小尺度散射体稀疏最小二乘逆时偏移方法研究

地震勘探方法在深部固体矿产资源勘探中发展潜力巨大,同时也面临挑战.由于固体矿产资源地下分布呈现陡峭构造、尺度小,物性差异小的特点,常规偏移方法对小尺度矿体成像的分辨率提高有限.本文研究了一种基于稀疏促进约束的最小二乘逆时偏移方法.首先,将非均匀分布的矿体等效为随机介质,建立小尺度扰动的矿体模型;其次,改进现有最小二乘偏移方法,以稀疏模型为先验信息约束成像结果,并通过Curvelet变换压缩成像空间,经过多次迭代计算,可以提高小尺度散射体的成像分辨率;再次,对炮域记录进行随机震源编码,减少成像所需的炮集个数,通过稀疏促进约束条件,降低串扰噪声引起的成像误差.通过庐枞金属矿模型数值计算,验证本文方法可以较好的成像包含小尺度散射体的金属矿地质模型.

     

Time-domain sparsity promoting least-squares reverse time migration with source estimation

Least-squares reverse-time migration is well known for its capability to generate artefact-free true-amplitude subsurface images through fitting observed data in the least-squares sense. However, when applied to realistic imaging problems, this approach is faced with issues related to overfitting and excessive computational costs induced by many wave-equation solves. The fact that the source function is unknown complicates this situation even further. Motivated by recent results in stochastic optimization and transform-domain sparsity promotion, we demonstrate that the computational costs of inversion can be reduced significantly while avoiding imaging artefacts and restoring amplitudes. While powerful, these new approaches do require accurate information on the source-time function, which is often lacking. Without this information, the imaging quality deteriorates rapidly. We address this issue by presenting an approach where the source-time function is estimated on the fly through a technique known as variable projection. Aside from introducing negligible computational overhead, the proposed method is shown to perform well on imaging problems with noisy data and problems that involve complex settings such as salt. In either case, the presented method produces high-resolution high-amplitude fidelity images including an estimate for the source-time function. In addition, due to its use of stochastic optimization, we arrive at these images at roughly one to two times the cost of conventional reverse-time migration involving all data.     

同时震源数据的加权结构增强最小二乘逆时偏移

同时震源（Simultaneous-source,SS）地震采集技术能有效地提高地震数据采集效率,但直接对SS混合数据偏移成像会在最后的成像剖面中引入很强的串扰噪声.将SS数据偏移成像看作一个反演问题,利用最小二乘（Least-squares,LS）求解是压制SS直接成像中串扰噪声的一种有效尝试.构造增强滤波（Structure-enhancing filter,SE）约束的最小二乘逆时偏移（LSRTM）方法可以有效地压制SS数据成像中的串扰噪声,但SE实质为低通滤波,会将成像中的陡倾角等细节信息平滑涂抹,降低成像分辨率.本文在利用SE对LSRTM约束的基础上,提出了基于加权构造增强约束的LSRTM方法（WSE-LSRTM）并应用于SS数据的反演成像中.该方法不仅能够有效地压制串扰噪声（cross-talk）、保留结构信息,而且可以保护成像中的陡倾角结构不被过度平滑而破坏.在对简单模型和复杂Marmousi模型的数值测试中,该方法都取得了良好的效果.

     

一种新的针对反射波的逆时偏移真振幅成像条件

真振幅成像是一种代表性的定量估计模型参数扰动高波数部分的地震波成像方法.经典的真振幅成像方法在高频近似和理想照明假设条件下求取显式对角Hessian逆矩阵作为偏移振幅加权算子,用以校正波传播过程中的几何扩散效应,得到模型参数扰动的带限估计.真振幅保真成像方法在利用逆时偏移（RTM）框架实现时会产生低波数噪声,影响对高波数参数估计的精度.本文给出了一种新的基于RTM框架的真振幅保真成像条件,该成像条件针对反射波数据,在高频近似下散射模式对应正问题及Bayes反问题框架下导出.与传统基于高频渐进反演的波动方程成像方法类似,利用本文提出RTM成像条件能够保证计算结果与高频近似下反演结果的一致性.同时,利用本文提出RTM真振幅成像条件能够在成像过程中自动保真的消除传统真振幅RTM算法中存在低波数噪声,模型数值实验结果验证了本文方法的正确性和有效性.

     

一种新的针对反射波的逆时偏移真振幅成像条件

真振幅成像是一种代表性的定量估计模型参数扰动高波数部分的地震波成像方法.经典的真振幅成像方法在高频近似和理想照明假设条件下求取显式对角Hessian逆矩阵作为偏移振幅加权算子,用以校正波传播过程中的几何扩散效应,得到模型参数扰动的带限估计.真振幅保真成像方法在利用逆时偏移（RTM）框架实现时会产生低波数噪声,影响对高波数参数估计的精度.本文给出了一种新的基于RTM框架的真振幅保真成像条件,该成像条件针对反射波数据,在高频近似下散射模式对应正问题及Bayes反问题框架下导出.与传统基于高频渐进反演的波动方程成像方法类似,利用本文提出RTM成像条件能够保证计算结果与高频近似下反演结果的一致性.同时,利用本文提出RTM真振幅成像条件能够在成像过程中自动保真的消除传统真振幅RTM算法中存在低波数噪声,模型数值实验结果验证了本文方法的正确性和有效性.     

Three‐term inversion of prestack seismic data using a weighted l2, 1 mixed norm

We present a new inversion method to estimate, from prestack seismic data, blocky P‐ and S‐wave velocity and density images and the associated sparse reflectivity levels. The method uses the three‐term Aki and Richards approximation to linearise the seismic inversion problem. To this end, we adopt a weighted mixed l_{2, 1}‐norm that promotes structured forms of sparsity, thus leading to blocky solutions in time. In addition, our algorithm incorporates a covariance or scale matrix to simultaneously constrain P‐ and S‐wave velocities and density. This a priori information is obtained by nearby well‐log data. We also include a term containing a low‐frequency background model. The l_{2, 1} mixed norm leads to a convex objective function that can be minimised using proximal algorithms. In particular, we use the fast iterative shrinkage‐thresholding algorithm. A key advantage of this algorithm is that it only requires matrix–vector multiplications and no direct matrix inversion. The latter makes our algorithm numerically stable, easy to apply, and economical in terms of computational cost. Tests on synthetic and field data show that the proposed method, contrarily to conventional l₂‐ or l₁‐norm regularised solutions, is able to provide consistent blocky and/or sparse estimators of P‐ and S‐wave velocities and density from a noisy and limited number of observations.     

2D and 3D amplitude-preserving elastic reverse time migration based on the vector-decomposed P- and S-wave records

The elastic reverse time migration approach based on the vector-wavefield decomposition generally uses the scalar product imaging condition to image the multicomponent seismic data. However, the resulting images contain the crosstalk artefacts and the polarity reversal problems, which are caused by the nonphysical wave modes and the angle-dependent reduction of image amplitudes, respectively. To overcome these two problems, we develop an amplitude-preserving elastic reverse time migration approach based on the vector-decomposed P- and S-wave seismic records. This approach includes two key points. The first is that we employ the vector-decomposed P- and S-wave multicomponent records to independently reconstruct the PP and PS reflection images to mitigate the crosstalk artefacts. The second is that we propose two schemes in addressing the issue of polarity reversal problem in the conventional PP image. One solution is to adopt the angle-dependent equation. Another one is to reconstruct an amplitude-preserving PP image with a separated scalar P-wave particle velocity, which has a clear physical meaning. Numerical examples using two-dimensional and three-dimensional models demonstrate that the proposed elastic reverse time migration approach can provide the images with better amplitude-preserving performance and fewer crosstalk artefacts, compared with the conventional elastic reverse time migration approach based on the scalar product imaging condition.     

最小二乘逆时偏移中黏弹性和各向异性的校正:以渤海湾地区地震数据为例

地下介质中存在黏弹性和各向异性,在应用最小二乘逆时偏移时,如果没有对黏弹性和各向异性的影响进行校正,在观测数据和模拟数据的匹配过程中就会发生错误,最终使得最小二乘逆时偏移无法得到准确的成像结果.因此,本论文首先对最小二乘逆时偏移的黏弹性和各向异性进行分别校正,然后对两种影响进行同时校正.在实际资料试算部分,通过对渤海湾数据进行测试,分别采用常规声波最小二乘逆时偏移、补偿黏弹性的最小二乘逆时偏移、校正各向异性的最小二乘逆时偏移及同时校正两种性质的最小二乘逆时偏移进行比较测试,证明了在同时校正了黏弹性和各向异性影响之后,最小二乘逆时偏移得到了更高质量的成像结果,具体表现在低频噪音压制、震源效应压制、深部能量改善、分辨率提升、目的层刻画等方面都明显优于其他三种最小二乘逆时偏移的成像结果,同时也证明了同时校正黏弹性和各向异性最小二乘逆时偏移方法的正确性及在实际资料处理中的适用性.

     

Topographic elastic least-squares reverse time migration based on vector P- and S-wave equations in the curvilinear coordinates

Elastic least-squares reverse time migration has been applied to multi-component seismic data to obtain high-quality images. However, the final images may suffer from artefacts caused by P- and S-wave crosstalk and severe spurious diffractions caused by complex topographic surface conditions. To suppress these crosstalk artefacts and spurious diffractions, we have developed a topographic separated-wavefield elastic least-squares reverse time migration algorithm. In this method, we apply P- and S-wave separated elastic velocity–stress wave equations in the curvilinear coordinates to derive demigration equations and gradient formulas with respect to P- and S-velocity. For the implementation of topographic separated-wavefield elastic least-squares reverse time migration, the wavefields, gradient directions and step lengths are all calculated in the curvilinear coordinates. Numerical experiments conducted with the two-component data synthetized by a three-topographic-layer with anomalies model and the Canadian Foothills model are considered to verify our method. The results reveal that compared with the conventional method, our method promises imaging results with higher resolution and has a faster residual convergence speed. Finally, we carry out numerical examples on noisy data, imperfect migration velocity and inaccurate surface elevation to analyse its sensitivity to noise, migration velocity and surface elevation error. The results prove that our method is less sensitive to noise compared with the conventional elastic least-squares reverse time migration and needs good migration velocities as other least-squares reverse time migration methods. In addition, when implementing the proposed method, an accurate surface elevation should be obtained by global positioning system to yield high-quality images.     

L1范数约束被动源数据稀疏反演一次波估计

对于被动源地震数据,运用常规的互相关算法得到的虚拟炮记录中,不仅含有一次波反射信息,还包括了表面相关多次波.然而,通过传统的被动源数据稀疏反演一次波估计(EPSI)方法,可以求得只含有一次波,不含表面相关多次波的虚拟炮记录.本文改进了传统的被动源数据稀疏反演一次波估计问题的求解方法,将被动源稀疏反演一次波估计求解问题转化为双凸L1范数约束的最优化求解问题,避免了在传统的稀疏反演一次波估计过程中用时窗防止反演陷入局部最优化的情况.在L1范数约束最优化的求解过程中,又结合了2D Curvelet变换和小波变换,在2D Curvelet-wavelet域中,数据变得更加稀疏,从而使求得的结果更加准确,成像质量得到了改善.通过简单模型和复杂模型,验证了本文提出方法的有效性.     

地震叠前逆时偏移中的去噪与存储

地震叠前逆时偏移是当前公认的地震成像的有效途径,然而它面临着计算量甚巨,低频成像噪音以及存储量大等问题,因此,业内科研工作者对其研究乐此不疲.借助GPU/CPU协同计算可以有效解决计算量的难点,笔者已在另文中阐述,本文着重探讨成像噪音抑制以及存储问题.文中分析了叠前逆时偏移产生成像噪音的机制,据此提出在叠前地震资料中先对数据进行相位与振幅校正,进而在成像后运用拉普拉斯算子滤波法消除成像噪音,从而有效去除成像所产生的低频噪音;针对存储量,采用随机边界,用计算换存储,并借助GPU实现,节省了GPU与CPU之间的数据通讯,数值实验结果表明,采用随机边界方法的逆时偏移结果与直接存储波场的方法得到的结果差别甚小.     

Imaging artefacts of artificial diving waves in reverse time migration: cause analysis in the angle domain and an effective removal strategy

In areas with strong velocity gradients, traditional reverse time migration based on cross-correlation imaging condition not only produces low-frequency noise but also generates diving wave artefacts. The artefacts caused by diving waves have no typical low-frequency characteristics and cannot be eliminated by simple high-pass filtering approaches. We apply the wave-field decomposition imaging condition to analyse the causes of false images in reverse time migration by decomposing the full wave-field into up-going and down-going components in the angle domain. We find that artificial diving wave imaging artefacts, which are generated by the cross-correlation between the up-going source and down-going receiver wave-fields in areas with strong velocity gradients, arise at large angles. We propose an efficient strategy by means of the wavelength-dependent smoothing operator to eliminate artefacts from artificial diving waves in reverse time migration. Specifically, the proposed method provides more reasonable down-going wave-fields in areas with sharp velocity constructs by considering the factor of varying seismic wavelengths during wave propagation, and the artificial components of diving waves are eliminated in a straightforward manner. Meanwhile, the other wave-field components that contribute to true subsurface images are minimally affected. Benefiting from a smoothed velocity, the proposed method can be adapted to the traditional reverse time migration imaging frame, which reveals significant implementation potential for the seismic exploration industry. A salt model is designed and included to demonstrate the effectiveness of our approach.     

起伏地表QR径向基函数有限差分及其在弹性波逆时偏移中的应用

弹性波逆时偏移不受倾角和偏移孔径的限制, 能够实现任意复杂构造的高精度多波成像, 是目前最精确的多分量资料偏移成像方法之一.逆时偏移算法的核心是波场延拓, 传统波场延拓以水平基准面为边界条件, 基于固定采样步长进行规则网格剖分, 采用阶梯近似法处理起伏地表和复杂构造界面时会产生台阶散射, 严重影响起伏地表复杂构造的成像精度.基于无网格节点模型, 定量分析了弹性波模拟中径向基函数有限差分法的频散关系和稳定性条件.基于此, 提出一种基于QR径向基函数的高精度有限差分方法, 并提出一种优化的起伏地表自适应节点剖分方法, 推导了精确的无网格自由边界条件和弹性波无网格混合吸收边界条件, 形成了新的基于无网格的起伏地表弹性波数值模拟方法.此外, 本文将此无网格径向基函数有限差分方法应用于精确的纵横波场矢量分解公式, 实现了起伏地表弹性波逆时偏移成像.通过对高斯山丘模型, 起伏凹陷模型和起伏地表Marmousi-2模型进行数值试算, 验证了本文方法的有效性和可行性.

     

Geomechanical property estimation of unconventional reservoirs using seismic data and rock physics

An extension of a previously developed rock physics model is made that quantifies the relationship between the ductile fraction of a brittle/ductile binary mixture and the isotropic seismic reflection response. By making a weak scattering (Born) approximation and plane wave (eikonal) approximation, with a subsequent ordering according to the angles of incidence, singular value decomposition analyses are performed to understand the stack weightings, number of stacks, and the type of stacks that will optimally estimate two fundamental rock physics parameters – the ductile fraction and the compaction and/or diagenesis. It is concluded that the full PP stack, i.e., sum of all PP offset traces, and the “full” PS stack, i.e., linear weighted sum of PS offset traces, are the two optimal stacks needed to estimate the two rock physics parameters. They dominate over both the second‐order amplitude variation offset “gradient” stack, which is a quadratically weighted sum of PP offset traces that is effectively the far offset traces minus the near offset traces, and the higher order fourth order PP stack (even at large angles of incidence). Using this result and model‐based Bayesian inversion, the seismic detectability of the ductile fraction (shown by others to be the important rock property for the geomechanical response of unconventional reservoir fracking) is demonstrated on a model characteristic of the Marcellus shale play.     

Non‐convex compressed sensing with frequency mask for seismic data reconstruction and denoising

Compressed Sensing has recently proved itself as a successful tool to help address the challenges of acquisition and processing seismic data sets. Compressed sensing shows that the information contained in sparse signals can be recovered accurately from a small number of linear measurements using a sparsity‐promoting regularization. This paper investigates two aspects of compressed sensing in seismic exploration: (i) using a general non‐convex regularizer instead of the conventional one‐norm minimization for sparsity promotion and (ii) using a frequency mask to additionally subsample the acquired traces in the frequency‐space () domain. The proposed non‐convex regularizer has better sparse recovery performance compared with one‐norm minimization and the additional frequency mask allows us to incorporate a priori information about the events contained in the wavefields into the reconstruction. For example, (i) seismic data are band‐limited; therefore one can use only a partial set of frequency coefficients in the range of reflections band, where the signal‐to‐noise ratio is high and spatial aliasing is low, to reconstruct the original wavefield, and (ii) low‐frequency characteristics of the coherent ground rolls allow direct elimination of them during reconstruction by disregarding the corresponding frequency coefficients (usually bellow 10 Hz) via a frequency mask. The results of this paper show that some challenges of reconstruction and denoising in seismic exploration can be addressed under a unified formulation. It is illustrated numerically that the compressed sensing performance for seismic data interpolation is improved significantly when an additional coherent subsampling is performed in the domain compared with the domain case. Numerical experiments from both simulated and real field data are included to illustrate the effectiveness of the presented method.     

Poynting and polarization vectors based wavefield decomposition and their application on elastic reverse time migration in 2D transversely isotropic media

With the progress in computational power and seismic acquisition, elastic reverse time migration is becoming increasingly feasible and helpful in characterizing the physical properties of subsurface structures. To achieve high-resolution seismic imaging using elastic reverse time migration, it is necessary to separate the compressional (P-wave) and shear (S-wave) waves for both isotropic and anisotropic media. In elastic isotropic media, the conventional method for wave-mode separation is to use the divergence and curl operators. However, in anisotropic media, the polarization direction of P waves is not exactly parallel to the direction of wave propagation. Also, the polarization direction of S-waves is not totally perpendicular to the direction of wave propagation. For this reason, the conventional divergence and curl operators show poor performance in anisotropic media. Moreover, conventional methods only perform well in the space domain of regular grids, and they are not suitable for elastic numerical simulation algorithms based on non-regular grids. Besides, these methods distort the original wavefield by taking spatial derivatives. In this case, a new anisotropic wave-mode separation scheme is developed using Poynting vectors. This scheme can be performed in the angle domain by constructing the relationship between group and polarization angles of different wave modes. Also, it is performed pointwise, independent of adjacent space points, suitable for parallel computing. Moreover, there is no need to correct the changes in phase and amplitude caused by the derivative operators. By using this scheme, the anisotropic elastic reverse time migration is more efficiently performed on the unstructured mesh. The effectiveness of our scheme is verified by several numerical examples.     

山地地震资料叠前时间偏移方法及其GPU实现

山地地区地下地质结构复杂,地表高差大,变化剧烈.目前该类地区地震勘探中主要的成像手段依然是Kirchhoff叠前时间偏移.但地表高程的剧烈变化使叠前时间偏移的基准面很难选择.本文在传统方法的基础上,提出了一种在浮动基准面上修正常规叠前时间偏移走时计算的叠前时间偏移方法,该方法能够很大程度上提高山地地区、特别是地表高差变化大地区的成像效果.本文还介绍了GPU 在叠前时间偏移上的应用,通过GPU 对〖JP2〗叠前时间偏移的优化和实现,得出如下结论：应用单颗NVIDIA Tesla C1060 GPU 进行叠前时间偏移,相比应用主频2.5 GHz〖JP〗的单核CPU计算效率可提高70倍以上.     

Kirchhoff型偏移反偏移串联地震数据炮检距转换技术

零炮检距数据在海洋地震资料处理中有很多优势和用途,然而,受海洋水平拖缆地震采集作业方式的限制,接收数据的最小炮检距一般在200 m左右,小于该炮检距的数据是无法直接获得的.通常的做法是通过对较大炮检距数据进行动校,通过外推来变相获得零炮检距（包括小炮检距）数据,其外推的精度会受到地震资料信噪比、动校正速度的精度等因素影响,并且保幅性较差.本文通过一种基于Kirchhoff真振幅偏移和反偏移串联的技术,在反偏移过程中改变观测系统,有效实现了大炮检距反射地震数据向零炮检距（包括小炮检距）数据之间的转换,且很好地保持了零炮检距（包括小炮检距）数据的振幅特性.同时,经偏移-反偏移串联处理后,有效压制了地震数据中的随机噪声,地震资料信噪比和成像精度均得到显著提高.

     

Increasing illumination and sensitivity of reverse‐time migration with internal multiples

Reverse‐time migration is a two‐way time‐domain finite‐frequency technique that accurately handles the propagation of complex scattered waves and produces a band‐limited representation of the subsurface structure that is conventionally assumed to be linear in the contrasts in model parameters. Because of this underlying linear single‐scattering assumption, most implementations of this method do not satisfy the energy conservation principle and do not optimally use illumination and model sensitivity of multiply scattered waves. Migrating multiply scattered waves requires preserving the non‐linear relation between the image and perturbation of model parameters. I modify the extrapolation of source and receiver wavefields to more accurately handle multiply scattered waves. I extend the concept of the imaging condition in order to map into the subsurface structurally coherent seismic events that correspond to the interaction of both singly and multiply scattered waves. This results in an imaging process referred to here as non‐linear reverse‐time migration. It includes a strategy that analyses separated contributions of singly and multiply scattered waves to a final non‐linear image. The goal is to provide a tool suitable for seismic interpretation and potentially migration velocity analysis that benefits from increased illumination and sensitivity from multiply scattered seismic waves. It is noteworthy that this method can migrate internal multiples, a clear advantage for imaging challenging complex subsurface features, e.g., in salt and basalt environments. The results of synthetic seismic imaging experiments, including a subsalt imaging example, illustrate the technique.     

The issues of prestack reverse time migration and solutions with Graphic Processing Unit implementation

Prestack reverse time migration (RTM) is a very useful tool for seismic imaging but has mainly three bottlenecks: highly intensive computation cost, low‐frequency band imaging noise and massive memory demand. Traditionally, PC‐clusters with thousands of computation nodes are used to perform RTM but it is too expensive for small companies and oilfields. In this article, we use Graphic Processing Unit (GPU) architecture, which is cheaper and faster to implement RTM and we obtain an order of magnitude higher speedup ratio to solve the problem of intensive computation cost. Aiming at the massive memory demand, we adopt the pseudo random boundary condition that sacrifices the computation cost but reduces the memory demand. For rugged topography RTM, it is difficult to deal with the rugged free boundary condition with the finite difference method. We employ a simplified boundary condition that avoids the abundant logical judgment to make the GPU implementation possible and does not induce any sacrifice on efficiency. Besides, we have also done some tests on multi‐GPU implementation for wide azimuth geometries using the latest GPU cards and drivers. Finally, we discuss the challenges of anisotropy RTM and GPU solutions. All the jobs stated above are based on GPU and the synthetic data examples will show the efficiency of the algorithm and solutions.