Accurate estimation of acoustic impedance based on spectral inversion

Acoustic impedance is one of the best attributes for seismic interpretation and reservoir characterisation. We present an approach for estimating acoustic impedance accurately from a band‐limited and noisy seismic data. The approach is composed of two stages: inverting for reflectivity from seismic data and then estimating impedance from the reflectivity inverted in the first stage. For the first stage, we achieve a two‐step spectral inversion that locates the positions of reflection coefficients in the first step and determines the amplitudes of the reflection coefficients in the second step under the constraints of the positions located in the first step. For the second stage, we construct an iterative impedance estimation algorithm based on reflectivity. In each iteration, the iterative impedance estimation algorithm estimates the absolute acoustic impedance based on an initial acoustic impedance model that is given by summing the high‐frequency component of acoustic impedance estimated at the last iteration and a low‐frequency component determined in advance using other data. The known low‐frequency component is used to restrict the acoustic impedance variation tendency in each iteration. Examples using one‐ and two‐dimensional synthetic and field seismic data show that the approach is flexible and superior to the conventional spectral inversion and recursive inversion methods for generating more accurate acoustic impedance models.     

地层衰减对地震波速度逆散射反演的影响研究

在利用地震波数据进行地球物理反演时,地层对地震波的吸收衰减效应会对地层物性参数的准确反演产生较大的影响,因此利用黏弹性声波方程进行反演更符合实际情形.本文在考虑地层衰减效应进行频率空间域正演模拟的基础上,提出基于黏弹性声波方程的频率域逆散射反演算法并对地震波传播速度进行反演重建,在反演过程中分别用地震波传播复速度和实速度来表征是否考虑地层吸收衰减效应.基于反演参数总变差的正则化处理使反演更加稳定,在反演中将低频反演速度模型作为高频反演的背景模型进行逐频反演,由于单频反演过程中背景模型保持不变,故该方法不需要在每次迭代中重新构造正演算子,具有较高的反演效率;此外本文在反演过程中采用了基于MPI的并行计算策略,进一步提高了反演计算的效率.在二维算例中分别对是否考虑地层吸收衰减效应进行了地震波速度反演,反演结果表明考虑衰减效应可以得到与真实模型更加接近的速度分布结果,相反则无法得到正确的地震波速度重建结果.本文算法对复杂地质模型中浅层可以反演得到分辨率较高的速度模型,为其他地震数据处理提供比较准确的速度信息,在地层深部由于地震波能量衰减导致反演分辨率不太理想.     

子波相位不准对反演结果的影响(英文)

本文重点讨论在振幅谱估计准确的情况下,采用不同相位谱子波作为实际估计子波进行线性最小二乘反演,并对结果进行分析。除子波相位外,所有其它影响反演结果的因素均忽略。稀疏反射系数模型(块状波阻抗模型)反演结果表明:(1)使用不同相位谱子波进行反演,其反演结果合成的记录与原始记录都非常匹配,但反演的反射系数和声波阻抗结果与真实模型有差异;(2)反演结果的可靠程度主要与不同相位子波z变换的根的分布有关,当估计子波与真实子波Z变换的根的分布仅在单位圆附近有差异时,反演的反射系数和声波阻抗与真实模型很接近;(3)尽管反演前后地震记录都匹配了,并且评价反演结果好坏的柯西准则或改进柯西准则(反演参数没有进行自适应处理)已经达到了最优(最小),但反演结果与真实模型仍存在较大差异。最后,针对子波相位估计不准可能导致反演效果较差这个问题,我们提出采用求L1范数、丰度、变分、柯西准则(反演参数进行了自适应处理)或/和改进柯西准则(反演参数进行了自适应处理)的最优值或次优值作为评价准则的一种解决办法,理论上得到了好的效果。     

基于矩阵Toeplitz稀疏分解的相对波阻抗反演方法

针对利用地震道进行相对波阻抗反演中遇到的横向连续性难以保持、初始子波容错度差以及随机噪声干扰影响反演结果等问题,提出了一种基于矩阵Toeplitz稀疏分解的相对波阻抗反演方法.该方法将地震数据剖面的Toeplitz稀疏分解问题分解为两个子反演问题,其一以Toeplitz子波矩阵元素为待反演的参数,用Fused Lasso方法求解,可保证子波具有紧支集且是光滑的;其二以稀疏反射系数矩阵元素为待反演参数,用基于回溯的快速萎缩阈值迭代算法求解,大大降低了目标函数中参数选择的难度.通过交替迭代求解上述两个子反演问题可将地震数据剖面因式分解为一个Toeplitz子波矩阵和一个稀疏反射系数矩阵;然后由反射系数矩阵递推反演可以得到高分辨率的相对波阻抗剖面;利用测井资料加入低频分量后,也可得到高分辨率的绝对波阻抗剖面.Marmousi2模型生成的合成记录算例和实际地震资料算例均表明:本文方法可以从带限地震数据中有效地反演相对波阻抗,反演结果分辨率高并且能够很好地保持地震数据的横向连续性;即使在初始估计子波存在误差和地震数据被随机噪声污染的情况下也能取得较好的效果.     

Joint viscoacoustic waveform inversion with the separated upgoing and downgoing wavefields in zero-offset vertical seismic profile data

The attenuation of seismic waves propagating in reservoirs can be obtained accurately from the data analysis of vertical seismic profile in terms of the quality-factor Q. The common methods usually use the downgoing wavefields in vertical seismic profile data. However, the downgoing wavefields consist of more than 90% energy of the spectrum of the vertical seismic profile data, making it difficult to estimate the viscoacoustic parameters accurately. Thus, a joint viscoacoustic waveform inversion of velocity and quality-factor is proposed based on the multi-objective functions and analysis of the difference between the results inverted from the separated upgoing and downgoing wavefields. A simple separating step is accomplished by the reflectivity method to obtain the individual wavefields in vertical seismic profile data, and then a joint inversion is carried out to make full use of the information of the individual wavefields and improve the convergence of viscoacoustic full-waveform inversion. The sensitivity analysis of the different wavefields to the velocity and quality-factor shows that the upgoing and downgoing wavefields contribute differently to the viscoacoustic parameters. A numerical example validates our method can improve the accuracy of viscoacoustic parameters compared with the direct inversion using full wavefield and the separate inversion using upgoing or downgoing wavefield. The application on real field data indicates our method can recover a reliable viscoacoustic model, which helps reservoir appraisal.     

PARAMETRIZATION OF GRT INVERSION FOR ACOUSTIC AND P–P SCATTERING1

The generalized Radon transform (GRT) inversion contains an explicit relationship between seismic amplitude variations, the reflection angle and the physical parameters which can be used to describe the earth efficiently for inversion purposes. Using this relationship, we have derived parametrizations for acoustic and P–P scattering so that the variations in seismic amplitude with reflection angle for each parameter are sufficiently independent. These parametrizations show that small offset and large offset amplitudes are related to different physical parameters. In the case of acoustic scattering, the small-offset amplitudes are related to impedance variations while large-offset amplitudes are related to velocity variations. A similar result has been established for P–P scattering. The Born approximation (which is used to derive the GRT inversion) does not correctly predict the amplitude due to velocity variations at large offsets, and thus the inversion of velocity is not as satisfactory as the inversion of impedance.     

基于初至波走时层析成像的Tikhonov正则化与梯度优化算法

初至波走时层析成像是利用地震初至波走时和其传播的射线路径来反演地下介质速度的技术.该问题本质上是一个不适定问题,需要使用正则化方法并辅之以适当的最优化技巧.本文从数值优化的角度介绍了初至波走时层析成像的反演原理,建立了Tikhonov正则化层析成像反演模型并提出求解极小化问题的加权修正步长的梯度下降算法.该方法可以从速度模型的可行域中迭代找到一个最优解.数值试验表明,该方法是可行和有应用前景的.     

基于α稳定分布的地震反演方法

本文介绍了α稳定分布的统计特征,并对比分析了实际地震信号与α稳定分布的动态样本方差特征,提出地震信号服从非高斯α稳定分布的假设.在此基础上,利用地震记录估计误差的p阶统计量作为代价函数,提出了基于非高斯α稳定分布的最小p范数地震反演方法.将该方法应用到单道反射系数理论模型及实际叠前弹性阻抗反演实例中,均取得了良好的反演效果.实际反演结果验证了本文提出的地震信号服从非高斯α稳定分布假设的合理性,以及最小p范数地震反演方法的可行性和有效性.     

Geostatistical seismic Amplitude‐versus‐angle inversion

Seismic inversion plays an important role in reservoir modelling and characterisation due to its potential for assessing the spatial distribution of the sub‐surface petro‐elastic properties. Seismic amplitude‐versus‐angle inversion methodologies allow to retrieve P‐wave and S‐wave velocities and density individually allowing a better characterisation of existing litho‐fluid facies. We present an iterative geostatistical seismic amplitude‐versus‐angle inversion algorithm that inverts pre‐stack seismic data, sorted by angle gather, directly for: density; P‐wave; and S‐wave velocity models. The proposed iterative geostatistical inverse procedure is based on the use of stochastic sequential simulation and co‐simulation algorithms as the perturbation technique of the model parametre space; and the use of a genetic algorithm as a global optimiser to make the simulated elastic models converge from iteration to iteration. All the elastic models simulated during the iterative procedure honour the marginal prior distributions of P‐wave velocity, S‐wave velocity and density estimated from the available well‐log data, and the corresponding joint distributions between density versus P‐wave velocity and P‐wave versus S‐wave velocity. We successfully tested and implemented the proposed inversion procedure on a pre‐stack synthetic dataset, built from a real reservoir, and on a real pre‐stack seismic dataset acquired over a deep‐water gas reservoir. In both cases the results show a good convergence between real and synthetic seismic and reliable high‐resolution elastic sub‐surface Earth models.     

Look-ahead vertical seismic profiling inversion approach for density and compressional wave velocity in Bayesian framework

To reduce drilling uncertainties, zero-offset vertical seismic profiles can be inverted to quantify acoustic properties ahead of the bit. In this work, we propose an approach to invert vertical seismic profile corridor stacks in Bayesian framework for look-ahead prediction. The implemented approach helps to successfully predict density and compressional wave velocity using prior knowledge from drilled interval. Hence, this information can be used to monitor reservoir depth as well as quantifying high-pressure zones, which enables taking the correct decision during drilling. The inversion algorithm uses Gauss–Newton as an optimization tool, which requires the calculation of the sensitivity matrix of trace samples with respect to model parameters. Gauss–Newton has quadratic rate of convergence, which can speed up the inversion process. Moreover, geo-statistical analysis has been used to efficiently utilize prior information supplied to the inversion process. The algorithm has been tested on synthetic and field cases. For the field case, a zero-offset vertical seismic profile data taken from an offshore well were used as input to the inversion algorithm. Well logs acquired after drilling the prediction section was used to validate the inversion results. The results from the synthetic case applications were encouraging to accurately predict compressional wave velocity and density from just a constant prior model. The field case application shows the strength of our proposed approach in inverting vertical seismic profile data to obtain density and compressional wave velocity ahead of a bit with reasonable accuracy. Unlike the commonly used vertical seismic profile inversion approach for acoustic impedance using simple error to represent the prior covariance matrix, this work shows the importance of inverting for both density and compressional wave velocity using geo-statistical knowledge of density and compressional wave velocity from the drilled section to quantify the prior covariance matrix required during Bayesian inversion.     

Exact elastic impedance tensor for isotropic media

The existing expressions of elastic impedance,as the generalized form of acoustic impedance,represent the resistance of subsurface media to seismic waves of non-normal incidence,and thus include information on the shear-wave velocity.In this sense,conventional elastic impedance is an attribute of the seismic reflection and not an intrinsic physical property of the subsurface media.The derivation of these expressions shares the approximations made for reflectivity,such as weak impedance contrast andisotropic or weakly anisotropic media,which limits the accuracy of reflectivity reconstruction and seismic inversion.In this paper,we derive exact elastic impedance tensors of seismic P-and S-waves for isotropic media based on the stress-velocity law.Each componentof the impedance tensor represents a unique mechanical property of the medium.Approximations of P-wave elastic impedance tensor components are discussed for seismic inversion and interpretation.Application to synthetic data and real data shows the accuracy and robust interpretation capability of the derived elastic impedance in lithology characterizations.     

频率多尺度全波形速度反演

以二维声波方程为模型,在时间域深入研究了全波形速度反演.全波形反演要解一个非线性的最小二乘问题,是一个极小化模拟数据与已知数据之间残量的过程.针对全波形反演易陷入局部极值的困难,本文提出了基于不同尺度的频率数据的"逐级反演"策略,即先基于低频尺度的波场信息进行反演,得出一个合理的初始模型,然后再利用其他不同尺度频率的波场进行反演,并且用前一尺度的迭代反演结果作为下一尺度反演的初始模型,这样逐级进行反演.文中详细阐述和推导了理论方法及公式,包括有限差分正演模拟、速度模型修正、梯度计算和算法描述,并以Marmousi复杂构造模型为例,进行了MPI并行全波形反演数值计算,得到了较好的反演结果,验证了方法的有效性和稳健性.     

SLOPE DATA WATER-BOTTOM MULTIPLE ATTENUATION1

Methods for predicting and attenuating water-bottom multiples by wavefield extrapolation have been discussed by several investigators. Because these prediction methods operate on shot records, boundary conditions must be specified for every shot record. The approach presented operates in the common-offset plane; a model of expected water-bottom multiples is generated from the observed surface wavefield using a finite-difference wave-equation migration algorithm with an offset term. An accurate water-depth profile is required, but there is no restriction on the shape of the water bottom other than a dip limit of approximately 18–20°. In generating a multiple model, the water-bottom primary and each water-bottom multiple reflection of the observed surface wavefield are extrapolated to a higher order. Thus, the extrapolated water-bottom primary of the model is lined up with a water-bottom multiple in the data and each multiple in the model is lined up with a higher-order (or later) multiple in the data. Prestack multiple attenuation is achieved, for one offset at a time, by first adapting the model of expected multiples to the observed data and then subtracting the predicted multiple energy. An error-constrained adaptation algorithm is proposed in order to control instabilities. No assumptions are made about primary reflections and no subwater-bottom velocities are required. Computational efficiency of modelling and adaptation can be improved by applying this method only to near and intermediate offsets as the stacking process usually provides sufficient multiple attenuation at far offsets. A field data example demonstrates the potential of the proposed method for improving the primary-to-multiple ratio in prestack and post-stack data.     

3D acoustic waveform inversion in the Laplace domain using an iterative solver

In this paper we propose a 3D acoustic full waveform inversion algorithm in the Laplace domain. The partial differential equation for the 3D acoustic wave equation in the Laplace domain is reformulated as a linear system of algebraic equations using the finite element method and the resulting linear system is solved by a preconditioned conjugate gradient method. The numerical solutions obtained by our modelling algorithm are verified through a comparison with the corresponding analytical solutions and the appropriate dispersion analysis. In the Laplace‐domain waveform inversion, the logarithm of the Laplace transformed wavefields mainly contains long‐wavelength information about the underlying velocity model. As a result, the algorithm smoothes a small‐scale structure but roughly identifies large‐scale features within a certain depth determined by the range of offsets and Laplace damping constants employed. Our algorithm thus provides a useful complementary process to time‐ or frequency‐domain waveform inversion, which cannot recover a large‐scale structure when low‐frequency signals are weak or absent. The algorithm is demonstrated on a synthetic example: the SEG/EAGE 3D salt‐dome model. The numerical test is limited to a Laplace‐domain synthetic data set for the inversion. In order to verify the usefulness of the inverted velocity model, we perform the 3D reverse time migration. The migration results show that our inversion results can be used as an initial model for the subsequent high‐resolution waveform inversion. Further studies are needed to perform the inversion using time‐domain synthetic data with noise or real data, thereby investigating robustness to noise.     

Cauchy prior distribution-based AVO elastic parameter estimation via weakly nonlinear waveform inversion

Cauchy priori distribution-based Bayesian AVO reflectivity inversion may lead to sparse estimates that are sensitive to large reflectivities. For the inversion, the computation of the covariance matrix and regularized terms requires prior estimation of model parameters, which makes the iterative inversion weakly nonlinear. At the same time, the relations among the model parameters are assumed linear. Furthermore, the reflectivities, the results of the inversion, or the elastic parameters with cumulative error recovered by integrating reflectivities are not well suited for detecting hydrocarbons and fuids. In contrast, in Bayesian linear AVO inversion, the elastic parameters can be directly extracted from prestack seismic data without linear assumptions for the model parameters. Considering the advantages of the abovementioned methods, the Bayesian AVO reflectivity inversion process is modified and Cauchy distribution is explored as a prior probability distribution and the time-variant covariance is also considered. Finally, we propose a new method for the weakly nonlinear AVO waveform inversion. Furthermore, the linear assumptions are abandoned and elastic parameters, such as P-wave velocity, S-wave velocity, and density, can be directly recovered from seismic data especially for interfaces with large reflectivities. Numerical analysis demonstrates that all the elastic parameters can be estimated from prestack seismic data even when the signal-to-noise ratio of the seismic data is low.     

Two‐dimensional waveform inversion of multi‐component data in acoustic‐elastic coupled media

In order to account for the effects of elastic wave propagation in marine seismic data, we develop a waveform inversion algorithm for acoustic‐elastic media based on a frequency‐domain finite‐element modelling technique. In our algorithm we minimize residuals using the conjugate gradient method, which back‐propagates the errors using reverse time migration without directly computing the partial derivative wavefields. Unlike a purely acoustic or purely elastic inversion algorithm, the Green's function matrix for our acoustic‐elastic algorithm is asymmetric. We are nonetheless able to achieve computational efficiency using modern numerical methods. Numerical examples show that our coupled inversion algorithm produces better velocity models than a purely acoustic inversion algorithm in a wide variety of cases, including both single‐ and multi‐component data and low‐cut filtered data. We also show that our algorithm performs at least equally well on real field data gathered in the Korean continental shelf.     

各向异性介质Low-rank有限差分法纯qP波叠前平面波最小二乘逆时偏移

拟声波最小二乘逆时偏移是一种极具潜力的地震波成像工具,但该方法遭受各向异性拟声波近似的限制,TTI介质正演模拟不稳定、反偏移记录中遭受伪横波二次扰动及数值频散假象,另外拟声波最小二乘逆时偏移还面临计算效率低、收敛速度慢、对速度等模型参数依赖性高等问题.为了克服各向异性拟声波最小二乘逆时偏移的缺陷,在反演框架下,本文借助Low-rank有限差分算法首次提出并实现了TTI介质纯qP波线性正演模拟及纯qP波最小二乘逆时偏移;为了进一步提升反演成像效率,同时改善反演成像方法对模型参数误差的依赖性及对地震数据噪声的适应性,通过引入叠前平面波优化策略,发展了TTI介质纯qP波叠前平面波最小二乘逆时偏移成像方法.在编程实现方法的基础上,通过开展模型成像测试,展示了本方法的优势和潜力：一方面加快了反演成像效率,另一方面也提升了方法的抗噪性,同时还降低了方法对模型参数的依赖性.     

Interpretation of shallow refraction seismic data by reflection/refraction tomography

A new algorithm for tomographic inversion of traveltimes of reflected and refracted seismic waves is developed. The inversion gives interface configurations and velocity distributions in layers. The important features of the algorithm are: (a) the inclusion of shot time delays in the list of unknown parameters; (b) the regularization is applied in such a way that the most probable model is characterized by the similarity of neighbouring interfaces. As the problem under consideration is non-linear, several iterations are necessary in order to obtain the final model. In the case of a very inexact initial model, a 'layer-by-layer' inversion strategy is recommended as a first inversion step. The inversion program is supplied with a user interface, thanks to which one can: (a) pick interactively and identify seismic traveltimes; (b) build and edit depth/velocity models; and (c) display calculated traveltime curves and compare them with picked traveltimes as well as with the original seismic sections. The efficiency of the inversion software developed is illustrated by a numerical example and a field example in which shallow seismic data are considered. Application to wide-aperture reflection/refraction profiling (WARRP) data is also possible.     

Nonstationary deconvolution using maximum kurtosis optimization

Deconvolution is an essential step for high-resolution imaging in seismic data processing. The frequency and phase of the seismic wavelet change through time during wave propagation as a consequence of seismic absorption. Therefore, wavelet estimation is the most vital step of deconvolution, which plays the main role in seismic processing and inversion. Gabor deconvolution is an effective method to eliminate attenuation effects. Since Gabor transform does not prepare the information about the phase, minimum-phase assumption is usually supposed to estimate the phase of the wavelet. This manner does not return the optimum response where the source wavelet would be dominantly a mixed phase. We used the kurtosis maximization algorithm to estimate the phase of the wavelet. First, we removed the attenuation effect in the Gabor domain and computed the amplitude spectrum of the source wavelet; then, we rotated the seismic trace with a constant phase to reach the maximum kurtosis. This procedure was repeated in moving windows to obtain the time-varying phase changes. After that, the propagating wavelet was generated to solve the inversion problem of the convolutional model. We showed that the assumption of minimum phase does not reflect a suitable response in the case of mixed-phase wavelets. Application of this algorithm on synthetic and real data shows that subtle reflectivity information could be recovered and vertical seismic resolution is significantly improved.     

Joint AVO inversion, wavelet estimation and noise-level estimation using a spatially coupled hierarchical Bayesian model

The main objective of the AVO inversion is to obtain posterior distributions for P-wave velocity, S-wave velocity and density from specified prior distributions, seismic data and well-log data. The inversion problem also involves estimation of a seismic wavelet and the seismic-noise level. The noise model is represented by a zero mean Gaussian distribution specified by a covariance matrix. A method for joint AVO inversion, wavelet estimation and estimation of the noise level is developed in a Bayesian framework. The stochastic model includes uncertainty of both the elastic parameters, the wavelet, and the seismic and well-log data. The posterior distribution is explored by Markov-chain Monte-Carlo simulation using the Gibbs' sampler algorithm. The inversion algorithm has been tested on a seismic line from the Heidrun Field with two wells located on the line. The use of a coloured seismic-noise model resulted in about 10% lower uncertainties for the P-wave velocity, S-wave velocity and density compared with a white-noise model. The uncertainty of the estimated wavelet is low. In the Heidrun example, the effect of including uncertainty of the wavelet and the noise level was marginal with respect to the AVO inversion results.