Non‐uniqueness with refraction inversion – a syncline model study

Non‐uniqueness occurs with the 1D parametrization of refraction traveltime graphs in the vertical dimension and with the 2D lateral resolution of individual layers in the horizontal dimension. The most common source of non‐uniqueness is the inversion algorithm used to generate the starting model. This study applies 1D, 1.5D and 2D inversion algorithms to traveltime data for a syncline (2D) model, in order to generate starting models for wave path eikonal traveltime tomography. The 1D tau‐p algorithm produced a tomogram with an anticline rather than a syncline and an artefact with a high seismic velocity. The 2D generalized reciprocal method generated tomograms that accurately reproduced the syncline, together with narrow regions at the thalweg with seismic velocities that are less than and greater than the true seismic velocities as well as the true values. It is concluded that 2D inversion algorithms, which explicitly identify forward and reverse traveltime data, are required to generate useful starting models in the near‐surface where irregular refractors are common. The most likely tomogram can be selected as either the simplest model or with a priori information, such as head wave amplitudes. The determination of vertical velocity functions within individual layers is also subject to non‐uniqueness. Depths computed with vertical velocity gradients, which are the default with many tomography programs, are generally 50% greater than those computed with constant velocities for the same traveltime data. The average vertical velocity provides a more accurate measure of depth estimates, where it can be derived. Non‐uniqueness is a fundamental reality with the inversion of all near‐surface seismic refraction data. Unless specific measures are taken to explicitly address non‐uniqueness, then the production of a single refraction tomogram, which fits the traveltime data to sufficient accuracy, does not necessarily demonstrate that the result is either ‘correct’ or the most probable.     

2D inversion of refraction traveltime curves using homogeneous functions

A method using simple inversion of refraction traveltimes for the determination of 2D velocity and interface structure is presented. The method is applicable to data obtained from engineering seismics and from deep seismic investigations. The advantage of simple inversion, as opposed to ray‐tracing methods, is that it enables direct calculation of a 2D velocity distribution, including information about interfaces, thus eliminating the calculation of seismic rays at every step of the iteration process. The inversion method is based on a local approximation of the real velocity cross‐section by homogeneous functions of two coordinates. Homogeneous functions are very useful for the approximation of real geological media. Homogeneous velocity functions can include straight‐line seismic boundaries. The contour lines of homogeneous functions are arbitrary curves that are similar to one another. The traveltime curves recorded at the surface of media with homogeneous velocity functions are also similar to one another. This is true for both refraction and reflection traveltime curves. For two reverse traveltime curves, non‐linear transformations exist which continuously convert the direct traveltime curve to the reverse one and vice versa. This fact has enabled us to develop an automatic procedure for the identification of waves refracted at different seismic boundaries using reverse traveltime curves. Homogeneous functions of two coordinates can describe media where the velocity depends significantly on two coordinates. However, the rays and the traveltime fields corresponding to these velocity functions can be transformed to those for media where the velocity depends on one coordinate. The 2D inverse kinematic problem, i.e. the computation of an approximate homogeneous velocity function using the data from two reverse traveltime curves of the refracted first arrival, is thus resolved. Since the solution algorithm is stable, in the case of complex shooting geometry, the common‐velocity cross‐section can be constructed by applying a local approximation. This method enables the reconstruction of practically any arbitrary velocity function of two coordinates. The computer program, known as godograf , which is based on this theory, is a universal program for the interpretation of any system of refraction traveltime curves for any refraction method for both shallow and deep seismic studies of crust and mantle. Examples using synthetic data demonstrate the accuracy of the algorithm and its sensitivity to realistic noise levels. Inversions of the refraction traveltimes from the Salair ore deposit, the Moscow region and the Kamchatka volcano seismic profiles illustrate the methodology, practical considerations and capability of seismic imaging with the inversion method.     

P‐wave velocity distribution in basalt flows of the Enni Formation in the Faroe Islands from refraction seismic analysis

The main objective of this work is to establish the applicability of shallow surface‐seismic traveltime tomography in basalt‐covered areas. A densely sampled ～1300‐m long surface seismic profile, acquired as part of the SeiFaBa project in 2003 ( Japsen et al. 2006 ) at Glyvursnes in the Faroe Islands, served as the basis to evaluate the performance of the tomographic method in basalt‐covered areas. The profile is centred at a ～700‐m deep well. V_P, V_S and density logs, a zero‐offset VSP, downhole‐geophone recordings and geological mapping in the area provided good means of control. The inversion was performed with facilities of the Wide Angle Reflection/Refraction Profiling program package ( Ditmar et al. 1999 ). We tested many inversion sequences while varying the inversion parameters. Modelled traveltimes were verified by full‐waveform modelling. Typically an inversion sequence consists in several iterations that proceed until a satisfactory solution is reached. However, in the present case with high velocity contrasts in the subsurface we obtained the best result with two iterations: first obtaining a smooth starting model with small traveltime residuals by inverting with a high smoothing constraint and then inverting with the lowest possible smoothing constraint to allow the inversion to have the full benefit of the traveltime residuals. The tomogram gives usable velocity information for the near‐surface geology in the area but fails to reproduce the expected velocity distribution of the layered basalt flows. Based on the analysis of the tomogram and geological mapping in the area, a model was defined that correctly models first arrivals from both surface seismic data and downhole‐geophone data.     

Parsimonious wave‐equation travel‐time inversion for refraction waves

We present a parsimonious wave‐equation travel‐time inversion technique for refraction waves. A dense virtual refraction dataset can be generated from just two reciprocal shot gathers for the sources at the endpoints of the survey line, with N geophones evenly deployed along the line. These two reciprocal shots contain approximately 2N refraction travel times, which can be spawned into refraction travel times by an interferometric transformation. Then, these virtual refraction travel times are used with a source wavelet to create N virtual refraction shot gathers, which are the input data for wave‐equation travel‐time inversion. Numerical results show that the parsimonious wave‐equation travel‐time tomogram has about the same accuracy as the tomogram computed by standard wave‐equation travel‐time inversion. The most significant benefit is that a reciprocal survey is far less time consuming than the standard refraction survey where a source is excited at each geophone location.     

A new direction for shallow refraction seismology: integrating amplitudes and traveltimes with the refraction convolution section

The refraction convolution section (RCS) is a new method for imaging shallow seismic refraction data. It is a simple and efficient approach to full‐trace processing which generates a time cross‐section similar to the familiar reflection cross‐section. The RCS advances the interpretation of shallow seismic refraction data through the inclusion of time structure and amplitudes within a single presentation. The RCS is generated by the convolution of forward and reverse shot records. The convolution operation effectively adds the first‐arrival traveltimes of each pair of forward and reverse traces and produces a measure of the depth to the refracting interface in units of time which is equivalent to the time‐depth function of the generalized reciprocal method (GRM). Convolution also multiplies the amplitudes of first‐arrival signals. To a good approximation, this operation compensates for the large effects of geometrical spreading, with the result that the convolved amplitude is essentially proportional to the square of the head coefficient. The signal‐to‐noise (S/N) ratios of the RCS show much less variation than those on the original shot records. The head coefficient is approximately proportional to the ratio of the specific acoustic impedances in the upper layer and in the refractor. The convolved amplitudes or the equivalent shot amplitude products can be useful in resolving ambiguities in the determination of wave speeds. The RCS can also include a separation between each pair of forward and reverse traces in order to accommodate the offset distance in a manner similar to the XY spacing of the GRM. The use of finite XY values improves the resolution of lateral variations in both amplitudes and time‐depths. The use of amplitudes with 3D data effectively improves the spatial resolution of wave speeds by almost an order of magnitude. Amplitudes provide a measure of refractor wave speeds at each detector, whereas the analysis of traveltimes provides a measure over several detectors, commonly a minimum of six. The ratio of amplitudes obtained with different shot azimuths provides a detailed qualitative measure of azimuthal anisotropy and, in turn, of rock fabric. The RCS facilitates the stacking of refraction data in a manner similar to the common‐midpoint methods of reflection seismology. It can significantly improve S/N ratios.Most of the data processing with the RCS, as with the GRM, is carried out in the time domain, rather than in the depth domain. This is a significant advantage because the realities of undetected layers, incomplete sampling of the detected layers and inappropriate sampling in the horizontal rather than the vertical direction result in traveltime data that are neither a complete, an accurate nor a representative portrayal of the wave‐speed stratification. The RCS facilitates the advancement of shallow refraction seismology through the application of current seismic reflection acquisition, processing and interpretation technology.     

Refraction traveltime and amplitude corrections for very near- surface inhomogeneities

The performance of refraction inversion methods that employ the principle of refraction migration, whereby traveltimes are laterally migrated by the offset distance (which is the horizontal separation between the point of refraction and the point of detection on the surface), can be adversely affected by very near‐surface inhomogeneities. Even inhomogeneities at single receivers can limit the lateral resolution of detailed seismic velocities in the refractor. The generalized reciprocal method ‘statics’ smoothing method (GRM SSM) is a smoothing rather than a deterministic method for correcting very near‐surface inhomogeneities of limited lateral extent. It is based on the observation that there are only relatively minor differences in the time‐depths to the target refractor computed for a range of XY distances, which is the separation between the reverse and forward traveltimes used to compute the time‐depth. However, any traveltime anomalies, which originate in the near‐surface, migrate laterally with increasing XY distance. Therefore, an average of the time‐depths over a range of XY values preserves the architecture of the refractor, but significantly minimizes the traveltime anomalies originating in the near‐surface. The GRM statics smoothing corrections are obtained by subtracting the average time‐depth values from those computed with a zero XY value. In turn, the corrections are subtracted from the traveltimes, and the GRM algorithms are then re‐applied to the corrected data. Although a single application is generally adequate for most sets of field data, model studies have indicated that several applications of the GRM SSM can be required with severe topographic features, such as escarpments. In addition, very near‐surface inhomogeneities produce anomalous head‐wave amplitudes. An analogous process, using geometric means, can largely correct amplitude anomalies. Furthermore, the coincidence of traveltime and amplitude anomalies indicates that variations in the near‐surface geology, rather than variations in the coupling of the receivers, are a more likely source of the anomalies. The application of the GRM SSM, together with the averaging of the refractor velocity analysis function over a range of XY values, significantly minimizes the generation of artefacts, and facilitates the computation of detailed seismic velocities in the refractor at each receiver. These detailed seismic velocities, together with the GRM SSM‐corrected amplitude products, can facilitate the computation of the ratio of the density in the bedrock to that in the weathered layer. The accuracy of the computed density ratio improves where lateral variations in the seismic velocities in the weathered layer are known.     

基于交叉梯度约束的地震初至纵波与瑞雷面波联合反演

本文提出了一种初至纵波(P波)与瑞雷面波的交叉梯度联合反演策略.通过对初至P波进行全波形反演可以获得近地表P波速度结构;通过对仅含瑞雷面波信息的地震数据转换到频率-波数域进行加窗振幅波形反演(Windowed-Amplitude Waveform Inversion,w-AWI)可获得近地表横波(S波)速度结构.在二者反演的目标函数中均加入P波速度和S波速度的交叉梯度作为正则化约束项,使得在反演过程中P波速度和S波速度相互制约,相互约束,从而实现对地震初至P波与瑞雷面波的联合反演.数值模拟结果表明交叉梯度联合反演可以提高S波速度反演分辨率,而P波速度反演结果并没有得到提高.实际资料的反演结果表明,交叉梯度联合反演能够获得更加可信的近地表速度结构.     

Seismic refraction traveltime inversion for static corrections in a glaciated shield rock environment: a case study

A traveltime inversion technique is applied to model the upper ∼40 m of the subsurface of a glaciated shield rock area in order to calculate static corrections for a multi-azimuth multi-depth walk-away vertical seismic profile and a surface seismic reflection profile. First break information from a seismic refraction survey is used in conjunction with a ray-tracing program and an iterative damped least-squares inversion algorithm to create a two-dimensional model of the subsurface. The layout of the seismic survey required crooked seismic lines and substantial gaps in the source and receiver coverage to be accounted for. Additionally, there is substantial topographical variation and a complex geology consisting of glaciofluvial sediment and glacial till overlying a crystalline bedrock. The resolution and reliability of the models is measured through a parameter perturbation technique, normalized χ² values, root means square traveltime residuals and comparison to known geology.     

First‐arrival traveltime tomography with modified total‐variation regularization

First‐arrival traveltime tomography is a robust tool for near‐surface velocity estimation. A common approach to stabilizing the ill‐posed inverse problem is to apply Tikhonov regularization to the inversion. However, the Tikhonov regularization method recovers smooth local structures while blurring the sharp features in the model solution. We present a first‐arrival traveltime tomography method with modified total‐variation regularization to preserve sharp velocity contrasts and improve the accuracy of velocity inversion. To solve the minimization problem of the new traveltime tomography method, we decouple the original optimization problem into the two following subproblems: a standard traveltime tomography problem with the traditional Tikhonov regularization and a L₂ total‐variation problem. We apply the conjugate gradient method and split‐Bregman iterative method to solve these two subproblems, respectively. Our synthetic examples show that the new method produces higher resolution models than the conventional traveltime tomography with Tikhonov regularization, and creates less artefacts than the total variation regularization method for the models with sharp interfaces. For the field data, pre‐stack time migration sections show that the modified total‐variation traveltime tomography produces a near‐surface velocity model, which makes statics corrections more accurate.     

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.     

初至波相位走时层析

近地表速度结构通常是利用射线走时层析或菲涅尔体走时层析等反演方法得到的,但它们的目标函数仍利用射线走时残差构建,导致反演精度不高.为此,本文提出了基于散射积分算法的初至波相位走时层析成像方法.该方法的核心是:(1)提出了依赖于频率的相位走时概念;(2)利用依赖于频率的相位走时信息,而非单一的无限频率射线走时;(3)发展了一种改进的相位展开方法,即通过监测相位不连续性和2π周期判定来消除相位折叠现象;(4)考虑了地震波传播的有限频特征,即基于波动理论而非传统的射线路径或有限空间的菲涅尔体构建核函数.通过利用Overthrust模型的数值实验及与传统射线走时层析和菲涅尔体走时层析的对比表明:本文提出的方法是一种有效的初至波走时反演方法.同时,基于Overthrust模型的数值试验还证明了下列结论,即通过挖掘更多的走时信息的确可以获得更高的反演精度和分辨率.     

3-D multi-parameter type traveltime tomography in a spherical coordinate frame: comparison of double and triple class simultaneous inversions

It is now common practice to perform simultaneous traveltime inversion for the velocity field and the reflector geometry in reflection/refraction tomography, or the velocity field and the hypocenter locations in regional earthquake tomography, but seldom are all three classes of model parameters updated simultaneously. This is mainly due to the trade-off between the different types of model parameters and the lack of different seismic phases to constrain the model parameters. Using a spherical-coordinate ray tracing algorithm for first and later(primary reflected) arrival tracing algorithm in combination with a popular linearized inversion solver, it is possible to simultaneously recover the three classes of model parameters in regional or global tomographic studies. In this paper we incorporate the multistage irregular shortest-path ray tracing algorithm(in a spherical coordinate system) with a subspace inversion solver to formulate a simultaneous inversion algorithm for triple model parameters updating using direct and later arrival time information.Comparison tests for two sets of data(noise free and added noise) indicate that the new triple-class parameter inversion algorithm is capable of obtaining nearly the same results as the double-class parameter inversion scheme. Furthermore,the proposed multi-parameter type inversion method is not sensitive to a modest level of picking error in the traveltime data, and also performs well with a relatively large uncertainty in earthquake hypocentral locations. This shows it to be a feasible and promising approach in regional or global tomographic applications.     

The use of low frequencies in a full‐waveform inversion and impedance inversion land seismic case study

Velocity model building and impedance inversion generally suffer from a lack of intermediate wavenumber content in seismic data. Intermediate wavenumbers may be retrieved directly from seismic data sets if enough low frequencies are recorded. Over the past years, improvements in acquisition have allowed us to obtain seismic data with a broader frequency spectrum. To illustrate the benefits of broadband acquisition, notably the recording of low frequencies, we discuss the inversion of land seismic data acquired in Inner Mongolia, China. This data set contains frequencies from 1.5–80 Hz. We show that the velocity estimate based on an acoustic full‐waveform inversion approach is superior to one obtained from reflection traveltime inversion because after full‐waveform inversion the background velocity conforms to geology. We also illustrate the added value of low frequencies in an impedance estimate.     

起伏地形下的高精度反射波走时层析成像方法

全球造山带及中国大陆中西部普遍具有强烈起伏的地形条件.复杂地形条件下的地壳结构成像问题像一面旗帜引领了当前矿产资源勘探和地球动力学研究的一个重要方向.深地震测深记录中反射波的有效探测深度可达全地壳乃至上地幔顶部,而初至波通常仅能探测上地壳浅部.为克服和弥补初至波探测深度的不足,本文基于前人对复杂地形条件下初至波成像的已有研究成果,采用数学变换手段将笛卡尔坐标系的不规则模型映射到曲线坐标系的规则模型,并将快速扫描方法与分区多步技术相结合,发展了反射波走时计算和射线追踪的方法.进而利用反射波走时反演,实现起伏地形下高精度的速度结构成像,从而为起伏地形下利用反射波数据高精度重建全地壳速度结构提供了一种全新方案.数值算例从正演计算精度、反演中初始模型依赖性、反演精度、纵横向分辨率以及抗噪性等方面验证了算法的正确性和可靠性.     

Misfit functionals in Laplace‐Fourier domain waveform inversion,with application to wide‐angle ocean bottom seismograph data

In seismic waveform inversion, non‐linearity and non‐uniqueness require appropriate strategies. We formulate four types of L2 normed misfit functionals for Laplace‐Fourier domain waveform inversion: i) subtraction of complex‐valued observed data from complex‐valued predicted data (the ‘conventional phase‐amplitude’ residual), ii) a ‘conventional phase‐only’ residual in which amplitude variations are normalized, iii) a ‘logarithmic phase‐amplitude’ residual and finally iv) a ‘logarithmic phase‐only’ residual in which the only imaginary part of the logarithmic residual is used. We evaluate these misfit functionals by using a wide‐angle field Ocean Bottom Seismograph (OBS) data set with a maximum offset of 55 km. The conventional phase‐amplitude approach is restricted in illumination and delineates only shallow velocity structures. In contrast, the other three misfit functionals retrieve detailed velocity structures with clear lithological boundaries down to the deeper part of the model. We also test the performance of additional phase‐amplitude inversions starting from the logarithmic phase‐only inversion result. The resulting velocity updates are prominent only in the high‐wavenumber components, sharpening the lithological boundaries. We argue that the discrepancies in the behaviours of the misfit functionals are primarily caused by the sensitivities of the model gradient to strong amplitude variations in the data. As the observed data amplitudes are dominated by the near‐offset traces, the conventional phase‐amplitude inversion primarily updates the shallow structures as a result. In contrast, the other three misfit functionals eliminate the strong dependence on amplitude variation naturally and enhance the depth of illumination. We further suggest that the phase‐only inversions are sufficient to obtain robust and reliable velocity structures and the amplitude information is of secondary importance in constraining subsurface velocity models.     

Sensitivity analysis and application of time‐lapse full‐waveform inversion: synthetic testing and field data example from the North Sea,Norway

Time‐lapse refraction can provide complementary seismic solutions for monitoring subtle subsurface changes that are challenging for conventional P‐wave reflection methods. The utilization of refraction time lapse has lagged behind in the past partly due to the lack of robust techniques that allow extracting easy‐to‐interpret reservoir information. However, with the recent emergence of the full‐waveform inversion technique as a more standard tool, we find it to be a promising platform for incorporating head waves and diving waves into the time‐lapse framework. Here we investigate the sensitivity of 2D acoustic, time‐domain, full‐waveform inversion for monitoring a shallow, weak velocity change (?30 m/s, or ?1.6%). The sensitivity tests are designed to address questions related to the feasibility and accuracy of full‐waveform inversion results for monitoring the field case of an underground gas blowout that occurred in the North Sea. The blowout caused the gas to migrate both vertically and horizontally into several shallow sand layers. Some of the shallow gas anomalies were not clearly detected by conventional 4D reflection methods (i.e., time shifts and amplitude difference) due to low 4D signal‐to‐noise ratio and weak velocity change. On the other hand, full‐waveform inversion sensitivity analysis showed that it is possible to detect the weak velocity change with the non‐optimal seismic input. Detectability was qualitative with variable degrees of accuracy depending on different inversion parameters. We inverted, the real 2D seismic data from the North Sea with a greater emphasis on refracted and diving waves’ energy (i.e., most of the reflected energy was removed for the shallow zone of interest after removing traces with offset less than 300 m). The full‐waveform inversion results provided more superior detectability compared with the conventional 4D stacked reflection difference method for a weak shallow gas anomaly (320 m deep).     

多震相走时联合三参数同时反演成像

采用新近研制的分区多步不规则最短路径多震相地震射线追踪正演技术,结合流行的子空间反演算法,提出了一种联合多震相走时资料进行地震三参数 （速度、反射界面和震源位置） 同时反演的方法技术.数值模拟反演实例、以及与双参数 （速度和反射界面或速度和震源位置） 同时反演的对比分析表明：三参数同时反演成像结果大体接近双参数同时反演成像的结果.另外,噪声敏感性试验表明：所提算法对到时数据中可容许的随机误差并不敏感,结果说明多震相走时的联合三参数同时反演成像方法技术不失为一种提高走时成像空间分辨率、进而降低重建模型参数失真度、行之有效的方法技术.     

Frequency‐dependent multi‐offset phase analysis of surface waves: an example of high‐resolution characterization of a riparian aquifer

Multi‐offset phase analysis of seismic surface waves is an established technique for the extraction of dispersion curves with high spatial resolution and, consequently, for the investigation of the subsurface in terms of shear wave velocity distribution. However, field applications are rarely documented in the published literature. In this paper, we discuss an implementation of the multi‐offset phase analysis consisting of the estimation of the Rayleigh wave velocity by means of a moving window with a frequency‐dependent length. This allows maximizing the lateral resolution at high frequencies while warranting stability at the lower frequencies. In this way, we can retrieve the shallow lateral variability with high accuracy and, at the same time, obtain a robust surface‐wave velocity measurement at depth. In this paper, we apply this methodology to a dataset collected for hydrogeophysical purposes and compare the inversion results with those obtained by using refraction seismics and electrical resistivity tomography. The surface‐wave results are in good agreement with those provided by the other methods and demonstrate a superior capability in retrieving both lateral and vertical velocity variations, including inversions. Our results are further corroborated by the lithological information from a borehole drilled on the acquisition line. The availability of multi‐offset phase analysis data also allows disentangling a fairly complex interpretation of the other geophysical results.     

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.     

人工源宽角地震实验的谱元法模拟和逆时偏移成像方法研究

人工源宽角反射(折射)地震资料具有偏移距较大、信噪比较低等特点,通常用于地震波走时反演重建地壳速度结构。逆时偏移成像方法作为勘探地震学领域获取地下构造形态的有效手段之一,可以有效弥补走时反演方法的不足。本文针对大偏移距宽角反射(折射)地震实验,利用四边形网格谱元法进行波场模拟,结合了有限元法的灵活性和谱方法的指数收敛性,高效且高精度获取模型合成地震记录,后采用逆时偏移成像方法将合成地震记录偏移归位,获取地壳几何结构,验证了逆时偏移成像方法在宽角地震资料处理及结果解释中的适用性,为后期实际地震资料的偏移成像提供了理论依据和支持。