OFFSET CONTINUATION IN THEORY AND PRACTICE*

Offset continuation is a technique that was recently proposed for the dip moveout correction. This correction can be carried out in the time-wavenumber domain using a proper partial differential equation that links sections with different offset. It has been shown that a single spike in a common-offset section—corresponds to a semi-elliptically shaped reflector with foci located at the source and receiver in the section migrated after dip moveout correction. The sections that result after offset continuation, stack, and migration are thus a superposition not only of semicircles, but also of semi-ellipses with different lengths of axes. This effect smears the migration alias-noise which, without offset continuation, would appear as migration circles not close enough together to interfere destructively. Offset continuation can improve the quality of seismic sections in several ways: —the velocity analyses are more readable, less dispersed and dip independent; diffraction tails arrive with the same normal moveout velocity as the apex and thus diffraction-noise can be “stacked out”; —noise produced by aliasing in the migrated section is reduced. In this paper we give a practical and conceptual interpretation of the offset continuation method, with a generalization to three-dimensional volumes of data. A critical examination of several synthetic and field data examples shows the actual possibilities and advantages of offset continuation.     

OFFSET CONTINUATION OF SEISMIC SECTIONS*

Geometrical acoustic and wave theory lead to a second-order partial differential equation that links seismic sections with different offsets. In this equation a time-shift term appears that corresponds to normal moveout; a second term, dependent on offset and time only, corrects the moveout of dipping events. The zero-offset stacked section can thus be obtained by continuing the section with maximum offset towards zero, and stacking along the way the other common-offset sections. Without the correction for dip moveout, the spatial resolution of the section is noticeably impaired, thus limiting the advantages that could be obtained with expensive migration procedures. Trade-offs exist between multiplicity of coverage, spatial resolution, and signal-to-noise; in some cases the spatial resolution on the surface can be doubled and the aliasing noise averaged out. Velocity analyses carried out on data continued to zero offset show a better resolution and improved discrimination against multiples. For instance, sea-floor multiples always appear at water velocity, so that their removal is simplified. This offset continuation can be carried out either in the time-space domain or in the time-wave number domain. The methods are applied both to synthetic and real data.     

三维地震勘探数据的剩余静校正方法研究与软件实现

剩余静校正的目的是消除地震道中由近地表因素造成的静态剩余时差的影响,通常以时差的四因子分解模型为基础建立剩余静校正方程组,并采用迭代求解方法获得剩余静校正量。但实际上,由于地层的倾斜,时差中还应包含横向和纵向倾角项,因此本文首先对剩余校正的理论模型进行了改进,提出了以扩展面元为计算单元的时差分解六因子模型。又由于地层的走向具有局部线性性,因此剩余动校正项,横向及纵向倾角项系数仅在一些给定的面元上计     

STACKING OF P-SV SEISMIC REFLECTION DATA USING DIP MOVEOUT1

The moveout of P-SV mode-converted seismic reflection events in a common-midpoint gather is non-hyperbolic. This is true even if the medium has constant P- and SV-wave velocities. Furthermore, reflection-point smear occurs even along horizontal reflectors. These effects reduce the resolution of the zero-offset stack. In such a medium, the generalization of the dip moveout transformation to P-SV data can be calculated analytically. The resulting P-SV dip moveout operators solve the problem of reflection-point smear, and image any reflector regardless of dip or depth. The viability of this technique is demonstrated on synthetic and field data.     

Suppressing random noise to broaden the useful bandwidth of seismic reflection data

The signal-to-noise ratio （SNR） of seismic reflection data in many areas is rather poor and conventional two-dimensional filters designed to suppress noise with different moveout from the signal tend to generate artifacts. We have extended a method of multichannel filtering, based on the hypothesis that signals on adjacent channels are similar, for enhancing the SNR on stacked sections. Using only the mid-range frequencies where the SNR is highest, the event trend is found for overlapping windows on the section and the average signal vector is calculated. Then the data from the full bandwidth section are projected onto the spatially varying unit similarity vectors and the results are merged for the overlapping windows. Application of the method to synthetic data containing steeply dipping events and to a stacked section for a marine 2D line has produced good results. The modifications we have introduced carry a small overhead in computing time but they should enable the method to be used effectively even on sections containing steep dips.     

可展宽地震资料有效频宽的随机噪声衰减方法

很多地区地震资料的信噪比较低,而用于压制与信号具有不同方向的随机噪声的常规二维滤波方法常常产生假信息。基于相邻信号具有相干性这一假设,本文提出了一种叠后衰减随机噪声的多道滤波方法。该方法利用信噪比最高的中频段信息(含有主频的这一频率区间)分时窗计算信号单位矢量,并将该时窗内全频段数据向信号单位矢量方向投影,对各时窗(包括时间方向和空间方向)重叠部分按比例进行加权。我们利用这种方法对含有陡倾角的合成地震数据和海上二维实际地震资料进行了处理,处理效果很好。这种方法较为费时,但不受倾角限制,应用范围广。     

ANALYSIS OF DIFFRACTION PATTERN FILTERING OF VARIABLY DENSITY AND VARIABLY AREA RECORDINGS

When a small, transparent replica of a seismic section is illuminated by a homogeneous beam of coherent, monochromatic parallel light a diffraction pattern is created that is representation of the double Fourier spectrum of the recorded seismic waves, i.e. their spectrum in terms of frequency, f, and apparent wave number, k. Masking selected parts of this diffraction pattern causes the spectrum to be filtered: the recomposition of the filtered spectrum then provides a filtered section. The ideal seismic section for this purpose would be a continuous variable density section obtained from recording made at every point of the seismic line. The light transmission coefficient (in terms of light amplitude) at each spot of the replica should be linearly related to the instantaneous seismic signal strength at the spot on the seismic section to which it refers. Unfortunately we cannot make recordings at every point of a seismic line and in our practically realisable recordings we have to be content with sampling in the direction of the location coordinate x. This means that with variable density recordings aliasing will be present and evident in the spectrum obtained in the direction of k; furthermore, the aliased spectrum is also multiplied by a sine function of k because the recording obtained at a given station is not presented on the seismic section as a single line along the time axis, but occupies the entire width of the trace. The diffraction patterns created by variable density recordings of dipping sine waves, including clipped recordings, and of the effect of dip filtering in such sections are discussed. The efficiency of dip rejection is shown to decrease with increasing dip. The diffraction pattern of a variable density recording is found to be characterised by a relationship between point pairs in the pattern. No such simple relationship has been found for the diffraction pattern of a variable area section; the spectra of such VAR sections belong to a very special class, because the amplitude transmission coefficient has only two values, viz. 0 and 1. Consequently, selective masking of the diffraction pattern of a VAR section may give rise to a filtered profile that does not look like a VAR section at all. General statements about the diffraction pattern of VAR sections are hard to give, because the transmission coefficient at a given point in the replica is not proportional to the signal level in the seismic section at the relevant point. In the case of VAR presentation of harmonic waves it was found that, as well as the aliasing effect in the k direction, higher harmonics of the frequency are also introduced. Some synthetic examples are given that show dip filtering to be less effective with VAR than with variable density recordings. Some arguments are advanced in favour of the opinion that high-pass filtering of VAR sections will have less success than low-pass filtering. This is demonstrated by two synthetic examples.     

SIGNAL-TO-NOISE RATIO ENHANCEMENT IN MULTICHANNEL SEISMIC DATA VIA THE KARHUNEN-LOÉVE TRANSFORM*

The Karhunen-Loéve transform, which optimally extracts coherent information from multichannel input data in a least-squares sense, is used for two specific problems in seismic data processing. The first is the enhancement of stacked seismic sections by a reconstruction procedure which increases the signal-to-noise ratio by removing from the data that information which is incoherent trace-to-trace. The technique is demonstrated on synthetic data examples and works well on real data. The Karhunen-Loéve transform is useful for data compression for the transmission and storage of stacked seismic data. The second problem is the suppression of multiples in CMP or CDP gathers. After moveout correction with the velocity associated with the multiples, the gather is reconstructed using the Karhunen-Loéve procedure, and the information associated with the multiples omitted. Examples of this technique for synthetic and real data are presented.     

Dip‐adaptive singular‐value decomposition filtering for seismic reflection enhancement

We present a singular value decomposition (SVD) filtering method for the enhancement of coherent reflections and for attenuation of noise. The method is applied in two steps. First normal move‐out (NMO) correction is applied to shot or CMP records, with the purpose of flattening the reflections. We use a spatial SVD filter with a short sliding window to enhance coherent horizontal events. Then the data are sorted in common‐offset panels and the local dip is estimated for each panel. The next SVD filtering is performed on a small number of traces and a small number of time samples centred around the output sample position. Data in a local window are corrected for linear moveout corresponding to the dips before SVD. At the central time sample position, we sum over the dominant eigenimages of a few traces, corresponding to SVD dip filtering. We illustrate the method using land seismic data from the Tacutu basin, located in the north‐east of Brazil. The results show that the proposed method is effective and is able to reveal reflections masked by ground‐roll and other types of noise.     

一种倾角时差校正和叠前成象方法

本文从测量射线参数出发进行反向射线追踪,导出倾角时差校正（DMO）的公式。经过DMO后,可以从一组等炮检距剖面得出共分角线点道集。用于对这些道集进行叠加的速度值与界面倾角无关。对经过DMO的资料的等时切片进行叠前成象（PSI）,就可以把分布在圆上的绕射能量沿圆弧加起来,并放在圆弧上对应于最大炮检距的位置。经过这两种处理,再应用标准的速度分析和叠加方法,就可得出偏移后的剖面。这两种处理均与速度无关。最后用物理模型试验说明了DMO和PSI的效果是好的。     

A SIMPLE EFFICIENT METHOD OF DIP-MOVEOUT CORRECTION1

Much of the success of modern seismic data processing derives from the use of the stacking process. Unfortunately, as is well known, conventional normal moveout correction (NMO) introduces mispositioning of data, and hence mis-stacking, when dip is present. Dip moveout correction (DMO) is a technique that converts non-zero-offset seismic data after NMO to true zero-offset locations and reflection times, irrespective of dip. The combination of NMO and DMO followed by post-stack time migration is equivalent to, but can be implemented much more efficiently than, full time migration before stack. In this paper we consider the frequency-wavenumber DMO algorithm developed by Hale. Our analysis centres on the result that, for a given dip, the combination of NMO at migration velocity and DMO is equivalent to NMO at the appropriate, dip-dependent, stacking velocity. This perspective on DMO leads to computationally efficient methods for applying Hale DMO and also provides interesting insights on the nature of both DMO and conventional stacking.     

利用数字图像处理技术提高地震剖面图像信噪比

提出了利用数字图像处理技术提高地震剖面信噪比的新方法，首先根据数字图像处理要求的格式，对地震剖面数据进行转换，得到地震剖面图像，分析了地震数据特点和初步地震图像的实验结果后，设计了新的预处理方法——“二维沿层滤波”，在此基础上，利用可以计算帧间运动速度及其变化都较大的改进的光流分析技术，计算出多幅地震剖面对应点的偏移量，然后应用图像积累技术对这多幅地震剖面进行积累，实现对三维地震数据体提高信噪比的处理，该方法充分利用了三维地震信息，不但可以提高整个数据体的信噪比，而且可以减少信号能量的损失，并保持原来的信号能量关系，使地震剖面的质量得到明显提高，为地震解释奠定良好的基础。     

PLANE-WAVE CONSTRAINTS IN 2D FILTER DESIGN1

A method is presented for developing and/or evaluating 2D filters applied to seismic data. The approach used is to express linear 2D filtering operations in the space-frequency (x–ω) domain. Correction filters are then determined using plane-wave constraints. For example, requiring a vertically propagating plane wave to be unaffected by migration necessitates application of a half-derivative correction in Kirchhoff migration. The same approach allows determination of the region of time-offset space where half-derivative corrections are correct in x–t domain dip moveout. Finally, an x–ω domain dip filter is derived using the constraint that a plane wave be attenuated as its dip increases. This filter has the advantage that it is significantly faster than f–k domain dip filtering and can be used on irregularly spaced data. This latter property also allows the filter to be used for interpolation of irregular data onto a regular grid.     

Seismic data interpolation using generalised velocity‐dependent seislet transform

Data interpolation is an important step for seismic data analysis because many processing tasks, such as multiple attenuation and migration, are based on regularly sampled seismic data. Failed interpolations may introduce artifacts and eventually lead to inaccurate final processing results. In this paper, we generalised seismic data interpolation as a basis pursuit problem and proposed an iteration framework for recovering missing data. The method is based on non‐linear iteration and sparse transform. A modified Bregman iteration is used for solving the constrained minimisation problem based on compressed sensing. The new iterative strategy guarantees fast convergence by using a fixed threshold value. We also propose a generalised velocity‐dependent formulation of the seislet transform as an effective sparse transform, in which the non‐hyperbolic normal moveout equation serves as a bridge between local slope patterns and moveout parametres in the common‐midpoint domain. It can also be reduced to the traditional velocity‐dependent seislet if special heterogeneity parametre is selected. The generalised velocity‐dependent seislet transform predicts prestack reflection data in offset coordinates, which provides a high compression of reflection events. The method was applied to synthetic and field data examples, and the results show that the generalised velocity‐dependent seislet transform can reconstruct missing data with the help of the modified Bregman iteration even for non‐hyperbolic reflections under complex conditions, such as vertical transverse isotropic (VTI) media or aliasing.     

Common reflection surface stack using dip decomposition for rugged surface topography

We present an extension of the Common Reflection Surface （CRS） stack that provides support for an arbitrary top surface topography. CRS stacking can be applied to the original prestack data without the need for any elevation statics. The CRS-stacked zero- offset section can be corrected （redatumed） to a given planar level by kinematic wave field attributes. The seismic processing results indicate that the CRS stacked section for rugged surface topography is better than the conventional stacked section for S/N ratio and better continuity of reflection events. Considering the multiple paths of zero-offset rays, the method deals with reflection information coming from different dips and performs the stack using the method of dip decomposition, which improves the kinematic and dynamic character of CRS stacked sections.     

基于定点形变资料获取断裂浅层倾向和倾角的方法研究—以唐山台为例

本文利用唐山地震台1978—2016年跨断层定点形变资料探究唐山地震台所跨断层的浅层倾向和倾角。首先,对形变资料进行数字滤波处理,消除原始观测数据中的非构造信息;其次,对数据精度进行评价,得出1997—2016年滤波后的形变数据年累计残差普遍较小、精度较高;最后,采用精度较高的形变数据计算SE和NW两倾向不同倾角下基线与水准和的累计残差分布,进而获取断层的浅层倾向和倾角。结果显示,依据跨断层定点形变资料获得唐山地震台所跨断层的浅层倾向为SE,倾角为89°,该结果与前人探槽剖面中断层产状相一致,反映出本文提出的基于长期跨断层定点形变资料通过数字滤波、数据精度评价来获取断裂浅层倾向和倾角的方法具有可行性,但本文所得反演结果与唐山地震台目前采用的断层倾向NW、倾角72°存在一定偏差。      

PRACTICAL ASPECTS OF THE DETERMINATION OF 3-D STACKING VELOCITIES*

Proper stacking of three-dimensional seismic CDP-data generally requires the knowledge of normal moveout velocities in all source-receiver directions contributing to a CDP-gather. The azimuthal variation of the stacking velocities mainly depends on the dip of the seismic interfaces. For a single dipping plane a simple relation exists between the dip and the azimuthal variation of NMO-velocity. Varying strike and dip of subsequent reflectors, however, result in a complex dependency of the seismic parameters. Reliable information on the spatial distribution of the normal moveout (NMO)-velocity can be derived from a wavefront curvature estimation using a 3-D ray-tracing technique. These procedures require additional information, e.g. reflection time gradients or depth maps to show interval velocities between leading interfaces. Moreover, their application to an extended 3-D data volume is restricted by high costs. The need for a routine 3-D procedure resulted in a special data selection to create pseudo 2-D profiles and to apply existing velocity estimation routines to these profiles. At least three estimates in different directions are necessary to derive the full azimuthal velocity variation, characterized by the large and the small main axis and the orientation of the velocity ellipse. Errors are estimated by means of computer models. Stacking velocities obtained by mathematical routines (least-squares fit) and by seismic standard routines (NMO-correction and correlation) are compared. Finally, a general 3-D velocity procedure using cross-correlation of preliminarily NMO-corrected traces is proposed.     

MIGRATION TO ZERO OFFSET (DMO) FOR A CONSTANT VELOCITY GRADIENT: AN ANALYTICAL FORMULATION1

Migration to zero offset (MZO) is a prestack partial migration process that transforms finite-offset seismic data into a close approximation to zero-offset data, regardless of the reflector dips that are present in the data. MZO is an important step in the standard processing sequence of seismic data, but is usually restricted to constant velocity media. Thus, most MZO algorithms are unable to correct for the reflection point dispersal caused by ray bending in inhomogeneous media. We present an analytical formulation of the MZO operator for the simple possible variation of velocity within the earth, i.e. a constant gradient in the vertical direction. The derivation of the MZO operator is carried out in two steps. We first derive the equation of the constant traveltime surface for linear V(z) velocity functions and show that the isochron can be represented by a fourth-degree polynomial in x, y and z. This surface reduces to the well-known ellipsoid in the constant-velocity case, and to the spherical wavefront obtained by Slotnick in the coincident source-receiver case. We then derive the kinematic and dynamic zero-offset corrections in parametric form by using the equation of the isochron. The weighting factors are obtained in the high-frequency limit by means of a simple geometric spreading correction. Our analytical results show that the MZO operator is a multivalued, saddle-shaped operator with marked dip moveout effects in the cross-line direction. However, the amplitude analysis and the distribution of dips along the MZO impulse response show that the most important contributions of the MZO operator are concentrated in a narrow zone along the in-line direction. In practice, MZO processing requires approximately the same trace spacing in the in-line and cross-line directions to avoid spatial aliasing effects.     

Common-reflection-surface stack — a real data example

The simulation of a zero-offset (ZO) stack section from multi-coverage reflection data is a standard imaging method in seismic processing. It significantly reduces the amount of data and increases the signal-to-noise ratio due to constructive interference of correlated events. Conventional imaging methods, e.g., normal moveout (NMO)/dip moveout (DMO)/stack or pre-stack migration, require a sufficiently accurate macro-velocity model to yield appropriate results, whereas the recently introduced common-reflection-surface stack does not depend on a macro-velocity model. For two-dimensional seismic acquisition, its stacking operator depends on three wavefield attributes and approximates the kinematic multi-coverage reflection response of curved interfaces in laterally inhomogeneous media. The common-reflection-surface stack moveout formula defines a stacking surface for each particular sample in the ZO section to be simulated. The stacking surfaces that fit best to actual events in the multi-coverage data set are determined by means of coherency analysis. In this way, we obtain a coherency section and a section of each of the three wavefield attributes defining the stacking operator. These wavefield attributes characterize the curved interfaces and, thus, can be used for a subsequent inversion. In this paper, we focus on an application to a real land data set acquired over a salt dome. We propose three separate one-parametric search and coherency analyses to determine initial common-reflection-surface stack parameters. Optionally, a subsequent optimization algorithm can be performed to refine these initial parameters. The simulated ZO section obtained by the common-reflection-surface stack is compared to the result of a conventional NMO/DMO/stack processing sequence. We observe an increased signal-to-noise ratio and an improved continuity along the events for our proposed method — without loss of lateral resolution.     

OPTIMUM HYPERBOLIC MOVEOUT FILTERS WITH APPLICATIONS TO SEISMIC DATA*

Optimum multichannel filters can be designed to process seismic events falling on hyperbolic moveout curves using the conventional least-squares method. Contrary to the linear moveout filters, autocorrelation and crosscorrelation functions inherent in the normal equations have to be computed numerically. However, computation times of filter coefficients are comparable to linear moveout operators. For a given source-receiver geometry and assuming straight ray-path, relative moveout of a seismic reflection event is dependent on the two way arrival time and rms velocity. Consequently, to avoid overlapping of pass and reject moveout windows, hyperbolic moveout filters have to be designed over time gates rather than for the whole record lengths. Hyperbolic and hyperbolic-linear moveout filters applied to synthetic and field seismic reflection traces show good signal-to-noise (S/N) ratio improvements. Results of some combined synthetic and field data examples are presented.