Visco‐acoustic prestack reverse‐time migration based on the time‐space domain adaptive high‐order finite‐difference method

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.     

Experiences with the use of mass-density maps in residual gravity forward modelling

In many modern local and regional gravity field modelling concepts, the short-wavelength gravitational signal modeled by the residual terrain modelling (RTM) technique is used to augment global geopotential models, or to smooth observed gravity prior to data gridding. In practice, the evaluation of RTM effects mostly relies on a constant density assumption, because of the difficulty and complexity of obtaining information on the actual distribution of density of topographic masses. Where the actual density of topographic masses deviates from the adopted value, errors are present in the RTM mass-model, and hence, in the forward-modelled residual gravity field. In this paper we attempt to overcome this problem by combining the RTM technique with a high-resolution mass-density model. We compute RTM gravity quantities over New Zealand, with different combinations of elevation models and mass-density assumptions using gravity and GPS/levelling measurements, precise terrain and bathymetry models, a high-resolution mass-density model and constant density assumptions as main input databases. Based on gravity observations and the RTM technique, optimum densities are detected for North Island of ~2500 kg m^?3, South Island of ~2600 kg m^?3, and the whole New Zealand of ~2590 kg m^?3. Comparison among the three sets of residual gravity disturbances computed from different mass-density assumptions show that, together with a global potential model, the high-resolution New Zealand density model explains ~89.5% of gravitational signals, a constant density assumption of 2670 kg m^?3 explains ~90.2%, while a regionally optimum mass-density explains ~90.3%. Detailed comparison shows that the New Zealand density model works best over areas with small residual heights. Over areas with larger residual heights, subsurface density variations appear to affect the residual gravity disturbance. This effect is found to reach about 30 mGal over Southern Alpine Fault. In order to improve the RTM modelling with mass-density maps, a higher-quality mass-density model that provides radially varying mass-density data would be desirable.     

基于全波形反演的探地雷达数据逆时偏移成像

逆时偏移成像(RTM)常用来处理复杂速度模型,包括陡倾角及横向速度变化剧烈的模型.与常规偏移成像方法(如Kirchhoff偏移)相比,逆时偏移成像能提供更好的偏移成像结果,近些年逆时偏移成像越来越广泛地应用到勘探地震中,它逐渐成为石油地震勘探中的一种行业标准.电磁波和弹性波在动力学和运动学上存在相似性,故本文开发了基于麦克斯韦方程组的电磁波逆时偏移成像算法,并将其应用到探地雷达数据处理中.时间域有限差分(FDTD)用于模拟电磁波正向和逆向传播过程,互相关成像条件用于获得最终偏移结果.逆时偏移成像算法中,偏移成像结果受初始模型影响较大,而其中决定电磁波传播速度的介电常数的影响尤为重要.本文基于时间域全波形反演(FWI)算法反演获得了更为精确的地下介电常数模型,并将其反演结果作为逆时偏移成像的初始介电常数模型.为了验证此算法的有效性,首先构建了一个复杂地质结构模型,合成了共偏移距及共炮点探地雷达数据,分别应用常规Kirchhoff偏移算法及逆时偏移成像算法进行偏移处理,成像结果显示由逆时偏移成像算法得到的偏移结果与实际模型具有较高的一致性;此外本文在室内沙槽中进行了相关的物理模拟实验,采集了共偏移距及共炮点探地雷达数据,分别应用Kirchhoff和叠前逆时偏移成像算法进行处理,结果表明叠前逆时偏移成像在实际应用中能获得更好的成像效果.     

Implementation of Elastic Prestack Reverse-Time Migration Using an Efficient Finite-Difference Scheme

Elastic reverse-time migration (RTM) can reflect the underground elastic information more comprehensively than single-component Pwave migration. One of the most important requirements of elastic RTM is to solve wave equations. The imaging accuracy and efficiency of RTM depends heavily on the algorithms used for solving wave equations. In this paper, we propose an efficient staggered-grid finite-difference (SFD) scheme based on a sampling approximation method with adaptive variable difference operator lengths to implement elastic prestack RTM. Numerical dispersion analysis and wavefield extrapolation results show that the sampling approximation SFD scheme has greater accuracy than the conventional Taylor-series expansion SFD scheme. We also test the elastic RTM algorithm on theoretical models and a field data set, respectively. Experiments presented demonstrate that elastic RTM using the proposed SFD scheme can generate better images than that using the Taylor-series expansion SFD scheme, particularly for PS images. FurH. thermore, the application of adaptive variable difference operator lengths can effectively improve the computational efficiency of elastic RTM.     

Acoustic VTI modeling and pre-stack reverse-time migration based on the time–space domain staggered-grid finite-difference method

Reverse-time migration (RTM) is based on seismic numerical modeling algorithms, and the accuracy and efficiency of RTM strongly depend on the algorithm used for numerical solution of wave equations. Finite-difference (FD) methods have been widely used to solve the wave equation in seismic numerical modeling and RTM. In this paper, we derive a series of time–space domain staggered-grid FD coefficients for acoustic vertical transversely isotropic (VTI) equations, and adopt these difference coefficients to solve the equations, then analyze the numerical dispersion and stability, and compare the time–space domain staggered-grid FD method with the conventional method. The numerical analysis results demonstrate that the time–space domain staggered-grid FD method has greater accuracy and better stability than the conventional method under the same discretizations. Moreover, we implement the pre-stack acoustic VTI RTM by the conventional and time–space domain high-order staggered-grid FD methods, respectively. The migration results reveal that the time–space domain staggered-grid FD method can provide clearer and more accurate image with little influence on computational efficiency, and the new FD method can adopt a larger time step to reduce the computation time and preserve the imaging accuracy as well in RTM. Meanwhile, when considering the anisotropy in RTM for the VTI model, the imaging quality of the acoustic VTI RTM is better than that of the acoustic isotropic RTM.     

Acoustic Reverse-time Migration using Optimal Staggered-grid Finite-difference Operator Based on Least Squares

Reverse-time migration (RTM) directly solves the two-way wave equation for wavefield propagation; therefore, how to solve the wave equation accurately and quickly is very important for RTM. The conventional staggered-grid finite-difference (SFD) operators are usually based on the Taylor-series expansion theory. If they are used to solve wave equation on a larger frequency content, a strong dispersion will occur, which directly affects the seismic image quality. In this paper, we propose an optimal SFD operator based on least squares to solve acoustic wave equation for prestack RTM, and obtain a new antidispersion RTM algorithm that can use short spatial difference operators. The synthetic and real data tests demonstrate that the least squares SFD (LSSFD) operator can mitigate the numerical dispersion, and the acoustic RTM using the LSSFD operator can effectively improve image quality comparing with that using the Taylor-series expansion SFD (TESFD) operator. Moreover, the LSSFD method can adopt a shorter spatial difference operator to reduce the computing cost.     

基于自适应优化有限差分方法的全波VSP逆时偏移

与地面地震资料相比,VSP资料具有分辨率高、环境噪声小及能更好地反映井旁信息等优点.常规VSP偏移主要对上行反射波进行成像,存在照明度低、成像范围受限等问题.为了增加照明度、拓宽成像范围、提高成像精度,本文采用直达波除外的所有声波波场数据(全波),包括一次反射波、多次反射波等进行叠前逆时偏移成像.针对逆时偏移中的四个关键问题,即波场延拓、吸收边界条件、成像条件及低频噪声的压制,本文分别采用自适应变空间差分算子长度的优化有限差分方法(自适应优化有限差分方法)求解二维声波波动方程以实现高精度、高效率的波场延拓,采用混合吸收边界条件压制因计算区域有限所引起的人工边界反射,采用震源归一化零延迟互相关成像条件进行成像,采用拉普拉斯滤波方法压制逆时偏移中产生的低频噪声.本文对VSP模型数据的逆时偏移成像进行了分析,结果表明:自适应优化有限差分方法比传统有限差分方法具有更高的模拟精度与计算效率,适用于VSP逆时偏移成像;全波场VSP逆时偏移成像比上行波VSP逆时偏移的成像范围大、成像效果好;相对于反褶积成像条件,震源归一化零延迟互相关成像条件具有稳定性好、计算效率高等优点.将本文方法应用于某实际VSP资料的逆时偏移成像,进一步验证了本文方法的正确性和有效性.     

Viscoacoustic prestack reverse time migration based on the optimal time-space domain high-order finite-difference method

Prestack reverse time migration （RTM） is an accurate imaging method ofsubsurface media. The viscoacoustic prestack RTM is of practical significance because itconsiders the viscosity of the subsurface media. One of the steps of RTM is solving thewave equation and extrapolating the wave field forward and backward; therefore, solvingaccurately and efficiently the wave equation affects the imaging results and the efficiencyof RTM. In this study, we use the optimal time-space domain dispersion high-order finite-difference （FD） method to solve the viscoacoustic wave equation. Dispersion analysis andnumerical simulations show that the optimal time-space domain FD method is more accurateand suppresses the numerical dispersion. We use hybrid absorbing boundary conditions tohandle the boundary reflection. We also use source-normalized cross-correlation imagingconditions for migration and apply Laplace filtering to remove the low-frequency noise.Numerical modeling suggests that the viscoacoustic wave equation RTM has higher imagingresolution than the acoustic wave equation RTM when the viscosity of the subsurface isconsidered. In addition, for the wave field extrapolation, we use the adaptive variable-lengthFD operator to calculate the spatial derivatives and improve the computational efficiencywithout compromising the accuracy of the numerical solution.     

Error sources and data limitations for the prediction of surface gravity: a case study using benchmarks

Gravity-based heights require gravity values at levelled benchmarks (BMs), which sometimes have to be predicted from surrounding observations. We use the Earth Gravitational Model 2008 (EGM2008) and the Australian National Gravity Database (ANGD) as examples of model and terrestrial observed data respectively to predict gravity at Australian National Levelling Network (ANLN) BMs. The aim is to quantify errors that may propagate into the predicted BM gravity values and then into gravimetric height corrections (HCs). Our results indicate that an approximate ±1 arc-min horizontal position error of the BMs causes maximum errors in EGM2008 BM gravity of ~22 mGal (~55 mm in the HC at ~2200 m elevation) and ~18 mGal for ANGD BM gravity because the values are not computed at the true location of the BM. We use RTM (residual terrain modelling) techniques to show that ~50% of EGM2008 BM gravity error in a moderately mountainous region can be accounted for by signal omission. Non-representative sampling of ANGD gravity in this region may cause errors of up to 50 mGals (~120 mm for the Helmert orthometric correction at ~2200 m elevation). For modelled gravity at BMs to be viable, levelling networks need horizontal BM positions accurate to a few metres, while RTM techniques can be used to reduce signal omission error. Unrepresentative gravity sampling in mountains can be remedied by denser and more representative re-surveys, and/or gravity can be forward modelled into regions of sparser gravity.     

起伏地表叠前逆时偏移理论及GPU加速技术

从起伏地表直接进行叠前逆时偏移是解决地表起伏大并且地下构造复杂这种双复杂结构地区成像问题的有力工具.本文给出了起伏地表直接进行叠前逆时偏移的实现过程,针对有限差分方法处理起伏地表自由边界条件的复杂性,采用了一种简化的自由边界条件,避免了大量的逻辑判断,在此基础上,采用图形处理器(Graphic Processing U...     

三维逆时偏移GPU/CPU机群实现方案研究

叠前逆时偏移是当前最为准确的地震成像方法,由于计算量大、存储量大等原因需要合适的实现策略和高效的计算平台.本文以高阶有限差分逆时偏移为基础,重点讨论了在GPU上实现需要解决的显存不足问题和人工边界问题.利用区域分解技术可以在当前GPU上高效地实现任意生产规模的三维逆时偏移成像,不会受到GPU显存规模的制约.常规最佳匹配层边界条件边界区域控制方程与内部区域差异较大,不适于GPU高速运算.本文在GPU上实现近似最佳匹配层(NPML)边界条件,使得高阶有限差分计算不需要分支判断,边界区域辅助波场的存储量也较低,保证了在GPU上进行波场传播的高效性.三维理论数据和实际资料成像结果表明了本文方法的正确性.     

基于伪谱法的VSP逆时偏移及其应用研究

逆时偏移被认为是对地下复杂构造进行成像的精确偏移方法,尤其是能够有效地对回转波、绕射波、多次波等各种波动现象进行成像.近几年来随着并行计算机和存储设备的快速发展,逆时偏移方法备受关注.本文采用伪谱法实现了VSP逆时偏移,该方法不仅实施简便,而且计算效率高,精度好.并运用反周期扩展法来消除伪谱法中特殊的周期性边界效应问题.对VSP绕射点模型进行试算,分析了因覆盖次数不足在近井区产生的假象问题.对地堑模型和半圆隆起模型也获得了较好的VSP逆时偏移成像效果.并分别对VSP全波波场及分离出的上行波场进行了逆时偏移成像,可明显发现直达波在炮点和检波点位置处收敛成像,也产生了很强的成像噪声.最后对某地区实际观测的VSP资料进行了逆时偏移成像,并与Kirchhoff法VSP偏移结果和地面地震偏移结果进行了对比,显示了VSP逆时偏移在近井区成像上的优势.     

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.     

地震叠前逆时偏移高阶有限差分算法及GPU实现

叠前逆时偏移技术是解决地震成像问题的有力工具,但由于计算量大、成像噪音以及存储量大等原因没有得到广泛的应用.本文给出了逆时偏移的实现过程,分析了高阶有限差分格式的稳定性与频散关系.针对叠前逆时偏移计算量大的问题,使用图形处理器(Graphic Processing Unit,简称GPU)实现算法加速,比传统的CPU计算速度提高了一个数量级.文中对理论模型进行了计算,并与单程波偏移方法做比较,结果表明:叠前逆时偏移有效突破了成像倾角限制,对垂直断层、盐丘空腔内幕等特殊构造成像效果均有显著提高.本文尚未涉及成像噪音去除以及存储量等问题,笔者将另文阐述.     

基于激发振幅成像条件的探地雷达逆时偏移成像

针对基于互相关成像条件的探地雷达（GPR）逆时偏移计算效率低、存储量大及易产生低频假象的不足,本文将激发振幅成像条件应用于GPR逆时偏移成像中.通过在源点电磁波场正向传播过程计算每个网格点的能量密度,并保存最大能量密度的时刻和相应的电磁波场值;在接收点电磁波场逆向传播过程提取每个网格点最大能量密度时刻及对应的电磁波场值,并利用保存的最大能量源点电磁波场及走时做归一化,从而获得了依赖反射系数成像剖面,避免了源点正向传播电磁波场的存储和重建.此外,为了提高电磁波场的模拟精度,采用了基于三角形剖分的时间域有限单元法（FETD）计算电磁波正向和逆向传播过程.最后通过模型试算表明：激发振幅成像条件相比于归一化互相关成像条件,成像结果低频噪声更弱,空间分辨率更高,计算效率提高了近2倍.     

The stability problem of reverse time migration for viscoacoustic VTI media

In real strata anisotropy and viscosity extensively exists. They degraded waveforms in amplitude, resulting in which reducing of image resolution. To obtain high-precision imaging of deep reservoirs, we extended the separated viscous and anisotropic reverse time migration (RTM) to a stable viscoacoustic anisotropic RTM for vertical transverse isotropic (VTI) media, based on single generalized standard and linear solid (GSLS) media theory.. We used a pseudo-spectral method to develop the numerical simulation. By introducing a regularization operator to eliminate the high-frequency instability problem, we built a stable inverse propagator and achieved viscoacoustic VTI media RTM. High-resolution imaging results were obtained after correcting for the effects of anisotropy and viscosity. Synthetic tests verify the validity and accuracy of algorithm.     

叠前逆时深度偏移低频噪声压制策略研究

低波数噪音严重影响了逆时偏移的成像质量,选择合适的低波数噪音压制方法是进行逆时偏移时必然涉及到的一个重要方面.本文首先详细分析了逆时偏移中低波数噪音产生的本质原因,然后根据噪音的产生机制对目前各类低波数噪音压制方法进行了分析和归类:第一类低波数噪音压制策略的核心是在构建波场中避免发生背向反射;第二类低波数噪音压制策略的核心是进行选择性成像.最后通过对压噪方法进行合理的选择和搭配,构建了在不同实现条件和成像需求情况下逆时偏移去噪方法的最佳抉择策略.结合数值算例对几种压噪方案进行了测试和比较,实例表明了对噪音压制方法进行合理的搭配可以获得高信噪比逆时偏移成像结果.     

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.     

相对保幅的角度域VSP逆时偏移(英文)

本文介绍了一种改进的角度域VSP逆时偏移方法。对VSP逆时偏移中的逆推公式进行了改进,为方便数值计算出相对保幅的角度域共成像点道集(ADCIGs)。此外VSP记录到的波场信息丰富,包括上行波场、下行波场和直达波场等,本文分析了这些波场的响应特征,发现直达波和下行波在角度域共成像点道集(ADCIGs)上都产生了成像噪音,直达波产生的噪音尤为严重。把该方法用于我国西部地区实际观测的VSP资料,不仅获得相对保幅角度域共成像点道集(ADCIGs),而且压制了成像噪音。通过数值模型试算,实际资料的应用验证了该方法的实用性与有效性,从而为VSP偏移速度分析、VSP AVA/AVO分析和反演等提供可靠的基础资料。     

地震叠前逆时偏移算法的CPU/GPU实施对策

相较于单程波偏移算法而言,逆时偏移成像方法以其物理基础为依托优势,几十年来一直备受国内外地球物理学家的青睐.目前的逆时偏移(RTM)若直接采用双程波动方程进行延拓,尽管可以回避上下行波的分离处理,然就已有算法而言,其计算量和I/O(输入/输出)量却是最大的.针对此问题,本文在分析现行逆时偏移的多种算法基础上,提出利用CPU/GPU(中央处理器/图形处理器)作为数值计算核心,建立随机边界模型,从而克服存储I/O难题和提高计算效率.在实际的数据测试中,本文的方法可以大幅度的提高计算效率和减少存储单元,从而促使其高效地应用于生产实际.