Elastic reverse-time migration based on amplitude-preserving P- and S-wave separation

Imaging the PP- and PS-wave for the elastic vector wave reverse-time migration requires separating the P- and S-waves during the wave field extrapolation. The amplitude and phase of the P- and S-waves are distorted when divergence and curl operators are used to separate the P- and S-waves. We present a P- and S-wave amplitude-preserving separation algorithm for the elastic wavefield extrapolation. First, we add the P-wave pressure and P-wave vibration velocity equation to the conventional elastic wave equation to decompose the P- and S-wave vectors. Then, we synthesize the scalar P- and S-wave from the vector Pand S-wave to obtain the scalar P- and S-wave. The amplitude-preserved separated P- and S-waves are imaged based on the vector wave reverse-time migration (RTM). This method ensures that the amplitude and phase of the separated P- and S-wave remain unchanged compared with the divergence and curl operators. In addition, after decomposition, the P-wave pressure and vibration velocity can be used to suppress the interlayer reflection noise and to correct the S-wave polarity. This improves the image quality of P- and S-wave in multicomponent seismic data and the true-amplitude elastic reverse time migration used in prestack inversion.     

Point‐spread functions for interferometric imaging

Interferometric redatuming is a data‐driven method to transform seismic responses with sources at one level and receivers at a deeper level into virtual reflection data with both sources and receivers at the deeper level. Although this method has traditionally been applied by cross‐correlation, accurate redatuming through a heterogeneous overburden requires solving a multidimensional deconvolution problem. Input data can be obtained either by direct observation (for instance in a horizontal borehole), by modelling or by a novel iterative scheme that is currently being developed. The output of interferometric redatuming can be used for imaging below the redatuming level, resulting in a so‐called interferometric image. Internal multiples from above the redatuming level are eliminated during this process. In the past, we introduced point‐spread functions for interferometric redatuming by cross‐correlation. These point‐spread functions quantify distortions in the redatumed data, caused by internal multiple reflections in the overburden. In this paper, we define point‐spread functions for interferometric imaging to quantify these distortions in the image domain. These point‐spread functions are similar to conventional resolution functions for seismic migration but they contain additional information on the internal multiples in the overburden and they are partly data‐driven. We show how these point‐spread functions can be visualized to diagnose image defocusing and artefacts. Finally, we illustrate how point‐spread functions can also be defined for interferometric imaging with passive noise sources in the subsurface or with simultaneous‐source acquisition at the surface.     

Estimation and application of near‐surface full waveform redatuming operators

Land seismic data quality can be severely affected by near‐surface anomalies. The imprint of a complex near‐surface can be removed by redatuming the data to a level below the surface, from where the subsurface structures are assumed to be relatively smooth. However, to derive a velocity‐depth model that explains the propagation effects of the near‐surface is a non‐trivial task. Therefore, an alternative approach has been proposed, where the redatuming operators are obtained in a data‐driven manner from the reflection event related to the datum. In the current implementation, the estimation of these redatuming operators is done in terms of traveltimes only, based on a high‐frequency approximation. The accompanying amplitudes are usually derived from a local homogeneous medium, which is obviously a simplification of reality. Such parametrization has produced encouraging results in the past but cannot completely remove the near‐surface complexities, leaving artefacts in the redatumed results. In this paper we propose a method that estimates the redatuming operators directly from the data, i.e., without using a velocity model, in a full waveform manner, such that detailed amplitude and phase variations are included. The method directly outputs the inverse propagation operators that are needed for true‐amplitude redatuming. Based on 2D synthetic data it is demonstrated that the resulting redatuming quality is improved and artefacts are reduced.     

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.     

角度域弹性波Kirchhoff叠前深度偏移速度分析方法

为提高地震成像结果的准确性并真实反映实际地震波场在介质中的传播特性,应该充分利用多分量地震数据的矢量特征进行弹性波成像,其中,最为棘手的问题是纵横波偏移速度场的确定,为此,本文提出了直接利用多分量地震数据进行弹性波角度域偏移速度分析的方法.基于空移成像条件的弹性波Kirchhoff偏移方程提取了弹性波局部偏移距域共成像...     

结合基准面重建的叠前时间偏移方法

提出了一种结合虚拟界面、瑞利积分和相移法的混合的基准面重建方法.通过与叠前时间偏移方法结合,形成了针对起伏地表采集数据的叠前时间偏移方法和新流程.该方法能正确考虑波在近地表传播的实际路径,克服了高速层出露时静校正方法的误差;它也能自己确定虚拟层速度,避免了现行基于波场延拓的基准面重建方法需要准确近地表速度的困难.文中分别用近地表存在明显低速层和近地表有高速层出露这两类模型的理论数据,验证了所发展方法和流程的有效性.     

Source location using time‐reverse imaging

We present the chain of time‐reverse modeling, image space wavefield decomposition and several imaging conditions as a migration‐like algorithm called time‐reverse imaging. The algorithm locates subsurface sources in passive seismic data and diffractors in active data. We use elastic propagators to capitalize on the full waveforms available in multicomponent data, although an acoustic example is presented as well. For the elastic case, we perform wavefield decomposition in the image domain with spatial derivatives to calculate P and S potentials. To locate sources, the time axis is collapsed by extracting the zero‐lag of auto and cross‐correlations to return images in physical space. The impulse response of the algorithm is very dependent on acquisition geometry and needs to be evaluated with point sources before processing field data. Band‐limited data processed with these techniques image the radiation pattern of the source rather than just the location. We present several imaging conditions but we imagine others could be designed to investigate specific hypotheses concerning the nature of the source mechanism. We illustrate the flexible technique with synthetic 2D passive data examples and surface acquisition geometry specifically designed to investigate tremor type signals that are not easily identified or interpreted in the time domain.     

求解二阶解耦弹性波方程的低秩分解法和低秩有限差分法

时间域的波场延拓方法在本质上都可以归结为对一个空间-波数域算子的近似.本文基于一阶波数-空间混合域象征,提出一种新的方法求解解耦的二阶位移弹性波方程.该方法采用交错网格,连续使用两次一阶前向和后向拟微分算子,推导得到了解耦的二阶位移弹性波方程的波场延拓算子.由于该混合域象征在伪谱算子的基础上增加了一个依赖于速度模型的补偿项,可以补偿由于采用二阶中心差分计算时间微分项带来的误差,有效地减少模拟结果的数值频散,提高模拟精度.然而,在非均匀介质中,直接计算该二阶的波场延拓算子,每一个时间步上需要做N次快速傅里叶逆变换,其中N是总的网格点数.为了减少计算量,提出了交错网格低秩分解方法;针对常规有限差分数值频散问题,本文将交错网格低秩方法与有限差分法结合,提出了交错网格低秩有限差分法.数值结果表明,交错网格低秩方法和交错网格低秩有限差分法具有较高的精度,对于复杂介质的地震波数值模拟和偏移成像具有重要的价值.     

基于流体替换技术的地震AVO属性气藏识别(英文)

传统上,油藏地球物理工程师是基于测井数据进行流体替换,计算油藏饱和不同流体时的弹性参数,并通过地震正演模拟分析油藏饱和不同流体时的地震响应,从而进行油气藏识别研究。该研究方案为油藏研究提供了重要的弹性参数和地震响应信息,但这些信息仅限于井眼位置。对于实际油藏条件,地下储层参数都是随位置变化而变化的,如孔隙度、泥质含量和油藏厚度等,因此基于传统流体替换方案得到的流体变化地震响应信息对于油气藏识别具有很大的局限性。研究通过设定联系油藏弹性参数与孔隙度、矿物组分等参数的岩石物理模型,并基于三层地质模型,进行地震正演模拟与AVO属性计算。得到油藏孔隙度、泥质含量和储层厚度变化时地震AVO属性,并建立了饱和水储层和含气储层对应AVO属性(包括梯度与截距)之间的定量关系。建立的AVO属性之间的线性关系可以实现基于地震AVO属性直接进行流体替换。最后,应用建立的流体替换前后AVO属性之间线性方程,对模拟地震数据直接进行流体替换,并通过流体替换前后AVO属性交汇图分析实现了气藏识别。     

CRS-stack-based seismic imaging considering top-surface topography

In this case study we consider the seismic processing of a challenging land data set from the Arabian Peninsula. It suffers from rough top‐surface topography, a strongly varying weathering layer, and complex near‐surface geology. We aim at establishing a new seismic imaging workflow, well‐suited to these specific problems of land data processing. This workflow is based on the common‐reflection‐surface stack for topography, a generalized high‐density velocity analysis and stacking process. It is applied in a non‐interactive manner and provides an entire set of physically interpretable stacking parameters that include and complement the conventional stacking velocity. The implementation introduced combines two different approaches to topography handling to minimize the computational effort: after initial values of the stacking parameters are determined for a smoothly curved floating datum using conventional elevation statics, the final stack and also the related residual static correction are applied to the original prestack data, considering the true source and receiver elevations without the assumption of nearly vertical rays. Finally, we extrapolate all results to a chosen planar reference level using the stacking parameters. This redatuming procedure removes the influence of the rough measurement surface and provides standardized input for interpretation, tomographic velocity model determination, and post‐stack depth migration. The methodology of the residual static correction employed and the details of its application to this data example are discussed in a separate paper in this issue. In view of the complex near‐surface conditions, the imaging workflow that is conducted, i.e. stack – residual static correction – redatuming – tomographic inversion – prestack and post‐stack depth migration, leads to a significant improvement in resolution, signal‐to‐noise ratio and reflector continuity.     

粘弹性介质单程波法非零偏移距地震数值模拟与偏移

地震资料分辨率降低,得不到深层介质的精确信息实际上是由于大地吸收效应的影响.同时与双程波动方程相比单程波动方程避免了多次波的干扰并且计算效率高、占用内存少.本文首先基于开尔芬粘弹性介质模型将品质因子与单程波分步傅立叶法波场延拓算子相结合,实现了粘弹性介质波场延拓,从而将单程波弹性介质波场延拓推广到了粘弹性介质.然后在定位原理,数学检波器原理以及等时叠加原理的基础之上实现了粘弹性介质非零偏移距叠前正演模拟.最后将数值模拟得到的正演记录进行弹性偏移和粘弹性偏移并进行对比分析.通过数值算例可以看出,粘弹性介质叠前正演深层的反射波能量减弱,同相轴变粗,频带变窄,主频减小,分辨率降低;粘弹性偏移不但实现了振幅的恢复,而且同时偏移剖面的垂向空间分辨率也得到了提高.     

Target-oriented imaging using extended image volumes: a low-rank factorization approach

Imaging in geological challenging environments has led to new developments, including the idea of generating reflection responses by means of interferometric redatuming at a given target datum in the subsurface, when the target datum lies beneath a complex overburden. One way to perform this redatuming is via conventional model-based wave-equation techniques. But those techniques can be computationally expensive for large-scale seismic problems since the number of wave-equation solves is equal to two times the number of sources involved during seismic data acquisition. Also conventional shot-profile techniques require lots of memory to save full subsurface extended image volumes. Therefore, we can only form subsurface image volumes in either horizontal or vertical directions. To exploit the information hidden in full subsurface extended image volumes, we now present a randomized singular value decomposition-based approach built upon the matrix probing scheme, which takes advantage of the algebraic structure of the extended imaging system. This low-rank representation enables us to overcome both the computational cost associated with the number of wave-equation solutions and memory usage due to explicit storage of full subsurface extended image volumes employed by conventional migration methods. Experimental results on complex geological models demonstrate the efficacy of the proposed methodology and allow practical reflection-based extended imaging for large-scale five-dimensional seismic data.     

The added value of joint PP–PS inversion for reservoir characterization: A case study using Jubarte PRM seismic data (offshore Brazil)

The added value of the joint pre-stack inversion of PP (incident P-wave and reflected P-wave) and PS (incident P-wave and reflected S-wave) seismic data for the time-lapse application is shown. We focus on the application of this technique to the time-lapse (four-dimensional) multicomponent Jubarte field permanent reservoir monitoring seismic data. The joint inversion results are less sensitive to noise in the input data and show a better match with the rock physics models calibrated for the field. Further, joint inversion improves S-impedance estimates and provides a more robust quantitative interpretation, allowing enhanced differentiation between pore pressure and fluid saturation changes, which will be extremely useful for reservoir management. Small changes in reservoir properties are expected in the short time between the time-lapse seismic acquisitions used in the Jubarte project (only 1 year apart). The attempt to recover subtle fourth-dimensional effects via elastic inversion is recurrent in reservoir characterization projects, either due to the small sensitivity of the reservoirs to fluid and pressure changes or the short interval between the acquisitions. Therefore, looking for methodologies that minimize the uncertainty of fourth-dimensional inversion outputs is of fundamental importance. Here, we also show the differences between PP only and joint PP–PS inversion workflows and parameterizations that can be applied in other projects. We show the impact of using multicomponent data as input for elastic seismic inversions in the analysis of the time-lapse differences of the elastic properties. The larger investment in the acquisition and processing of multicomponent seismic data is shown to be justified by the improved results from the fourth-dimensional joint inversion.     

基于静主元消元法的频率域波动方程正演(英文)

频率域波动方程正演是求解一个大型线性稀疏方程组问题,其受到计算效率和内存存储问题的限制。常规的高斯消元法不能满足大型数据的并行计算,本文提出基于静主元消元法(GESP)进行稀疏矩阵LU分解和多炮有限差分正演,该方法不仅提高了稳定性,更有利于单频点内LU分解的分布式并行计算。通过Marmousi模型模拟试验,单频波场和转化到时间域地震剖面的试验表明模拟精度和计算效率得到提高,节约并充分利用内存,为波形反演奠定基础。     

Stochastic inversion of pressure and saturation changes from time-lapse multi component data

Knowledge about saturation and pressure distributions in a reservoir can help in determining an optimal drainage pattern, and in deciding on optimal well designs to reduce risks of blow‐outs and damage to production equipment. By analyzing time‐lapse PP AVO or time‐lapse multicomponent seismic data, it is possible to separate the effects of production related saturation and pressure changes on seismic data. To be able to utilize information about saturation and pressure distributions in reservoir model building and simulation, information about uncertainty in the estimates is useful. In this paper we present a method to estimate changes in saturation and pressure from time‐lapse multicomponent seismic data using a Bayesian estimation technique. Results of the estimations will be probability density functions (pdfs), giving immediate information about both parameter values and uncertainties. Linearized rock physical models are linked to the changes in saturation and pressure in the prior probability distribution. The relationship between the elastic parameters and the measured seismic data is described in the likelihood model. By assuming Gaussian distributed prior uncertainties the posterior distribution of the saturation and pressure changes can be calculated analytically. Results from tests on synthetic seismic data show that this method produces more precise estimates of changes in effective pressure than a similar methodology based on only PP AVO time‐lapse seismic data. This indicates that additional information about S‐waves obtained from converted‐wave seismic data is useful for obtaining reliable information about the pressure change distribution.     

基于波场分离的弹性波逆时偏移

尽管叠前逆时偏移成像精度高,但仅针对单一纵波的成像也可能形成地下介质成像盲区,由于基于弹性波方程的逆时偏移成像可形成多波模式的成像数据,因此弹性波逆时偏移成像可提供更为丰富的地下构造信息.本文依据各向同性介质的一阶速度-应力方程组构建震源和检波点矢量波场,再利用Helmholtz分解提取纯纵波和纯横波波场,使用震源归一化的互相关成像条件获得纯波成像,避免了直接使用坐标分量成像而引起的纵横波串扰问题.针对转换波成像的极性反转问题,文中提出一种共炮域极性校正方法.为有效节约存储成本,也提出一种适用于弹性波逆时偏移的震源波场逆时重建方法,在震源波场正传过程中,仅保存PML边界内若干层的速度分量波场,进而逆时重建出所有分量的震源波场.本文分别对地堑模型和Marmousi2模型进行了弹性波逆时偏移成像测试,结果表明:所提出的共炮域极性校正方法正确有效,基于波场分离的弹性波逆时偏移成像的纯波数据能够对复杂地下构造准确成像.     

Markov chain Monte Carlo algorithms for target-oriented and interval-oriented amplitude versus angle inversions with non-parametric priors and non-linear forward modellings

In geophysical inverse problems, the posterior model can be analytically assessed only in case of linear forward operators, Gaussian, Gaussian mixture, or generalized Gaussian prior models, continuous model properties, and Gaussian-distributed noise contaminating the observed data. For this reason, one of the major challenges of seismic inversion is to derive reliable uncertainty appraisals in cases of complex prior models, non-linear forward operators and mixed discrete-continuous model parameters. We present two amplitude versus angle inversion strategies for the joint estimation of elastic properties and litho-fluid facies from pre-stack seismic data in case of non-parametric mixture prior distributions and non-linear forward modellings. The first strategy is a two-dimensional target-oriented inversion that inverts the amplitude versus angle responses of the target reflections by adopting the single-interface full Zoeppritz equations. The second is an interval-oriented approach that inverts the pre-stack seismic responses along a given time interval using a one-dimensional convolutional forward modelling still based on the Zoeppritz equations. In both approaches, the model vector includes the facies sequence and the elastic properties of P-wave velocity, S-wave velocity and density. The distribution of the elastic properties at each common-mid-point location (for the target-oriented approach) or at each time-sample position (for the time-interval approach) is assumed to be multimodal with as many modes as the number of litho-fluid facies considered. In this context, an analytical expression of the posterior model is no more available. For this reason, we adopt a Markov chain Monte Carlo algorithm to numerically evaluate the posterior uncertainties. With the aim of speeding up the convergence of the probabilistic sampling, we adopt a specific recipe that includes multiple chains, a parallel tempering strategy, a delayed rejection updating scheme and hybridizes the standard Metropolis–Hasting algorithm with the more advanced differential evolution Markov chain method. For the lack of available field seismic data, we validate the two implemented algorithms by inverting synthetic seismic data derived on the basis of realistic subsurface models and actual well log data. The two approaches are also benchmarked against two analytical inversion approaches that assume Gaussian-mixture-distributed elastic parameters. The final predictions and the convergence analysis of the two implemented methods proved that our approaches retrieve reliable estimations and accurate uncertainties quantifications with a reasonable computational effort.     

Seismic data analysis using local time‐frequency decomposition

Many natural phenomena, including geologic events and geophysical data, are fundamentally nonstationary ‐ exhibiting statistical variation that changes in space and time. Time‐frequency characterization is useful for analysing such data, seismic traces in particular. We present a novel time‐frequency decomposition, which aims at depicting the nonstationary character of seismic data. The proposed decomposition uses a Fourier basis to match the target signal using regularized least‐squares inversion. The decomposition is invertible, which makes it suitable for analysing nonstationary data. The proposed method can provide more flexible time‐frequency representation than the classical S transform. Results of applying the method to both synthetic and field data examples demonstrate that the local time‐frequency decomposition can characterize nonstationary variation of seismic data and be used in practical applications, such as seismic ground‐roll noise attenuation and multicomponent data registration.     

Wide-angle linear forward modelling of synthetic seismograms

We address the issue of linearity and scale dependence in forward modelling of seismic data from well logs, for large ray parameters, wide angles or large offsets. We present a forward model, within the context of seismic‐to‐well matching, that is linearized in the elastic properties of the earth. This model preserves linearity at large ray parameters and can handle fine‐layering effects such as induced anisotropy. Starting from a low‐contrast small‐ray‐parameter model, we extend it to a large‐ray‐parameter model by fully linearizing the elastic‐property contrasts. Overall linearity of the forward model is extended by partitioning the compressional‐wave and shear‐wave velocity fields into two fundamental scales: a kinematic scale that governs wavefield propagation effects and a dynamic scale that governs wavefield scattering effects. This analysis reveals that the standard practice in forward modelling of strongly filtering the ratio of compressional‐wave velocity to shear‐wave velocity is well founded in the underlying physics. The partitioning of the velocity fields also leads naturally to forward modelling that accounts fully for stretch effects, to resolution of the angle‐of‐incidence versus ray‐parameter dichotomy in seismic‐amplitude analysis, and to full accounting for induced anisotropy and dispersion effects due to fine‐layering of isotropic media. With the onset of routine long‐offset acquisition and the compelling need to optimize asset management in order to maximize reserve recovery, this forward model recognizes the physics of seismic wave propagation and enables a more complete exploitation of amplitude information in pre‐critical seismic data.     

3D sparse-data Kirchhoff redatuming

Wave‐equation redatuming can be a very efficient method of overcoming the overburden imprint on the target area. Owing to the growing amount of 3D data, it is increasingly important to develop a feasible method for the redatuming of 3D prestack data. Common 3D acquisition designs produce relatively sparse data sets, which cannot be redatumed successfully by applying conventional wave‐equation redatuming. We propose a redatuming approach that can be used to perform wave‐equation redatuming of sparse 3D data. In this new approach, additional information about the medium velocity below the new datum is included, i.e. redatumed root‐mean‐square (RMS) velocities, which can be extracted from the input data set by conventional velocity analysis, are used. Inclusion of this additional information has the following implications: (i) it becomes possible to simplify the 4D redatuming integral into a 2D integral such that the number of traces needed to calculate one output time sample and the computational effort are both reduced; (ii) the information about the subsurface enables an infill of traces which are needed for the integral calculation but which are missing in the sparse input data set. Two tests applying this new approach to fully sampled 2D data show satisfactory results, implying that this method can certainly be used for the redatuming of sparse 3D data sets.