Sea surface shape derivation above the seismic streamer

The rough sea surface causes perturbations in the seismic data that can be significant for time‐lapse studies. The perturbations arise because the reflection response of the non‐flat sea perturbs the seismic wavelet. In order to remove these perturbations from the received seismic data, special deconvolution methods can be used, but these methods require, as input, the time varying wave elevation above each hydrophone in the streamer. In addition, the vertical displacement of the streamer itself must also be known at the position of each hydrophone and at all times. This information is not available in conventional seismic acquisition. However, it can be obtained from the hydrophone measurements provided that the hydrophones are recorded individually (not grouped), that the recording bandwidth is extended down to 0.05 Hz and that data are recorded without gaps between the shot records. The sea surface elevation, and also the wave‐induced vertical displacement of the streamer, can be determined from the time‐varying pressure that the sea waves cause in the hydrophone measurements. When this was done experimentally, using a single sensor seismic streamer without a conventional low cut filter, the wave induced pressure variations were easily detected. The inversion of these experimental data gives results for the sea surface elevation that are consistent with the weather and sea state at the time of acquisition. A high tension approximation allows a simplified solution of the equations that does not demand a knowledge of the streamer tension. However, best results at the tail end of the streamer are obtained using the general equation.     

Rough seas and time-lapse seismic

Time‐lapse seismic surveying has become an accepted tool for reservoir monitoring applications, thus placing a high premium on data repeatability. One factor affecting data repeatability is the influence of the rough sea‐surface on the ghost reflection and the resulting seismic wavelets of the sources and receivers. During data analysis, the sea‐surface is normally assumed to be stationary and, indeed, to be flat. The non‐flatness of the sea‐surface introduces amplitude and phase perturbations to the source and receiver responses and these can affect the time‐lapse image. We simulated the influence of rough sea‐surfaces on seismic data acquisition. For a typical seismic line with a 48‐fold stack, a 2‐m significant‐wave‐height sea introduces RMS errors of about 5–10% into the stacked data. This level of error is probably not important for structural imaging but could be significant for time‐lapse surveying when the expected difference anomaly is small. The errors are distributed differently for sources and receivers because of the different ways they are towed. Furthermore, the source wavelet is determined by the sea shape at the moment the shot is fired, whereas the receiver wavelet is time‐varying because the sea moves significantly during the seismic record.     

Deghosting towed streamer data in τ/p domain based on rough sea surface reflectivity

Currently, the deghosting of towed streamer seismic data assumes a flat sea level and a sea-surface reflection coefficient of ?1; this decreases the precision of deghosting. A new method that considers the rough sea surface is proposed to suppress ghost reflections. The proposed deghosting method obtains the rough sea surface reflection coefficient using Gaussian statistics, and calculates the optimized deghosting operator in the τ/p domain. The proposed method is closer to the actual sea conditions, offers an improved deghosting operator, removes the ghost reflections from marine towed seismic data, widens the bandwidth and restores the low-frequency information, and finally improves the signal-tonoise ratio and resolution of the seismic data.     

Spectral factorization technique for estimation of an ARMA operator for multichannel deconvolution of seismic data

A new spectral factorization method is presented for the estimation of a causal as well as a causally invertible ARMA operator from the correlation sequence of seismic traces. The method has been implemented for multichannel deconvolution of seismic traces with the aim of exploiting the trace-to-trace correlation that exists within seismograms. A layered earth model with a small reflectivity sequence has been considered, and the seismic traces have been considered as the output of a linear system driven by white noise reflection coefficient sequences. The present method is the concatenation of three algorithms, namely Kung's method for state variable ( F , G , H ) realization using a singular value decomposition (SVD) algorithm, Faurre's technique for computation of the strong spectral factor and Leverrier's algorithm for ARMA representation of the spectral factor. The inverted ARMA operator is used as a recursive filter for deconvolution of seismic traces. In the example shown, two traces with a covariance sequence of 160 ms length have been considered for multichannel deconvolution of stacked seismic traces. The results presented, when compared with those obtained from a conventional deconvolution algorithm, have shown encouraging prospects.     

3D seismic residual statics solutions derived from refraction interferometry

We apply interferometric theory to solve a three‐dimensional seismic residual statics problem to improve reflection imaging. The approach calculates the static solutions without picking the first arrivals from the shot or receiver gathers. The static correction accuracy can be significantly improved by utilising stacked virtual refraction gathers in the calculations. Shots and receivers may be placed at any position in a three‐dimensional seismic land survey. Therefore, it is difficult to determine stationary shots and receivers to form the virtual refraction traces that have identical arrival times, as in a two‐dimensional scenario. To overcome this problem, we use a three‐dimensional super‐virtual interferometry method for residual static calculations. The virtual refraction for a stationary shot/receiver pair is obtained via an integral along the receiver/shot lines, which does not require knowledge of the stationary locations. We pick the maximum energy times on the interferometric stacks and solve a set of linear equations to derive reliable residual static solutions. We further apply the approach to both synthetic and real data.     

Sparsity‐enhanced wavelet deconvolution

We propose a three‐step bandwidth enhancing wavelet deconvolution process, combining linear inverse filtering and non‐linear reflectivity construction based on a sparseness assumption. The first step is conventional Wiener deconvolution. The second step consists of further spectral whitening outside the spectral bandwidth of the residual wavelet after Wiener deconvolution, i.e., the wavelet resulting from application of the Wiener deconvolution filter to the original wavelet, which usually is not a perfect spike due to band limitations of the original wavelet. We specifically propose a zero‐phase filtered sparse‐spike deconvolution as the second step to recover the reflectivity dominantly outside of the bandwidth of the residual wavelet after Wiener deconvolution. The filter applied to the sparse‐spike deconvolution result is proportional to the deviation of the amplitude spectrum of the residual wavelet from unity, i.e., it is of higher amplitude; the closer the amplitude spectrum of the residual wavelet is to zero, but of very low amplitude, the closer it is to unity. The third step consists of summation of the data from the two first steps, basically adding gradually the contribution from the sparse‐spike deconvolution result at those frequencies at which the residual wavelet after Wiener deconvolution has small amplitudes. We propose to call this technique “sparsity‐enhanced wavelet deconvolution”. We demonstrate the technique on real data with the deconvolution of the (normal‐incidence) source side sea‐surface ghost of marine towed streamer data. We also present the extension of the proposed technique to time‐varying wavelet deconvolution.     

频率慢度域自适应迭代反演算法压制海上倾斜缆鬼波方法及其应用

海上倾斜缆采集技术具有多样的陷波特征,通过去鬼波处理可获得宽频数据.针对海水面波浪起伏及缆深误差引起的鬼波延迟时间估计误差以及崎岖海底和目的层深度变化使得鬼波和一次反射波的振幅差异系数随偏移距的变化而难以给定一个固定值的问题,本文推导出频率慢度域中鬼波滤波算子以及自适应迭代反演求解上行波算法,该鬼波滤波算子与不同水平慢度对应的鬼波和一次反射波的振幅差异系数以及鬼波延迟时间有关.并基于计算出的理论下行波与实际下行波之间的平方误差最小理论实现自适应反演迭代最优计算该振幅差异系数和鬼波延迟时间.合成的及某海上采集的倾斜缆数据去鬼波处理结果表明,频率慢度域自适应迭代反演算法能较好地去除海上变深度缆鬼波,能达到拓宽地震记录频带目的.     

基于波动方程的上下缆地震数据鬼波压制方法研究

本文发展基于波动方程的上下缆鬼波压制方法,推导了上下缆地震波场频率波数域波动方程延拓合并公式.基于Fourier变换的波场解析延拓确保上下缆资料振幅相位的一致性,消除了长拖缆远偏移距信号的计算误差,同时具有较高的计算效率;上下缆地震波场的波动方程法合并有效解偶鬼波干涉,实现综合利用上下缆地震数据压制鬼波.理论模型数据和实际采集地震数据的测试表明了方法的有效性.     

叠前地震数据特征波场分解、偏移成像与层析反演

本文提出了一套叠前地震数据稀疏表达(特征波场合成)、深度偏移成像和层析成像的处理流程.不同于传统的变换域中的数据稀疏表达理论,本文利用局部平面波的传播方向(慢度矢量),在中心炮检点处同时进行波束合成,从而将地震数据投影到局部平面波域(高维空间)中.由于波束合成后的地震数据描述了局部平面波的方向特征,因此称之为特征波场.然而波束合成算法需要估计局部平面波的慢度矢量.当地震数据受噪声干扰时,难以在常规τ-p谱中自动估计局部平面波的射线参数(慢度矢量).本文提出了基于反演理论的特征波场合成方法,可以同时反演局部平面波及其传播方向,从而提高特征波合成的自动化程度并保持方法的稳健性.通过特征波场合成,可以将地震数据分解为单独的震相(波形).这样的数据可以直接用来成像及反演.在局部平面波域中,由于局部平面波的入射与出射射线参数已知,传统的Kirchhoff叠前深度偏移(PSDM)和高斯束/控制束PSDM可以实现从"沿等时面的画弧"到"向反射点(段)的直接投影"的转变,叠前偏移的效率以及成像质量可以同时提高.此外,特征波场与地下反射点(段)的一对一映射关系使得叠前深度偏移与层析成像融为一体,可以极大地提高速度反演的效率.数值试验证明了特征波场合成、叠前深度成像以及层析反演的有效性.     

Wavelet correlation filter for wide-angle seismic data

A new filtering technique for single‐fold wide‐angle reflection/refraction seismic data is presented. The technique is based on the wavelet decomposition of a set of adjacent traces followed by coherence analysis. The filtering procedure consists of three steps. In the first, a wavelet decomposition of traces into different detail levels is performed. In the second, the coherence attributes for each level are evaluated by calculating cross‐correlation functions of detail portions contained in a space–time moving window. Finally, the filtered traces are obtained as a weighted reconstruction of the trace details. Each weight is obtained from the coherence‐attributes distribution estimated in a proper interval. A sequence of tests is then conducted in order to select possible optimum or unsuitable wavelet bases. The efficiency of the filter proposed was assessed by calculating some properly designed parameters in order to compare it with other standard de‐noising techniques. The proposed method produced a clear signal enhancement in high‐density wide‐angle seismic data, thus proving that it is a useful processing tool for a reliable correlation of seismic phases.     

Interferometric interpolation of sparse marine data

We present the theory and numerical results for interferometrically interpolating 2D and 3D marine surface seismic profiles data. For the interpolation of seismic data we use the combination of a recorded Green's function and a model‐based Green's function for a water‐layer model. Synthetic (2D and 3D) and field (2D) results show that the seismic data with sparse receiver intervals can be accurately interpolated to smaller intervals using multiples in the data. An up‐ and downgoing separation of both recorded and model‐based Green's functions can help in minimizing artefacts in a virtual shot gather. If the up‐ and downgoing separation is not possible, noticeable artefacts will be generated in the virtual shot gather. As a partial remedy we iteratively use a non‐stationary 1D multi‐channel matching filter with the interpolated data. Results suggest that a sparse marine seismic survey can yield more information about reflectors if traces are interpolated by interferometry. Comparing our results to those of f‐k interpolation shows that the synthetic example gives comparable results while the field example shows better interpolation quality for the interferometric method.     

A COMPARISON OF STATISTICAL AND DETERMINISTIC WIENER DECONVOLUTION OF DEEP-TOW SEISMIC DATA*

Wiener ‘spiking’ deconvolution of seismic traces in the absence of a known source wavelet relies upon the use of digital filters, which are optimum in a least-squares error sense only if the wavelet to be deconvolved is minimum phase. In the marine environment in particular this condition is frequently violated, since bubble pulse oscillations result in source signatures which deviate significantly from minimum phase. The degree to which the deconvolution is impaired by such violation is generally difficult to assess, since without a measured source signature there is no optimally deconvolved trace with which the spiked trace may be compared. A recently developed near-bottom seismic profiler used in conjunction with a surface air gun source produces traces which contain the far-field source signature as the first arrival. Knowledge of this characteristic wavelet permits the design of two-sided Wiener spiking and shaping filters which can be used to accurately deconvolve the remainder of the trace. In this paper the performance of such optimum-lag filters is compared with that of the zero-lag (one-sided) operators which can be evaluated from the reflected arrival sequence alone by assuming a minimum phase source wavelet. Results indicate that the use of zero-lag operators on traces containing non-minimum phase wavelets introduces significant quantities of noise energy into the seismic record. Signal to noise ratios may however be preserved or even increased during deconvolution by the use of optimum-lag spiking or shaping filters. A debubbling technique involving matched filtering of the trace with the source wavelet followed by optimum-lag Wiener deconvolution did not give a higher quality result than can be obtained simply by the application of a suitably chosen Wiener shaping filter. However, cross correlation of an optimum-lag spike filtered trace with the known ‘actual output’ of the filter when presented with the source signature is found to enhance signal-to-noise ratio whilst maintaining improved resolution.     

最小二乘反演迭代算法在压制海上变深度缆采集数据虚反射中的应用

海水面的虚反射(鬼波)引起海上拖缆采集数据陷波,导致地震记录频带变窄,而近年发展的变深度缆采集技术,具有多样的陷波特征,通过专门的去虚反射处理方法可获得宽频数据.本文基于已有研究成果,将最小二乘反演迭代压制虚反射算法应用于某海上变深度缆宽频处理.基于频率波数域镜像记录生成方法获得镜像炮集记录,并采用最小二乘解从变深度缆原始和镜像炮集记录中提取上行波.针对镜像炮集记录生成受初始速度模型精度的影响,使得某深度缆接收的上行波和下行波之间的实际延迟时间存在误差,采用最小二乘反演迭代算法最优化计算下行波与上行波之间的平均延迟时间和上行波记录,并采用时空数据窗口滑动克服延迟时间随炮检距和目的层深度变化问题.合成数据及某海上实际变深度缆数据处理测试结果表明,该方法能较好地压制变深度缆由海水面产生的虚反射,能达到拓宽地震记录频带目的.     

Design,modelling and imaging of marine seismic swarm surveys

Autonomous marine vehicles instrumented with seismic sensors allow for new efficient seismic survey designs. One such design is the swarm survey, where a group, or swarm, of slow moving autonomous marine vehicles record seismic data from shots fired by a source vessel sailing around circles within the swarm. The size of the swarm is dictated by the maximum offset requirement of the survey, and it can be shaped to acquire wide‐ and full‐azimuth data. The swarm survey design equation describes the relationship between the source and receiver positions of the survey and the subsurface coverage or fold. It is used to adapt the swarm to the seismic survey requirements and to calculate survey duration time estimates as function of available equipment. It is shown that a survey conducted by a slowly moving swarm requires six times fewer shots than an equivalent seabed node survey conducted over 85.5 km². Swarm surveys can also be adapted to efficiently conduct infill surveys and replace multi‐vessel undershoots. The efficiency of the survey can further be increased when the autonomous marine vehicles are towing short streamers with multiple receivers. Synthetic tests show that the seismic images for swarm surveys are comparable to those from streamer surveys, while little variation in image quality is found when reducing the number of autonomous marine vehicles but equipping them with a short streamer with multiple receivers.     

Noise transfer in variable‐depth streamer deghosting

Single‐component towed‐streamer marine data acquisition records the pressure variations of the upgoing compressional waves followed by the polarity‐reversed pressure variations of downgoing waves, creating sea‐surface ghost events in the data. The sea‐surface ghost for constant‐depth towed‐streamer marine data acquisition is usually characterised by a ghost operator acting on the upgoing waves, which can be formulated as a filtering process in the frequency–wavenumber domain. The deghosting operation, usually via the application of the inverse Wiener filter related to the ghost operator, acts on the signal as well as the noise. The noise power transfer into the deghosted data is proportional to the power spectrum of the inverse Wiener filter and is amplifying the noise strongly at the notch wavenumbers and frequencies of the ghost operator. For variable‐depth streamer acquisition, the sea‐surface ghost cannot be described any longer as a wavenumber–frequency operator but as a linear relationship between the wavenumber–frequency representation of the upgoing waves at the sea surface and the data in the space–frequency domain. In this article, we investigate how the application of the inverse process acts on noise. It turns out that the noise magnification is less severe with variable‐depth streamer data, as opposed to constant depth, and is inversely proportional to the local slant of the streamer. We support this statement via application of the deghosting process to real and numerical random noise. We also propose a more general concept of a wavenumber–frequency ghost power transfer function, applicable for variable‐depth streamer acquisition, and demonstrate that the inverse of the proposed variable‐depth ghost power transfer function can be used to approximately quantify the action of the variable‐depth streamer deghosting process on noise.     

Wavelet‐based cepstrum decomposition of seismic data and its application in hydrocarbon detection

How to use cepstrum analysis for reservoir characterization and hydrocarbon detection is an initial question of great interest to exploration seismologists. In this paper, wavelet‐based cepstrum decomposition is proposed as a valid technology for enhancing geophysical responses in specific frequency bands, in the same way as traditional spectrum decomposition methods do. The calculation of wavelet‐based cepstrum decomposition, which decomposes the original seismic volume into a series of common quefrency volumes, employs a sliding window to move over each seismic trace sample by sample. The key factor in wavelet‐based cepstrum decomposition is the selection of the sliding‐window length as it limits the frequency ranges of the common quefrency section. Comparison of the wavelet‐based cepstrum decomposition with traditional spectrum decomposition methods, such as short‐time Fourier transform and wavelet transform, is conducted to demonstrate the effectiveness of the wavelet‐based cepstrum decomposition and the relation between these two technologies. In hydrocarbon detection, seismic amplitude anomalies are detected using wavelet‐based cepstrum decomposition by utilizing the first and second common quefrency sections. This reduces the burden of needing dozens of seismic volumes to represent the response to different mono‐frequency sections in the interpretation of spectrum decomposition in conventional spectrum decomposition methods. The model test and the application of real data acquired from the Sulige gas field in the Ordos Basin, China, confirm the effectiveness of the seismic amplitude anomaly section using wavelet‐based cepstrum decomposition for discerning the strong amplitude anomalies at a particular quefrency buried in the broadband seismic response. Wavelet‐based cepstrum decomposition provides a new method for measuring the instantaneous cepstrum properties of a reservoir and offers a new field of processing and interpretation of seismic reflection data.     

Depth imaging in anisotropic media by symmetric non-stationary phase shift

We present a new depth‐imaging method for seismic data in heterogeneous anisotropic media. This recursive explicit method uses a non‐stationary extrapolation operator to allow lateral velocity variation, and it uses the relationship between phase angle and the spectral coordinates of seismic data to allow velocity variation with phase angle. A qualitative comparison of migration impulse responses suggests that, for an equivalent cost, the symmetric non‐stationary phase‐shift (SNPS) operator is superior to the phase‐shift plus interpolation (PSPI) operator, for very large depth intervals. To demonstrate the potential of the new method, seismic data from a physical model acquired over a transversely isotropic medium are imaged using a shot‐record migration based on the SNPS operator.     

Klauder wavelet removal before vibroseis deconvolution

The spiking deconvolution of a field seismic trace requires that the seismic wavelet on the trace be minimum phase. On a dynamite trace, the component wavelets due to the effects of recording instruments, coupling, attenuation, ghosts, reverberations and other types of multiple reflection are minimum phase. The seismic wavelet is the convolution of the component wavelets. As a result, the seismic wavelet on a dynamite trace is minimum phase and thus can be removed by spiking deconvolution. However, on a correlated vibroseis trace, the seismic wavelet is the convolution of the zero-phase Klauder wavelet with the component minimum-phase wavelets. Thus the seismic wavelet occurring on a correlated vibroseis trace does not meet the minimum-phase requirement necessary for spiking deconvolution, and the final result of deconvolution is less than optimal. Over the years, this problem has been investigated and various methods of correction have been introduced. In essence, the existing methods of vibroseis deconvolution make use of a correction that converts (on the correlated trace) the Klauder wavelet into its minimum-phase counterpart. The seismic wavelet, which is the convolution of the minimum-phase counterpart with the component minimum-phase wavelets, is then removed by spiking deconvolution. This means that spiking deconvolution removes both the constructed minimum-phase Klauder counterpart and the component minimum-phase wavelets. Here, a new method is proposed: instead of being converted to minimum phase, the Klauder wavelet is removed directly. The spiking deconvolution can then proceed unimpeded as in the case of a dynamite record. These results also hold for gap predictive deconvolution because gap deconvolution is a special case of spiking deconvolution in which the deconvolved trace is smoothed by the front part of the minimum-phase wavelet that was removed.     

Robust dual‐sensor data sea‐surface ghost attenuation for quality control purposes

Three‐dimensional receiver ghost attenuation (deghosting) of dual‐sensor towed‐streamer data is straightforward, in principle. In its simplest form, it requires applying a three‐dimensional frequency–wavenumber filter to the vertical component of the particle motion data to correct for the amplitude reduction on the vertical component of non‐normal incidence plane waves before combining with the pressure data. More elaborate techniques use three‐dimensional filters to both components before summation, for example, for ghost wavelet dephasing and mitigation of noise of different strengths on the individual components in optimum deghosting. The problem with all these techniques is, of course, that it is usually impossible to transform the data into the crossline wavenumber domain because of aliasing. Hence, usually, a two‐dimensional version of deghosting is applied to the data in the frequency–inline wavenumber domain. We investigate going down the “dimensionality ladder” one more step to a one‐dimensional weighted summation of the records of the collocated sensors to create an approximate deghosting procedure. We specifically consider amplitude‐balancing weights computed via a standard automatic gain control before summation, reminiscent of a diversity stack of the dual‐sensor recordings. This technique is independent of the actual streamer depth and insensitive to variations in the sea‐surface reflection coefficient. The automatic gain control weights serve two purposes: (i) to approximately correct for the geometric amplitude loss of the Z data and (ii) to mitigate noise strength variations on the two components. Here, Z denotes the vertical component of the velocity of particle motion scaled by the seismic impedance of the near‐sensor water volume. The weights are time‐varying and can also be made frequency‐band dependent, adapting better to frequency variations of the noise. The investigated process is a very robust, almost fully hands‐off, approximate three‐dimensional deghosting step for dual‐sensor data, requiring no spatial filtering and no explicit estimates of noise power. We argue that this technique performs well in terms of ghost attenuation (albeit, not exact ghost removal) and balancing the signal‐to‐noise ratio in the output data. For instances where full three‐dimensional receiver deghosting is the final product, the proposed technique is appropriate for efficient quality control of the data acquired and in aiding the parameterisation of the subsequent deghosting processing.