型差别较大时也能较好收敛等优点，但WT反演与波形反演相比其结果分辨率低.与之互补的是，波形反演的反演结果分辨率高，但是当所给初始模型和实际模型相差太大时，波形反演迭代算法容易陷入局部极小点.可见结合两种方法的WTW反演是一种比较好的联合反演方法.常规WTW迭代算法是首先以WT反演为主反演得到地质模型的整体特征，然后再以波形反演为主反演模型细节，该算法耗时和占用计算机存储空间接近WT反演或波形反演的两倍.为了节省运算耗时和计算机存储空间，往往采取首先单独利用WT反演然后再单独利用波形反演的算法.这样做的缺点是不能紧密结合两种反演方法，使得它们的优缺点在每一次迭代中无法得到互补，从而影响了最终的反演结果.针对以上事实，本文提出一种新的方法实现WTW，使得WTW运算速度和存储空间在任何情况下等同于WT反演或波形反演.模型计算表明新的算法具有更好的收敛性. 相似文献
11.
The lithosphere of the South American continent has been studied little, especially in northern Brazil (the Amazonian region). A 3D lithospheric S-velocity model of South America was obtained by first carrying out Rayleigh and Love wave group-velocity tomography, and then inverting the regionalized dispersion curves. Fundamental mode group velocities were measured using a Multiple Filtering Technique. More than 12,000 paths were examined and about 6000 Rayleigh- and 3500 Love-wave dispersion curves with good quality were retrieved. Checkerboard tests showed that our dataset permits the resolution of features 400-800 km across laterally in the central part of the continent from crustal to upper mantle depths. Our results confirm previous tomographic results and correlate well with the major geological provinces of South America. The 3D S-velocity model confirms both regional features of SE Brazil from P-wave travel-time tomography and continental-scale features of central and western South America from waveform inversion, e.g., lowest velocities in the Andean upper mantle; three parts of the Nazca plate with flat subduction; strong low-velocity anomalies in the upper-mantle depth beneath the Chaco basin. Furthermore, our 3D model revealed new features in the South American continent: (1) high velocities in the lower crust were consistently found in regions with high Bouguer or free-air anomalies; (2) the NE-SW trending TransBrasiliano shear zone was delineated by a NE-SW low-velocity belt at lithospheric depths; (3) the eastern Amazonian craton appears to have thicker lithosphere than the western craton; (4) in areas of Archean nuclei located in the northeastern Guaporé shield and southeastern São Francisco craton, high velocity anomalies were found down to 150 km. 相似文献
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The propagation of seismic waves through Earth models with slightly random lateral and vertical inhomogeneities superimposed on one composed of layers with vertical velocity gradients was investigated. The maximum deviation of velocity from a mean value at a given depth and a correlation distance derived from a two-dimensional smoothing filter were two parameters used to vary the amplitude and size of the velocity anomalies. The resulting models show short discontinuous reflectors scattered about at various depths throughout the model, and are thus in agreement with many deep seismic reflection experiments. On the other hand numerical experiments using ray-tracing techniques showed that the effect of the lateral and vertical velocity anomalies is to scatter the energy, and break up the continuous travel-time lines from vertical gradient models into travel-time segments with different slopes similar to those observed in many long range seismic refraction experiments, and to those resulting from layering effects in the media. Many of the numerical experiments which modelled the random crust produced a Pg segment and a P* segment with an apparent Conrad discontinuity at a depth of 10–20 km, this apparent depth being related to the correlation distance.When a seismic wave propagates through a heterogeneous Earth the amount of its energy which is converted into scattered energy will be a function of the inhomogeneous characteristics of the medium through which it has passed. If a ray passes through a homogeneous Earth the energy arriving at an array station should be relatively coherent whereas if the ray encounters lateral and vertical inhomogeneities its energy will be incoherent and much more complex. A series of coherency measurements done on array recordings of earthquakes at various distances showed that large lateral and vertical variations in complexity exist for different ray paths through the Earth with the region below the 650 km discontinuity in the mantle tending to be much simpler than the region just below the lithosphere. 相似文献
14.
中国大陆中西部乃至全球造山带普遍具有复杂地壳结构.随着矿产资源勘探和深部探测研究的深入,探测造山带及盆山耦合区下方地壳精细结构正逐渐成为当前面临的巨大挑战.人工源深地震测深方法正越来越清晰地揭示出不同构造域地壳速度结构的基本特征,然而传统的层状结构模型参数化方法难以准确描述复杂地质模型,通常情况下多忽略速度结构的精细间断面且采用层边界平滑处理,难以满足地壳精细结构成像的发展要求.针对上述困难,本文采用最近发展的块状结构建模方案构建三维复杂地壳模型,基于逐段迭代射线追踪正演走时计算方法,推导了走时对三角形界面深度以及网格速度的偏导数,开展了非线性共轭梯度走时反演方法研究.发展了利用直达波和反射波等多震相走时数据对界面深度和网格速度的多参数联合反演方法,并引人不同种类震相数据的权系数和不同类型参数偏导数归一化的方法.数值算例表明,基于块状结构的非线性共轭梯度走时反演方法适用于复杂地壳结构模型,在利用人工源走时数据反演复杂地壳精细结构领域具有良好的应用前景. 相似文献
15.
A.G. Green 《Earth and Planetary Science Letters》1976,31(3):403-412
In this paper seismic rays are traced through proposed models of the East African Rift and the predicted travel-time residuals are compared to those observed at a number of African seismic stations. The velocity models are based on published gravity models of the East African Rift and empirical velocity-density relationships. Searle's (1970) revision of the models first proposed by Girdler et al. (1969), comprising a low-density, low-velocity asthenolith that partly replaces and thins the continental lithosphere beneath East Africa, is found to be compatible with most of the observed travel-time residuals. Results from the ray tracing suggest that the model may be improved by increasing the volume of normal mantle material between the two branches of the rift. Some of the interesting travel-time residuals associated with anomalous material away from the rift are also discussed. 相似文献
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针对传统射线层析存在的种种局限性,菲涅尔带走时层析成像摒弃了传统的数学射线,考虑到地震信号具有一定的频带宽度,中央射线附近的介质对地震波的传播产生不同程度的影响。本文提出了多频段组合菲涅尔带走时层析成像方法。该方法以频率域波动方程Born和Rytov近似为基础,推导出建立在带限地震波理论基础上的波动方程 Rytov 近似走时敏感核函数,实现第一菲涅尔带约束下的波动方程走时层析反演方法。同时由于多个频段的引入,充分利用低频段和高频段的特有优势,从而兼顾菲涅尔带层析的计算效率与分辨率。模型试算结果证明了本方法的有效性和稳定性。 相似文献
18.
通过把地层格架信息作用于立体层析Fréchet导数矩阵,使得更新后的速度模型呈现出符合地质规律的块状特征.地层格架信息基于立体层析反演中得到的反射点位置进行非规则B样条插值拟合得到,因此在反演中它将会随着反射点位置的更新自然得到更新.与前人提出的保边缘层析算法或多层立体层析算法相比,本文提出的地层格架正则化无需引入混合正则化项或定义某种复杂的混合速度格式,更为直接也更容易实现.理论和实际数据算例证实了该正则化技巧的稳健性和可靠性,能够得到与实际地质构造特征更为一致的地质一致性反演结果. 相似文献
19.
用慢度分块均匀正方形模型将介质参数化，仅在正方形单元的边界上设置计算结点，这些结点构成界面网．根据Ｈｕｖｓｅｎｓ和Ｆｅｒｍａｔ原理，由不断扩张、收缩的波前点扫描代替波前面搜索，在波前点附近点的局部最小走时计算中对波前点之间的走时使用双曲线近似，通过比较确定最小走时和相应的次级源位置，记录在以界面网点位置为指针的３个一维数组中．借助这些数组通过向源搜索可计算任意点（包括界面网以外的点）上的全局最小走时和射线路径．这一方法不受介质慢度差异大小限制，占内存少，计算速度较快，适于走时反演和以Ｍａｓｌｏｖ射线理论为基础的波场计算． 相似文献
20.
Seismic envelope inversion: reduction of local minima and noise resistance 总被引：3，自引：0，他引：3 
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下载免费PDF全文 Waveform inversion met severe challenge in retrieving long‐wavelength background structure. We have proposed to use envelope inversion to recover the large‐scale component of the model. Using the large‐scale background recovered by envelope inversion as new starting model, we can get much better result than the conventional full waveform inversion. By comparing the configurations of the misfit functional between the envelope inversion and the conventional waveform inversion, we show that envelope inversion can greatly reduce the local minimum problem. The combination of envelope inversion and waveform inversion can deliver more faithful and accurate final result with almost no extra computation cost compared to the conventional full waveform inversion. We also tested the noise resistance ability of envelope inversion to Gaussian noise and seismic interference noise. The results showed that envelope inversion is insensitive to Gaussian noise and, to a certain extent, insensitive to seismic interference noise. This indicates the robustness of this method and its potential use for noisy data. 相似文献