再论地震数据偏移成像

利用地震波正向传播方程对属于波形线性反演问题近似求解方法的地震数据偏移成像进行重新推导,得到了适合散射地震数据的散射偏移成像方法和适合反射地震数据的反射偏移成像方法.以地震波传播的散射理论为出发点,首先根据描述一次散射波正向传播的线性方程研究建立散射地震数据的偏移成像方法理论;利用高频近似对产生散射波场的地下速度扰动函数的空间变化进行近似,推导出地下反射率函数,再由散射波传播方程推导出基于反射率函数的反射波传播方程,然后根据描述一次反射波正向传播的线性方程研究建立反射地震数据的偏移成像方法理论.本文指出和修正了Claerbout偏移成像方法中的不足,提出的地震数据偏移成像方法是对当前偏移成像方法理论的完善,使反射地震数据偏移成像具有了更坚实的数学物理理论基础,得到的偏移成像结果相位正确、位置准确、分辨率提高.     

ZERO MEMORY NON-LINEAR DECONVOLUTION*

A type of iterative deconvolution that extracts the source waveform and reflectivity from a seismogram through the use of zero memory, non-linear estimators of reflection coefficient amplitnde is developed. Here, we present a theory for iterative deconvolution that is based upon the specification of a stochastic model describing reflectivity. The resulting parametric algorithm deconvolves the seismogram by forcing a filtered version of the seismogram to resemble an estimated reflection coefficient sequence. This latter time series is itself obtained from the filtered seismogram, and so a degree of iteration is required. Algorithms utilizing zero memory non-linearities (ZNLs) converge to a family of processes, which we call Bussgang, of which any colored Gaussian process and any independent process are members. The direction of convergence is controlled by the choice of ZNL used in the algorithm. Synthetic and real data show that, generally, five to ten iterations are required for acceptable deconvolutions.     

A NONITERATIVE PROCEDURE FOR INVERTING PLANE-WAVE REFLECTION DATA AT SEVERAL ANGLES OF INCIDENCE USING THE RICCATI EQUATION*

Various exact methods of inverting the complete waveform of vertical seismic reflection data to produce acoustic impedance profiles have been suggested. These inverse methods generally remain valid for nonvertical, plane-wave data, provided total reflection does not occur. Thus, in principle, the “seismogram” at each ray parameter in a slant stack can be interpreted separately. Rather than invert each plane-wave seismogram separately, they can all be interpreted simultaneously and an “average” model thus obtained. Inversion for both the velocity and the density also becomes possible when two or more plane-wave seismograms are simultaneously inverted. The theory for a noniterative inversion method, based on the time-domain Riccati equation, is discussed. Numerical examples of inversions using this technique on synthetic data demonstrate its numerical stability and the advantage of simultaneous inversion of several seismograms to reduce the effect of noise in the data and increase the stability of the inversion process.     

INVERSION OF REFLECTION DATA *

An iterative inversion method which also takes into account wave energy absorption is described. This method allows estimates of the acoustic impedance in sedimentary layers with nearly plane and parallel stratification. A set of reflection data has been inverted and an impedance model was obtained which correlates well with the essential features of the borehole velocity log.     

地震数据的反射波动方程最小二乘偏移

基于反射波动方程,本文提出了一种估计地下反射率分布的地震数据最小二乘偏移方法.高频近似下,非齐次的一次反射波动方程的源项是由反射率与入射波场的时间一阶导数相互作用产生的.根据反射波动方程,利用线性最小二乘反演方法由地震反射数据重建出地下产生反射波的反射源,再结合波场正演计算出的地下入射波场,得到地下反射率分布的估计.在地下反射源的线性最小二乘反演重建中,我们采用迭代求解方法,并以地震波的检波器单向地下照明强度作为最小二乘优化问题中Hessian矩阵的近似.     

Seismic migration and absorbing boundaries with a one-way wave system for heterogeneous media1

A first-order one-way wave system has been created based on characteristic analysis of the acoustic wave system and optimization of the dispersion relation. We demonstrate that this system is equivalent to a third-order scalar partial-differential equation which, for a homogeneous medium, reduces to a form similar to the 45° paraxial wave equation. This system describes accurately waves propagating in a 2D heterogeneous medium at angles up to 75°. The one-way wave system representing downgoing waves is used for a modified reverse time migration method. As a wavefield extrapolator in migration, the downgoing wave system propagates the reflection events backwards to their reflectors without scattering at the discontinuities in the velocity model. Hence, images with amplitudes proportional to reflectivity can be obtained from this migration technique. We present examples of the application of the new migration method to synthetic seismic data where P-P reflections P-SV converted waves are present. Absorbing boundaries, useful in the generation of synthetic seismograms, have been constructed by using the one-way wave system. These boundaries absorb effectively waves impinging over a wide range of angles of incidence.     

LEVINSON INVERSION OF EARTHQUAKE GEOMETRY SH-TRANSMISSION SEISMOGRAMS IN THE PRESENCE OF NOISE*

The Kunetz-Claerbout equation for the acoustic transmission problem in a layered medium in its original form establishes the relation between the transmission and the reflec tion response for P-waves in an horizontally layered medium and with vertical incidence. It states that the reflection seismogram due to an impulsive source at the surface, is one side of the autocorrelation of the seismogram due to an impulsive source at depth and a surface receiver. By adapting Claerbout's formulation to the transmission of SH-waves, the Kunetz-Claerbout equation also holds for reflection and transmission coefficients dependent on the incident angle. Thus, earthquake geometry SH-transmission seismograms can be used to caculate corresponding pseudoreflection seismograms which, in turn, can be inverted for the impedance structure using the Levinson algorithm. If the average incidence angle is known, a geometrical correction on the resulting impedance model can improve the resolution of layer thicknesses. In contrast to the inversion of reflection seismograms, the Levinson algorithm is shown to yield stable results for the inversion of transmission seismograms even in the presence of additive noise. This noise stabilization is inherent to the Kunetz-Claerbout equation. Results of inverted SH-wave microearthquake seismograms from the Swabian Jura, SW Germany, seismic zone obtained at recording site Hausen im Tal have been compared with sonic-log data from nearby exploration drilling at Trochtelfingen. The agreement of the main structural elements is fair to a depth of several hundred metres.     

An Approximation to Sparse-Spike Reflectivity Using the Gold Deconvolution Method

Wiener deconvolution is generally used to improve resolution of the seismic sections, although it has several important assumptions. I propose a new method named Gold deconvolution to obtain Earth’s sparse-spike reflectivity series. The method uses a recursive approach and requires the source waveform to be known, which is termed as Deterministic Gold deconvolution. In the case of the unknown wavelet, it is estimated from seismic data and the process is then termed as Statistical Gold deconvolution. In addition to the minimum phase, Gold deconvolution method also works for zero and mixed phase wavelets even on the noisy seismic data. The proposed method makes no assumption on the phase of the input wavelet, however, it needs the following assumptions to produce satisfactory results: (1) source waveform is known, if not, it should be estimated from seismic data, (2) source wavelet is stationary at least within a specified time gate, (3) input seismic data is zero offset and does not contain multiples, and (4) Earth consists of sparse spike reflectivity series. When applied in small time and space windows, the Gold deconvolution algorithm overcomes nonstationarity of the input wavelet. The algorithm uses several thousands of iterations, and generally a higher number of iterations produces better results. Since the wavelet is extracted from the seismogram itself for the Statistical Gold deconvolution case, the Gold deconvolution algorithm should be applied via constant-length windows both in time and space directions to overcome the nonstationarity of the wavelet in the input seismograms. The method can be extended into a two-dimensional case to obtain time-and-space dependent reflectivity, although I use one-dimensional Gold deconvolution in a trace-by-trace basis. The method is effective in areas where small-scale bright spots exist and it can also be used to locate thin reservoirs. Since the method produces better results for the Deterministic Gold deconvolution case, it can be used for the deterministic deconvolution of the data sets with known source waveforms such as land Vibroseis records and marine CHIRP systems.     

频率域中的合成地震记录

波动理论的合成地震记录是地震资料处理和解释中的重要研究课题。 目前,制作波动理论的合成记录主要是用Trorey的克希霍夫方法,正在研究的有有限差分法和有限元素法。本文提出一种新的方法,在频率域中制作波动理论的合成记录,给出了与克希霍夫绕射波方程等价的频率域中的绕射波方程。在国产DJS-11型计算机上,应用两种绕射波方程实现了合成地震记录,并且进行了比较,认为频率域方法是有效的,可以用于波动方程偏移和地震资料解释,进一步工作有可能获得多层变速模型的波动理论记录。     

杨氏模量和泊松比反射系数近似方程及叠前地震反演

杨氏模量和泊松比等岩石弹性参数是表征页岩气储集体岩石脆性、评价储层含气特征的重要特征参数,而叠前地震反演是从地震资料中获取此类参数的有效途径.地震波反射系数方程是叠前反演的基础.首先,在平面波入射等假设条件下推导了基于杨氏模量(Y)、泊松比(σ)和密度(D)的纵波反射系数线性近似方程(YPD反射系数近似方程),该方程建立了地震纵波反射系数与杨氏模量反射系数、泊松比反射系数和密度反射系数的线性关系;其次,对该方程的精度和适用条件进行了分析,模型分析表明,在入射角为40°时,该方程具有较高的计算精度;最后,建立了一种稳定获取杨氏模量和泊松比的叠前地震直接反演方法.模型试算和实际资料试处理表明,基于新方程的反演方法能够稳定合理的直接从叠前地震资料中获取杨氏模量和泊松比参数,提供了一种高可靠性的页岩气"甜点"地震识别方法.     

利用偏移进行视反射率估计的初步研究

视反射率估计是地震数据处理解释中的一项重要内容,通常采用反演的方法得到.本文以地震偏移和地震线性反演理论相结合为基础,并利用保幅单程波传播算子和保幅波动方程叠前偏移算法以及成像空间中的角度域波动方程偏移成像和照明补偿等方法技术,提出了一种利用单程波波动方程偏移进行地下反射面视反射率估计方法,并进行了理论模型的数值试验.这种估计方法得到的视反射率估计是一种近法向入射的小角度反射率.     

WAVE EQUATION MIGRATION WITH THE ACCURATE SPACE DERIVATIVE METHOD*

A stacked seismic section represents a wave-field recorded at regularly spaced points on the surface. The seismic migration process transforms this recorded data into a reflectivity display. In recent years, Jon F. Claerbout and his co-workers developed migration techniques based on the numerical approximation of the wave equation by finite difference methods. This paper describes an alternative method, termed ASD (for Accurate Space Derivative), and its application to the wave equation migration problem. In this approach to the numerical solution of partial differential equations, partial derivatives are computed by finite Fourier transform methods. This migration method can accommodate media with vertical as well as horizontal velocity variations.     

地震波形反演技术在砂泥岩薄互层结构表征中的应用

基于传播矩阵理论开发砂泥岩薄互层地震合成记录算法,与褶积算法、基于界面模型的Zoeppritz方法以及波动方程等方法相比,该方法更适用于具有复杂结构的薄互层模型,能够在充分考虑地震反射波动力学因素的同时不受网格间距的限制.基于正演算法开发了基于波形对比的砂泥岩薄互层地震反演技术,由地震反射波形特征的变化反演薄地层单元中砂体含量与空间位置等参数,进而确定薄互层段砂泥岩组合结构以及砂体的空间展布.理论模型验证了反演方法的有效性.通过测井分析建立薄互层地震地质模型,并将该技术应用于研究区实际地震数据,反演的砂体空间分布与测井资料进行对比分析,验证了反演方法的实用性.     

地震转换波对叠前同时反演的影响研究

叠前同时反演是油气探测的一种有效工具.其理论基础是平面P波Zoeppritz方程计算的反射系数的近似,是入射角的函数.叠前同时反演可以利用三项或两项Fatti方程进行反演分析.本文针对实际油田的测井数据,利用反射率法模拟了仅包含P波一次反射记录,包含P波一次反射和P波层间多次波记录以及全波场地震记录,再利用叠前同时反演对合成地震记录进行反演研究.研究结果表明,在大偏移距处P波主要反射受到其它模式波的污染,从而影响了叠前同时反演结果的精度.对于薄互层介质当转换波影响严重时,使用小角度数据的两项AVO反演比使用大角度数据的三项AVO反演更合理可靠.     

频率域波动方程的双参数识别方法

利用反射波地震记录恢复波动方程的两个系数以研究地球内部构造，是当前应用地球物理研究的热点之一，本文在波动方程反演方法的理论基础上，导出了频率域识别介质的密度波速两个重要参数的新算法，从而把当前的波动方程单参数反演双参数反演方法，通过理论模型及实际测井资料的反演试算对比，均藜得良好效果，在算法中还省去了Ｇｒｅｅｎ函数的繁杂计算，节省了计算量，增加实用性。     

基于广义高斯分布的地震盲反褶积方法研究

Bussgang算法是针对褶积盲源分离问题提出的,本文将其用于地震盲反褶积处理.由于广义高斯概率密度函数具有逼近任意概率密度函数的能力,从反射系数序列的统计特征出发,引入广义高斯分布来体现反射系数序列超高斯分布特征.依据反射系数序列的统计特征和Bussgang算法原理,建立以Kullback-Leibler距离为非高斯性度量的目标函数,并导出算法中涉及到的无记忆非线性函数,最终实现了地震盲反褶积.模型试算和实际资料处理结果表明,该方法能较好地适应非最小相位系统,能够同时实现地震子波和反射系数估计,有效地提高地震资料分辨率.     

STABILIZATION OF NORMAL-INCIDENCE SEISMOGRAM INVERSION REMOVING THE NOISE-INDUCED BIAS*

A main problem in computing reflection coefficients from seismograms is the instability of the inversion procedure due to noise. This problem is attacked for two well-known inversion schemes for normal-incidence reflection seismograms. The crustal model consists of a stack of elastic, laterally homogeneous layers between two elastic half-spaces. The first method, which directly computes the reflection coefficients from the seismogram is called “Dynamic Deconvolution”. The second method, here called “Inversion Filtering”, is a two-stage procedure. The first stage is the construction of a causal filter by factorization of the spectral function via Levinson-recursion. Filtering the seismogram is the second stage. The filtered seismogram is a good approximation for the reflection coefficients sequence (unless the coefficients are too large). In the non-linear terms of dynamic deconvolution and Levinson-recursion the noise could play havoc with the computation. In order to stabilize the algorithms, the bias of these terms is estimated and removed. Additionally incorporated is a statistical test for the reflection coefficients in dynamic deconvolution and the partial correlation coefficients in Levinson-recursion, which are set to zero if they are not significantly different from noise. The result of stabilization is demonstrated on synthetic seismograms. For unit spike source pulse and white noise, dynamic deconvolution outperforms inversion filtering due to its exact nature and lesser computational burden. On the other hand, especially in the more realistic bandlimited case, inversion filtering has the great advantage that the second stage acts linearly on the seismogram, which allows the calculation of the effect of the inversion procedure on the wavelet shape and the noise spectrum.     

CORRECTING FOR COLOURED PRIMARY REFLECTIVITY IN DECONVOLUTION1

Statistical deconvolution, as it is usually applied on a routine basis, designs an operator from the trace autocorrelation to compress the wavelet which is convolved with the reflectivity sequence. Under the assumption of a white reflectivity sequence (and a minimum-delay wavelet) this simple approach is valid. However, if the reflectivity is distinctly non-white, then the deconvolution will confuse the contributions to the trace spectral shape of the wavelet and reflectivity. Given logs from a nearby well, a simple two-parameter model may be used to describe the power spectral shape of the reflection coefficients derived from the broadband synthetic. This modelling is attractive in that structure in the smoothed spectrum which is consistent with random effects is not built into the model. The two parameters are used to compute simple inverse- and forward-correcting filters, which can be applied before and after the design and implementation of the standard predictive deconvolution operators. For whitening deconvolution, application of the inverse filter prior to deconvolution is unnecessary, provided the minimum-delay version of the forward filter is used. Application of the technique to seismic data shows the correction procedure to be fast and cheap and case histories display subtle, but important, differences between the conventionally deconvolved sections and those produced by incorporating the correction procedure into the processing sequence. It is concluded that, even with a moderate amount of non-whiteness, the corrected section can show appreciably better resolution than the conventionally processed section.     

速度分布统计特征与地震拟测井问题

根据声测井得出的速度分布统计特征,给出了多层构造反射系数序列的自相关函数形式。在反射系数强度不太大的条件下,导出存在于速度分布统计特征与多层构造反射传递函数之间的一种简单关系。据此,对目前常用的线性地震拟测井处理过程进行了具体分析,指出畸变恒不可免;在此基础上,提出了实际处理中力求减小畸变的可能途径。