带有多道相关的抛物线Radon变换法分离P-P、P-SV波

因为多波多分量地震勘探中P-P波和P-SV波通常混杂在一起,所以较好地分离P-P波和P-SV波能够提高数据处理和解释的质量.抛物线Radon变换法在分离P-P波和P-SV波时取得了一定效果,但是在离散叠加的计算过程中会带来假频,这些假频会干扰波场分离.本文针对这一问题,将多道相关算法引入抛物线Radon变换,发展了带有多道相关的抛物线Radon变换法.该方法利用叠加信号具有相似性的特点,依据多道相关中衡量多道信号相似性的能量比标准,对叠加过程加以控制,压制变换中出现的假频.本文用该方法对合成地震记录进行了波场分离,取得了较好的效果.     

井孔高分辨率Radon变换算子研究

本文针对井间和3D VSP波场的线性特征,研究井孔地震波场线性高分辨率Radon变换算子,用于井孔地震波场分析与纵横波分离.在Radon变换原理分析基础上,采用基于柯西分布的高分辨率线性Radon变换对井孔数据进行Radon变换,其间通过对离散倾角叠加算子求取的研究,及对影响Radon能量收敛的重要参数阻尼因子算法的改进,使数据在Radon域以能量团的形式呈现,得到很好的收敛效果,基本解决了Radon域数据的一定程度的拖尾现象,消除了各能量团之间的平滑效应,采用柯西分布来规则化数据,提高了Radon域的分辨率,Radon域能量也收敛到一个点上,有利于上下行波或纵横波波场分离.最后通过反演结果和模型试算验证了该方法的可行性和稳定性.     

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.     

基于改进线性Radon变换的井孔地震上下行波场分离方法

反射波场分离是井孔地震资料处理中极其重要的一个环节,波场分离的质量直接影响成像结果的精度.不管是VSP还是井间地震资料,其反射波时距曲线都近似直线型,根据这一特征,本文提出一种改进的线性Radon变换方法来进行井孔资料的反射波上下行波场分离.该方法基于频率域线性Radon变换,通过引入一个新的变量λ来消除变换算子对频率的依赖性,避免了求取每一频率分量对应的不同变换算子,显著降低了计算成本;文中在求解该方法对应的最小二乘问题时,引入了发展较为成熟的高分辨率Radon变换技术来进一步提高波场分离的精度.采用本文方法进行井孔地震资料的上下行波场分离可以在保证分离精度的前提下有效地提高计算效率.根据上下行波在λ-f域内分布的特殊性,设计简单的滤波算子就可实现上下行波场的分离.最后通过合成数据试算以及实际资料处理（VSP数据和井间地震数据）验证了该方法的可行性和有效性.     

Data acquisition and pre-processing required for simultaneous P-SV inversion

The goal of seismic reflection surveys is the derivation of petrophysical subsurface parameters from surface measurements. Today's well established technique in data acquisition, as well as processing terms, is based on the acoustic approximation to the real world's wave propagation. In recent years a lot of work has been done to extend the technique to the elastic approximation. There was especially an important trend towards elastic inversion techniques operating on plane-wave seismograms, called simultaneous P-SV inversion (or short P-SV inversion) within this paper. Being still under investigation, some important aspects of P-SV inversion concerning data acquisition as well as pre-processing, should be pointed out. To fit the assumptions of P-SV inversion schemes, at least a two-dimensional picture of the reflected wavefield with vertical and in-line horizontal receivers has to be recorded. Moreover, the theoretical work done suggests that in addition to a survey with a compressional wave source, a second survey should be done using sources radiating vertically polarized shear waves, is needed. Finally, proper slant stacking must be performed to get plane-wave seismograms. The P/S separated plane-wave seismograms are then well prepared for feeding into the inversion algorithms. P/S separated planewave seismograms are then well prepared for feeding into the inversion algorithm.s In this paper, a tutorial overview of the data acquisition and pre-processing in accordance with the P-SV inversion philosophy is given and illustrated using synthetic seismograms. A judgement on the feasibility of the P-SV inversion philosophy must be left to ongoing research.     

High‐resolution Radon transforms for improved dipole acoustic imaging

Imaging using dipole acoustic logging reflections has become a research topic of increasing interest in recent years. Extracting reflections from the whole waveform is both important and extremely difficult because the reflections are obscured by large‐amplitude direct waves. A method of wavefield separation based on high‐resolution Radon transforms has been applied to separate the reflected waves. First, an analysis of the common offset gathers shows that the linear Radon transform can be used to separate the direct and reflected wave fields. However, traditional linear Radon transforms cannot focus the wave event using the least squares method. An improved high‐resolution linear Radon transform is achieved using the principles of maximum entropy and Bayesian methods based on previous studies. The separation method is tested using synthetic data for hard and soft formations, a void model, and a fault model. The high‐resolution Radon transform method is used to process a field dataset and exhibits improved results compared with those of the standard method.     

Seismic data reconstruction using a sparsity-promoting apex shifted hyperbolic Radon-curvelet transform

Apex shift hyperbolic Radon transform (ASHRT) is an extension of hyperbolic Radon transform (HRT). We have developed a novel sparsity-promoting framework for ASHRT by employing curvelet transform (CT) in the sparse inversion. RT-based seismic data processing can be considered as an optimization problem and a mixed norms inversion, therefore, objective function with CT can promote the sparsity of the transformed domain, which makes the sparse inversion more efficient. Compared with the conventional sparse inversion of ASHRT, the proposed method weights the sparse penalization, which indicates a sparser solution of ASHRT. We use synthetic and field data examples to demonstrate the performance of ASHRT. Compared to the conventional solution, the ours may lead to more accurately reconstructed results and have a better noise immunity.     

TRACE INTERPOLATION BY SLANT-STACK MIGRATION1

The slant-stack migration formula based on the Radon transform is studied with respect to the depth step Δz of wavefield extrapolation. It can be viewed as a generalized trace-interpolation procedure including wave extrapolation with an arbitrary step Δz. For Δz= 0 the formula yields the familiar plane-wave decomposition, while for Δz > 0 it provides a robust tool for migration transformation of spatially undersampled wavefields. Using the stationary phase method, it is shown that the slant-stack migration formula degenerates into the Rayleigh-Sommerfeld integral in the far-field approximation. Consequently, even a narrow slant-stack gather applied before the diffraction stack can significantly improve the representation of noisy data in the wavefield extrapolation process. The theory is applied to synthetic and field data to perform trace interpolation and dip reject filtration. The data examples presented prove that the Radon interpolator works well in the dip range, including waves with mutual stepouts smaller than half the dominant period.     

Reverse time migration of ground-penetrating radar with full wavefield decomposition based on the Hilbert transform

The conventional reverse time migration of ground-penetrating radar data is implemented with the two-way wave equation. The cross-correlation result contains low-frequency noise and false images caused by improper wave paths. To eliminate low-frequency noise and improve the quality of the migration image, we propose to separate the left-up-going, left-down-going, right-up-going and right-down-going wavefield components in the forward- and backward-propagated wavefields based on the Hilbert transform. By applying the reverse time migration of ground-penetrating radar data with full wavefield decomposition based on the Hilbert transform, we obtain the reverse time migration images of different wavefield components and combine correct imaging conditions to generate complete migration images. The proposed method is tested on the synthetic ground-penetrating radar data of a tilt-interface model and a complex model. The migration results show that the imaging condition of different wavefield components can highlight the desired structures. We further discuss the reasons for incomplete images by reverse time migration with partial wavefields. Compared with the conventional reverse time migration methods for ground-penetrating radar data, low-frequency noise can be eliminated in images generated by the reverse time migration method with full wavefield decomposition based on the Hilbert transform.     

共炮检距二维弹性波地震剖面的偏移方法

在均匀各向同性介质的分界面上入射纵波时，除产生纵波反射Ｐ－Ｐ波外，还会产生转换横波的反射Ｐ－ＳＶ波。同样，当入射波为ＳＶ横波时，在分界面上会同时产生ＳＶ－ＳＶ反射波和ＳＶ－Ｐ反射转换波，对这种二维弹性波地震记录如何进行偏移是正在探讨的问题。为了能够处理实际地震数据，本文提出在共炮检距剖面上进行二维弹性波记录的偏移方法。具体做法是，首先用弹性波方程将两分量的地震记录分解为Ｐ－Ｐ（或ＳＶ－ＳＶ）波和Ｐ－ＳＶ（或ＳＶ－Ｐ）波，然后用我们已导出的适合于处理共炮检距剖面的叠前偏移方法对它们进行处理。用模拟数据进行的试验说明方法正确，效果良好。     

线性同相轴波场分离的高分辨率τ-p变换法

基于最小二乘τ-p变换和τ-p域模型稀疏分布的假设，本文给出高分辨率τ-p变换的推导及其模型空间域的离散采样公式，同时给出了保振幅线性同相轴波场分离的算法流程.在求解本文给出的高分辨率τ-p正变换时，由于待求解的矩阵不具备最小平方法所具有的Toeplitz结构，故采用Cholesky分解法进行计算.本文模拟了井间地震和阵列声波测井中的Stoneley上下行波的分离算法过程，高分辨率正反τ-p变换且滤波所得结果显示本文算法误差小和保振幅的特点.对于在τ-p域距离很近或时间域同相轴近于水平的线性波场，高分辨率算法的聚焦作用使得所分离波场畸变小，体现本文算法精度高的优点.理论模型试算表明本文给出的高分辨率τ-p变换线性波场分离算法具有稳定性、精度高和保振幅的特点.     

基于解析时间波场外推与波场分解的逆时偏移方法研究

双程波方程逆时深度偏移是复杂介质高精度成像的有效技术,但其结果中通常包含成像方法引起的噪音和假象,一般的滤波方法会破坏成像剖面上的振幅,其中的假象也会给后续地质解释带来困扰.将波场进行方向分解然后实现入射波与反射波的相关成像能够有效地消除这类成像噪音,并提高逆时偏移成像质量.波传播方向的分解通常在频率波数域实现,它会占用大量的存储和计算资源,不便于在沿时间外推的逆时深度偏移中应用.本文提出解析时间波场外推方法,可以在时间外推的每个时间片上实现波传播方向的显式分解,逆时深度偏移中利用分解后的炮检波场进行对应的相关运算,实现成像噪音和成像信号的分离.在模型和实际数据上的测试表明,相比于常规互相关逆时偏移成像结果,本文方法能够有效地消除低频成像噪音和特殊地质构造导致的成像假象.     

Inversion-based deblending using migration operators

In this paper, we compare the denoising- and inversion-based deblending methods using Stolt migration operators. We use Stolt operator as a kernel to efficiently compute apex-shifted hyperbolic Radon transform. Sparsity promoting transforms, such as Radon transform, can focus seismic data into a sparse model to separate signals, remove noise or interpolate missing traces. Therefore, Radon transforms are a suitable tool for either the denoising- or the inversion-based deblending methods. The denoising-based deblending treats blending interferences as random noise by sorting the data into new gathers, such as common receiver gather. In these gathers, blending interferences exhibit random structures due to the randomization of the source firing times. Alternatively, the inversion-based deblending treats blending interferences as a signal, and the transform models this signal by incorporating the blending operator to formulate an inversion problem. We compare both methods using a robust inversion algorithm with sparse regularization. Results of synthetic and field data examples show that the inversion-based deblending can produce more accurate signal separation for highly blended data.     

一种基于高效迭代解法的频率域全波形反演

巨大的计算量是制约全波形反演（FWI）生产实用化的难题之一.为此,本文提出了一种高效的波场迭代解法,将其应用于频率域常密度声波方程FWI,并给出了详细的反演流程.通过建立用于波场迭代的目标函数,推导相应梯度、步长公式,新方法将反演中波场正传和残差波场反传过程转化为无约束优化问题,从理论上分析了新方法的计算效率显著高于常规FWI.在数值试验中,本文方法通过几次迭代便能获得高精度的正传、残差反传波场,收敛速度明显高于未经预处理的GMRES方法.进一步引入高效编码策略,新方法的计算时间约为常规编码FWI的1/8,与理论分析结果吻合（波场迭代次数为8,模型未知量个数约为7万）,且波场迭代次数为6时,反演效果已与常规编码FWI相近.     

不依赖源子波的跨孔雷达时间域波形反演

波形反演是近年来较热门的反演方法,其分辨率可以达到亚波长级别.在波形反演的实际应用中,源子波的估计十分重要.传统方法使用反褶积来估计源子波并随着反演过程更新,该方法在合成数据波形反演中效果较好,但在实际数据反演过程中存在一系列的问题.由于实际数据信噪比较低,在源子波估计过程中需要大量的人为干涉,且结果并不一定可靠.本文使用一种基于褶积波场的新型目标函数,令反演过程不再依赖源子波.详细推导了针对跨孔雷达波形反演的梯度及步长公式,实现介电常数和电导率的同步反演.针对一个合成数据模型同时反演介电常数和电导率,结果表明该方法能够反演出亚波长尺寸异常体的形状和位置.接着,将该方法应用到两组实际数据中,并与基于估计源子波的时间域波形反演结果进行比较.结果表明不依赖源子波的时间域波形反演结果分辨率更高,也更准确.     

高保真VSP波场分离方法研究

三维VSP资料中,各种不同类型的波混杂一起形成复杂的波场.因此,波场分离是三维VSP数据处理关键的第一步.从不同波场的偏振方向和传播方向之差异着手,提出了一种高保真的VSP波场分离方法.首先通过射线追踪和偏振滤波的结合,把复杂波场(分解为简单波场;然后根据简单波场中不同波的传播方向截然相反的特点,进行方向滤波,达到波场分离的目的.实际数据处理表明,与常规波场分离方法相比,本方法大大降低了混波作用以及由此而生的波形畸变.     

MULTICOMPONENT COMMON-RECEIVER GATHER MIGRATION OF SINGLE-LEVEL WALK-AWAY SEISMIC PROFILES1

Seismic data are usually separated into P-waves and S-waves before being put through a scalar (acoustic) migration. The relationship between polarization and moveout is exploited to design filters that extract the desired wavetype. While these filters can always be applied to shot records, they can only be applied to a triaxial common-receiver gather in special cases since the moveout of scattered energy on the receiver gather relates to path differences between the surface shots and the scatterer while the polarization is determined by the path from scatterer to downhole geophone. Without the ability to separate wavefields before migration, a ‘vector scalar’ or an elastic migration becomes a necessity. Here the propagation of the elastic wavefield for a given mode (e.g. P-S) is approximated by two scalar (acoustic) propagation steps in a ‘vector scalar’ migration. ‘Vector’ in that multicomponent data is migrated and 'scalar’ in that each propagation step is based on a scalar wave equation for the appropriate mode. It is assumed that interaction between the wavefields occurs only once in the far-field of both the source and receiver. Extraction of the P, SV and SH wavefields can be achieved within the depth migration (if one assumes isotropy in the neighbourhood of the downhole receiver) by a projection onto the polarization for the desired mode. Since the polarization of scattered energy is only a function of scatterer position and receiver position (and not source position), the projection may be taken outside the migration integral in the special case of the depth migration of a common-receiver gather. The extraction of the desired mode is then performed for each depth migration bin after the separate scalar migration of each receiver gather component. This multicomponent migration of triaxial receiver gathers is conveniently implemented with a hybrid split-step Fourier-excitation-time imaging condition depth migration. The raytracing to get the excitation-time imaging condition also provides the expected polarization for the post-migration projection. The same downward extrapolated wavefield can be used for both the P-P and P-S migrations, providing a flexible and efficient route to the migration of multicomponent data. The technique is illustrated on a synthetic example and a single-level Walk-away Seismic Profile (WSP) from the southern North Sea. The field data produced images showing a P-P reflector below the geophone and localized P-P and P-S scatterers at the level of the geo-phone. These scatterers, which lie outside the zone of specular illumination, are interpreted as faults in the base Zechstein/top Rotliegendes interface.     

Wavefield interpolation in 3D large‐step Fourier wavefield extrapolation

Extrapolating wavefields and imaging at each depth during three‐dimensional recursive wave‐equation migration is a time‐consuming endeavor. For efficiency, most commercial techniques extrapolate wavefields through thick slabs followed by wavefield interpolation within each thick slab. In this article, we develop this strategy by associating more efficient interpolators with a Fourier‐transform‐related wavefield extrapolation method. First, we formulate a three‐dimensional first‐order separation‐of‐variables screen propagator for large‐step wavefield extrapolation, which allows for wide‐angle propagations in highly contrasting media. This propagator significantly improves the performance of the split‐step Fourier method in dealing with significant lateral heterogeneities at the cost of only one more fast Fourier transform in each thick slab. We then extend the two‐dimensional Kirchhoff and Born–Kirchhoff local wavefield interpolators to three‐dimensional cases for each slab. The three‐dimensional Kirchhoff interpolator is based on the traditional Kirchhoff formula and applies to moderate lateral velocity variations, whereas the three‐dimensional Born–Kirchhoff interpolator is derived from the Lippmann–Schwinger integral equation under the Born approximation and is adapted to highly laterally varying media. Numerical examples on the three‐dimensional salt model of the Society of Exploration Geophysicists/European Association of Geoscientists demonstrate that three‐dimensional first‐order separation‐of‐variables screen propagator Born–Kirchhoff depth migration using thick‐slab wavefield extrapolation plus thin‐slab interpolation tolerates a considerable depth‐step size of up to 72 ms, eventually resulting in an efficiency improvement of nearly 80% without obvious loss of imaging accuracy. Although the proposed three‐dimensional interpolators are presented with one‐way Fourier extrapolation methods, they can be extended for applications to general migration methods.     

基于Bregman迭代的复杂地震波场稀疏域插值方法

在地震勘探中,野外施工条件等因素使观测系统很难记录到完整的地震波场,因此,资料处理中的地震数据插值是一个重要的问题。尤其在复杂构造条件下,缺失的叠前地震数据给后续高精度处理带来严重的影响。压缩感知理论源于解决图像采集问题,主要包含信号的稀疏表征以及数学组合优化问题的求解,它为地震数据插值问题的求解提供了有效的解决方案。在应用压缩感知求解复杂地震波场的插值问题中,如何最佳化表征复杂地震波场以及快速准确的迭代算法是该理论应用的关键问题。Seislet变换是一个特殊针对地震波场表征的稀疏多尺度变换,该方法能有效地压缩地震波同相轴。同时,Bregman迭代算法在以稀疏表征为核心的压缩感知理论中,是一种有效的求解算法,通过选取适当的阈值参数,能够开发地震波动力学预测理论、图像处理变换方法和压缩感知反演算法相结合的地震数据插值方法。本文将地震数据插值问题纳入约束最优化问题,选取能够有效压缩复杂地震波场的OC-seislet稀疏变换,应用Bregman迭代方法求解压缩感知理论框架下的混合范数反问题,提出了Bregman迭代方法中固定阈值选取的H曲线方法,实现地震波场的快速、准确重建。理论模型和实际数据的处理结果验证了基于H曲线准则的Bregman迭代稀疏域插值方法可以有效地恢复复杂波场的缺失信息。     

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.