VTI介质速度与δ参数qP波全波形反演

获取准确的速度与各向异性参数模型,是全波形反演的主要目标.由于各向异性参数的敏感性较差,常规全波形反演方法很难同时得到满意的速度和各向异性参数模型.本文提出一种新的VTI介质qP波全波形反演方法.采用动校正速度参数化方式得到新的VTI介质qP波方程,改善各向异性参数δ对近偏移距数据的敏感性.在新的方程中,推导了VTI介质全波形反演梯度公式.基于敏感核分析设计了合理的分步反演策略,来缓解不同参数之间的串扰,进而提高速度和各向异性参数的反演精度.模型算例表明,新的反演策略能够有效提高速度和δ参数的反演精度.分步反演方法在非线性更强的各向异性反演中,能够得到更接近真实值的反演结果.     

基于Born敏感核函数的VTI介质多参数全波形反演

本文基于VTI介质拟声波方程,利用散射积分原理,在Born近似下导出了速度与各向异性参数的敏感核函数,同时结合作者前期研究提出的矩阵分解算法实现了一种新的VTI介质多参数全波形反演方法.矩阵分解算法通过对核函数-向量乘进行具有明确物理含义的向量-标量乘分解累加运算实现目标函数一阶方向或二阶方向的直接求取,从而避免了庞大核函数矩阵与Hessian矩阵的存储,该方法同时可以大大降低常规全波形反演在计算二阶方向时的庞大计算量.为了克服不同参数对波场影响程度的不同,本文利用作者前期在VTI介质射线走时层析成像研究中提出的分步反演策略实现了多参数联合全波形反演.理论模型实验表明,本文提出的基于Born敏感核函数的各向异性矩阵分解全波形反演方法可以获得较好的多参数反演结果.     

变密度声波方程多参数全波形反演策略

多参数全波形反演中各参数之间的相互耦合增加了反演的非线性程度.通过分析各参数之间的相互影响,提出合理的多参数反演策略是解决该问题的有效途径.本文从变密度声波方程出发,首先研究了密度在速度反演中的重要作用,然后分析了速度对密度反演的影响程度,进而提出了一种有利于速度、密度分步联合反演的策略.第一步,利用给定的初始模型对速度、密度进行同时反演,得到比较可靠的速度反演结果;第二步,利用第一步反演得到的速度和给定的初始密度作为初始模型,继续进行双参数同时反演,这样可以同时得到比较可靠的速度、密度反演结果.为了进一步提高反演精度,将第二步反演得到的速度、密度作为初始模型,再进行下一轮双参数联合反演.二维理论模型实验结果充分说明了本文提出的这种反演策略的有效性.     

基于Born敏感核函数的速度、密度双参数全波形反演

速度、密度之间的相互耦合使得密度在多参数全波形反演中较难获得.本文将截断高斯-牛顿法用于声介质速度、密度双参数全波形反演,通过考虑近似Hessian矩阵中反映速度、密度相互作用的非主对角块元素,有效解决了多参数全波形反演中速度、密度之间的耦合问题,在不采用反演策略的情况下,仍能够获得精度较高的速度、密度反演结果.常规的截断牛顿类全波形反演通常利用一阶伴随状态法求取目标函数对模型参数的梯度,利用二阶伴随状态法或有限差分法求解Hessian-向量乘,在每一步内循环迭代过程中需要额外求解两次正演问题,计算量较大.本文基于Born近似,将梯度计算中的核函数-向量乘表示为具有明确物理意义的向量-标量乘的累加运算,同时将Hessian-向量乘转化为两次核函数-向量乘,无需额外求解正演问题,有效降低了计算量.数值实验证明了本文提出的方法的有效性.     

各向异性介质弹性波多参数全波形反演

各向异性介质弹性波方程全波形反演过程中多参数之间的相互耦合,使得弱参数在反演过程中难得到理想的结果.本文以VTI介质为例,在各参数辐射模式分析的基础上,基于改进的散射积分算法实现目标函数梯度的直接求取,进一步构建高斯牛顿方向,实现Hessian矩阵的有效利用,以考虑Hessian矩阵非主对角线元素包含的各参数间的耦合效应,在不使用任何反演策略的情况下实现高精度的VTI介质弹性波方程多参数同步反演.同时,该方法在计算过程中无需存储庞大的核函数矩阵,且无需传统截断牛顿法中额外的正演计算,因此内存占用小,计算效率高.本文数值试验验证了该方法的有效性,为各向异性多参数全波形反演提供了一种新的解决方案.

     

基于修正拟牛顿公式的全波形反演

波形反演是一种利用全波场信息,通过最小化预测波场和实际波场的残差来揭示地下岩性和构造信息的方法.本文首先简述了常规拟牛顿算法的原理,之后利用一种新的拟牛顿公式对Davidon-Fletcher-Powell(DFP)和Broyden-Fletcher-Goldfarb-Shanno(BFGS)算法进行了修正,改进后的BFGS算法在近似Hessian矩阵逆矩阵时,不仅考虑了梯度和模型信息,还加入了目标函数本身的信息,而且对于每次迭代,基本没有增加计算量.数值试验表明,相对常规拟牛顿方法,修正BFGS算法在保证反演精度的同时,明显提高了反演效率.     

非均匀流-固边界耦合介质多参数全波形反演方法

海洋勘探环境可以抽象为下伏固体与上覆流体相互耦合的介质,本文针对流-固边界耦合介质提出了一种高效、稳定的多参数（速度和密度）全波形反演方法.本文采用弹性波一阶位移-应力方程作为过渡层耦合声波压力方程与弹性波位移方程来模拟耦合环境,相比于传统的交错网格建模方法或者构建连续性条件,本文提出的方法在正演精度和稳定性上凸显出很大优势,极大降低了计算内存.反演策略对多参数全波形反演至关重要,由于不同参数之间的相互耦合使得密度在多参数全波形反演中较难获得,因此本文将非均匀流-固边界耦合介质多参数全波形反演分为两个步骤完成：第一步利用变密度声波方程结合推导出的密度梯度算子进行纵波速度和密度的双参数反演;第二步根据链式法则求取横波速度的梯度,结合第一步的反演结果使用流-固边界耦合方程反演横波速度.最后通过与声波动方程数值模拟结果对比证明正演算法的准确性;上覆流体的Marmousi-2模型的数值试验测试说明反演方法的有效性和适应性.

     

基于改进全变差正则化的GPR多尺度全波形双参数同步反演

针对探地雷达（GPR）双参数全波形反演中电导率反演精度差、双参数存在串扰现象、反演计算量大、易陷入局部极值等问题.作者将具有多参数调节功能的L-BFGS算法引入到GPR时间域全波形反演中,它避免了对Hessian矩阵的直接存储与精确求解,减小了存储量和计算量.结合参数调节因子的选取,有效减小了同步反演时介电常数与电导率的串扰影响,在不降低介电常数反演精度的前提下,提高电导率参数的反演精度.通过在反演目标函数中加载改进全变差正则化方法,提高了反演的稳定性,使目标体边缘轮廓更加清晰.首先以简单模型为例,对比了单尺度反演与多尺度串行反演策略的优劣,说明多尺度串行反演有利于逐步搜索全局最优解;而开展参数调节因子的选取实验,说明合适的参数调节因子可以有效改善介质电导率的反演精度;测试了不同正则化的反演效果,表明改进全变差正则化能提高反演稳定性,显著降低模型重构误差.最后,分别对含噪合成数据和实测数据进行了反演测试,说明本文提出的多尺度、双参数反演具有较强的鲁棒性,能提供更丰富的信息约束,重构图像界面清晰、反演效果好.

     

基于改进全变差正则化的GPR多尺度全波形双参数同步反演

针对探地雷达（GPR）双参数全波形反演中电导率反演精度差、双参数存在串扰现象、反演计算量大、易陷入局部极值等问题.作者将具有多参数调节功能的L-BFGS算法引入到GPR时间域全波形反演中,它避免了对Hessian矩阵的直接存储与精确求解,减小了存储量和计算量.结合参数调节因子的选取,有效减小了同步反演时介电常数与电导率的串扰影响,在不降低介电常数反演精度的前提下,提高电导率参数的反演精度.通过在反演目标函数中加载改进全变差正则化方法,提高了反演的稳定性,使目标体边缘轮廓更加清晰.首先以简单模型为例,对比了单尺度反演与多尺度串行反演策略的优劣,说明多尺度串行反演有利于逐步搜索全局最优解;而开展参数调节因子的选取实验,说明合适的参数调节因子可以有效改善介质电导率的反演精度;测试了不同正则化的反演效果,表明改进全变差正则化能提高反演稳定性,显著降低模型重构误差.最后,分别对含噪合成数据和实测数据进行了反演测试,说明本文提出的多尺度、双参数反演具有较强的鲁棒性,能提供更丰富的信息约束,重构图像界面清晰、反演效果好.     

基于优化参数Adam算法的全波形反演

常规的全波形反演(FWI)计算得到的梯度往往不做优化处理, 并且每次计算模型更新量时还需要额外的波场延拓计算来获取迭代步长, 导致收敛效率和反演精度降低.本文将深度学习中的Adam算法引入到全波形反演中来, 其可在仅付出极小计算代价的前提下实现梯度的优化处理, 由梯度直接计算出模型更新量, 避免了迭代步长的计算, 且能显著提升收敛效率和反演精度; 同时针对Adam算法的默认参数优化和选取问题, 通过数值实验系统分析了不同参数的全波形反演效果, 并给出了更适合于全波形反演的优化参数.实验结果表明, 相比于默认参数的Adam算法以及L-BFGS算法的全波形反演, 基于优化参数的Adam算法其收敛速度和反演精度更高.

     

Improved hybrid iterative optimization method for seismic full waveform inversion

In full waveform inversion (FWI), Hessian information of the misfit function is of vital importance for accelerating the convergence of the inversion; however, it usually is not feasible to directly calculate the Hessian matrix and its inverse. Although the limited memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) or Hessian-free inexact Newton (HFN) methods are able to use approximate Hessian information, the information they collect is limited. The two methods can be interlaced because they are able to provide Hessian information for each other; however, the performance of the hybrid iterative method is dependent on the effective switch between the two methods. We have designed a new scheme to realize the dynamic switch between the two methods based on the decrease ratio (DR) of the misfit function (objective function), and we propose a modified hybrid iterative optimization method. In the new scheme, we compare the DR of the two methods for a given computational cost, and choose the method with a faster DR. Using these steps, the modified method always implements the most efficient method. The results of Marmousi and over thrust model testings indicate that the convergence with our modified method is significantly faster than that in the L-BFGS method with no loss of inversion quality. Moreover, our modified outperforms the enriched method by a little speedup of the convergence. It also exhibits better efficiency than the HFN method.     

Full waveform inversion using oriented time‐domain imaging method for vertical transverse isotropic media

Full waveform inversion for reflection events is limited by its linearised update requirements given by a process equivalent to migration. Unless the background velocity model is reasonably accurate, the resulting gradient can have an inaccurate update direction leading the inversion to converge what we refer to as local minima of the objective function. In our approach, we consider mild lateral variation in the model and, thus, use a gradient given by the oriented time‐domain imaging method. Specifically, we apply the oriented time‐domain imaging on the data residual to obtain the geometrical features of the velocity perturbation. After updating the model in the time domain, we convert the perturbation from the time domain to depth using the average velocity. Considering density is constant, we can expand the conventional 1D impedance inversion method to two‐dimensional or three‐dimensional velocity inversion within the process of full waveform inversion. This method is not only capable of inverting for velocity, but it is also capable of retrieving anisotropic parameters relying on linearised representations of the reflection response. To eliminate the crosstalk artifacts between different parameters, we utilise what we consider being an optimal parametrisation for this step. To do so, we extend the prestack time‐domain migration image in incident angle dimension to incorporate angular dependence needed by the multiparameter inversion. For simple models, this approach provides an efficient and stable way to do full waveform inversion or modified seismic inversion and makes the anisotropic inversion more practicable. The proposed method still needs kinematically accurate initial models since it only recovers the high‐wavenumber part as conventional full waveform inversion method does. Results on synthetic data of isotropic and anisotropic cases illustrate the benefits and limitations of this method.     

基于多网格的频率域全波形反演(英文)

频率域全波形反演虽然克服了时间方向上的局部极小值问题,但是地下介质的复杂性使其在空间域仍然存在局部极小值缺陷。在优化梯度法基础上,本文采用预条件双共轭梯度稳定算法和多重网格方法计算反演中的波场传播和目标函数的梯度,在保证计算速度的同时,减小计算机内存的消耗。频率域波形反演和多重网格的多尺度性质有效改善问题极小值缺陷,加快反演的收敛速度。以局部非均匀的三孔模型和Marmousi模型的数值模拟结果验证了该算法的有效性。     

Full waveform inversion and the truncated Newton method: quantitative imaging of complex subsurface structures

Full waveform inversion is a powerful tool for quantitative seismic imaging from wide‐azimuth seismic data. The method is based on the minimization of the misfit between observed and simulated data. This amounts to the solution of a large‐scale nonlinear minimization problem. The inverse Hessian operator plays a crucial role in this reconstruction process. Accounting accurately for the effect of this operator within the minimization scheme should correct for illumination deficits, restore the amplitude of the subsurface parameters, and help to remove artefacts generated by energetic multiple reflections. Conventional minimization methods (nonlinear conjugate gradient, quasi‐Newton methods) only roughly approximate the effect of this operator. In this study, we are interested in the truncated Newton minimization method. These methods are based on the computation of the model update through a matrix‐free conjugate gradient solution of the Newton linear system. We present a feasible implementation of this method for the full waveform inversion problem, based on a second‐order adjoint state formulation for the computation of Hessian‐vector products. We compare this method with conventional methods within the context of 2D acoustic frequency full waveform inversion for the reconstruction of P‐wave velocity models. Two test cases are investigated. The first is the synthetic BP 2004 model, representative of the Gulf of Mexico geology with high velocity contrasts associated with the presence of salt structures. The second is a 2D real data‐set from the Valhall oil field in North sea. Although, from a computational cost point of view, the truncated Newton method appears to be more expensive than conventional optimization algorithms, the results emphasize its increased robustness. A better reconstruction of the P‐wave velocity model is provided when energetic multiple reflections make it difficult to interpret the seismic data. A better trade‐off between regularization and resolution is obtained when noise contamination of the data requires one to regularize the solution of the inverse problem.     

基于声学全波形反演的油气藏地震成像方法

岩性油气藏在我国天然气勘探开发中占有非常重要的位置,其分布区域的成像是合理布设井位,提高钻井成功率的关键之一.本文首先基于地下介质的声学近似和波场回传理论,利用频率域单程声波方程延拓计算地震波场,进行全波形反演,获得地层密度和体积模量的定量成像,并依据油气藏物性特征和流体饱和多孔介质岩石物理模型,简要讨论了孔隙度和饱和度与密度及体积模量的关系,明确了地震油气藏成像新概念.在此基础上,定义了基于流体体积模量和孔隙度的成像函数,进行油气藏成像.理论模型计算表明该方法是可行的.通过对西部地区某气田二维地震数据处理,实现了致密砂岩气藏成像,钻井结果证实了气藏区域成像位置的准确性和方法的有效性.     

基于常分数阶拉普拉斯算子的黏声方程重建速度与衰减参数的全波形反演方法

地震波在地下介质传播过程中由于非弹性衰减的存在将导致能量损失和相位变化, 精确的速度与衰减参数建模对油气识别、提高强衰减介质中地震波成像的质量都起着至关重要的作用.常分数阶拉普拉斯算子黏声方程由于完全分离的速度频散项与振幅衰减项的优势, 以及在强非均质衰减介质中可以高精度求解的特点, 已被应用于速度与衰减参数的建模中.本文将二阶常分数阶拉普拉斯算子黏声方程拆分为等价的一阶方程组, 并在此一阶方程组的基础上推导出新的梯度公式与伴随方程, 建立了一种新的速度与衰减参数同时重建的全波形反演方法.相较于原二阶常分数阶拉普拉斯算子黏声方程建立的全波形反演流程, 数值实验表明, 新建立的反演流程可以有效避免原梯度数值计算中的噪声, 尤其是可以有效提高衰减参数梯度的反演精度, 从而显著提高反演的收敛速度与反演精度.

     

Target-level waveform inversion: a prospective application of the convolution-type representation for the acoustic wavefield

Nowadays, full-waveform inversion, based on fitting the measured surface data with modelled data, has become the preferred approach to recover detailed physical parameters from the subsurface. However, its application is computationally expensive for large inversion domains. Furthermore, when the subsurface has a complex geological setting, the inversion process requires an appropriate pre-conditioning scheme to retrieve the medium parameters for the desired target area in a reliable manner. One way of dealing with both aspects is by waveform inversion schemes in a target-oriented fashion. Therefore, we propose a prospective application of the convolution-type representation for the acoustic wavefield in the frequency–space domain formulated as a target-oriented waveform inversion method. Our approach aims at matching the observed and modelled upgoing wavefields at a target depth level in the subsurface, where the seismic wavefields, generated by sources distributed above this level, are available. The forward modelling is performed by combining the convolution-type representation for the acoustic wavefield with solving the two-way acoustic wave-equation in the frequency–space domain for the target area. We evaluate the effectiveness of our inversion method by comparing it with the full-domain full-waveform inversion process through some numerical examples using synthetic data from a horizontal well acquisition geometry, where the sources are located at the surface and the receivers are located along a horizontal well at the target level. Our proposed inversion method requires less computational effort and, for this particular acquisition, it has proven to provide more accurate estimates of the target zone below a complex overburden compared to both full-domain full-waveform inversion process and local full-waveform inversion after applying interferometry by multidimensional deconvolution to get local-impulse responses.     

Optimized experimental design for seismic full waveform inversion: A computationally efficient method including a flexible implementation of acquisition costs

Optimized experimental design aims at reducing the cost of a seismic survey by identifying the optimal locations and amounts of sources and receivers. While the acquisition design in the context of seismic imaging applies criteria like fold, offset and spatial sampling, different attributes such as the sensitivity kernels are more relevant for seismic full waveform inversion. An ideal measure to quantify the goodness of an acquisition design relies on the eigenvalue spectrum of the approximate Hessian matrix, but this technique is computationally too expensive for practical use. A more affordable goodness measure has been proposed in the past, but we demonstrate that this measure is inappropriate for target‐oriented optimized experimental design. To address those issues, we derived a sequential receiver‐based procedure using a goodness measure based on the determinant of the approximate Hessian matrix. We show with numerical tests that it efficiently provides an optimized design for target‐oriented as well as for extensive full waveform inversion. This design allows a better reconstruction of the subsurface than an evenly spaced acquisition geometry. Furthermore, the optimization algorithm itself can easily be parallelized, therefore making it attractive for applications to large‐scale three‐dimensional surveys. In addition, our algorithm is able to incorporate variable costs, representing any kind of acquisition‐related costs, for every individual source location. The combined optimization with respect to the information content of sources and to the true cost will allow a more comprehensive and realistic survey planning and has a high potential for further applications.