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.     

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.     

基于格林函数理论的波场预测和鬼波压制方法

作为一种特殊的噪声,鬼波对一次波的波形及频带宽度产生极大的影响,鬼波压制是提高海上地震资料分辨率及保真度的重要因素.以格林公式为基础,详细论述了基于格林函数理论的鬼波压制方法,在不需要地下介质信息的条件下,进行地震数据驱动鬼波压制,并根据"Double Dirichlet"(双狄利克雷)边界条件,预测压力波场和垂直速度波场.建立了基于格林函数理论鬼波压制的处理流程,数值模拟和实际资料处理结果表明,基于格林函数理论鬼波压制方法在很好地去除鬼波的同时极大地拓宽了地震资料的频带,尤其提升了低频端能量,有利于后续资料的处理解释.     

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.     

Joint up/down decomposition and reconstruction using three‐component streamers with or without ghost model: the sampling theory

This paper addresses two artefacts inherent to marine towed‐streamer surveys: 1) ghost reflections and 2) too sparse a sampling in the crossline direction. A ghost reflection is generated when an upcoming reflection bounces off the sea surface back into the sensors and can, in principle, be removed by decomposing the measured wavefield into its up‐ and downgoing constituents. This process requires a dense sampling of the wavefield in both directions along and perpendicular to the streamers. A dense sampling in the latter direction is, however, often impossible due to economical and operational constraints. Recent multi‐component streamers have been designed to record the spatial gradients on top of the pressure, which not only benefits the wavefield decomposition but also facilitates a lower‐than‐Nyquist sampling rate of the pressure. In this paper, wavefield reconstruction and deghosting are posed as a joint inverse problem. We present two approaches to establish a system matrix that embeds both a deghosting and an interpolation operator. The first approach is derived with a ghost model, whereas the second approach is derived without a ghost model. The embodiment of a ghost model leads to an even lower sampling rate but relies on a more restrictive assumption on the sea surface.     

How rough sea affects marine seismic data and deghosting procedures

Most seismic processing algorithms generally consider the sea surface as a flat reflector. However, acquisition of marine seismic data often takes place in weather conditions where this approximation is inaccurate. The distortion in the seismic wavelet introduced by the rough sea may influence (for example) deghosting results, as deghosting operators are typically recursive and sensitive to the changes in the seismic signal. In this paper, we study the effect of sea surface roughness on conventional (5–160 Hz) and ultra‐high‐resolution (200–3500 Hz) single‐component towed‐streamer data. To this end, we numerically simulate reflections from a rough sea surface using the Kirchhoff approximation. Our modelling demonstrates that for conventional seismic frequency band sea roughness can distort results of standard one‐dimensional and two‐dimensional deterministic deghosting. To mitigate this effect, we introduce regularisation and optimisation based on the minimum‐energy criterion and show that this improves the processing output significantly. Analysis of ultra‐high‐resolution field data in conjunction with modelling shows that even relatively calm sea state (i.e., 15 cm wave height) introduces significant changes in the seismic signal for ultra‐high‐frequency band. These changes in amplitude and arrival time may degrade the results of deghosting. Using the field dataset, we show how the minimum‐energy optimisation of deghosting parameters improves the processing result.     

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.     

Deghosting by echo‐deblending

A marine source generates both a direct wavefield and a ghost wavefield. This is caused by the strong surface reflectivity, resulting in a blended source array, the blending process being natural. The two unblended response wavefields correspond to the real source at the actual location below the water level and to the ghost source at the mirrored location above the water level. As a consequence, deghosting becomes deblending (‘echo‐deblending’) and can be carried out with a deblending algorithm. In this paper we present source deghosting by an iterative deblending algorithm that properly includes the angle dependence of the ghost: It represents a closed‐loop, non‐causal solution. The proposed echo‐deblending algorithm is also applied to the detector deghosting problem. The detector cable may be slanted, and shot records may be generated by blended source arrays, the blending being created by simultaneous sources. Similar to surface‐related multiple elimination the method is independent of the complexity of the subsurface; only what happens at and near the surface is relevant. This means that the actual sea state may cause the reflection coefficient to become frequency dependent, and the water velocity may not be constant due to temporal and lateral variations in the pressure, temperature, and salinity. As a consequence, we propose that estimation of the actual ghost model should be part of the echo‐deblending algorithm. This is particularly true for source deghosting, where interaction of the source wavefield with the surface may be far from linear. The echo‐deblending theory also shows how multi‐level source acquisition and multi‐level streamer acquisition can be numerically simulated from standard acquisition data. The simulated multi‐level measurements increase the performance of the echo‐deblending process. The output of the echo‐deblending algorithm on the source side consists of two ghost‐free records: one generated by the real source at the actual location below the water level and one generated by the ghost source at the mirrored location above the water level. If we apply our algorithm at the detector side as well, we end up with four ghost‐free shot records. All these records are input to migration. Finally, we demonstrate that the proposed echo‐deblending algorithm is robust for background noise.     

Evolution of deghosting process for single‐sensor streamer data from 2D to 3D

In marine acquisition, reflections of sound energy from the water–air interface result in ghosts in the seismic data, both in the source side and the receiver side. Ghosts limit the bandwidth of the useful signal and blur the final image. The process to separate the ghost and primary signals, called the deghosting process, can fill the ghost notch, broaden the frequency band, and help achieve high‐resolution images. Low‐signal‐to‐noise ratio near the notch frequencies and 3D effects are two challenges that the deghosting process has to face. In this paper, starting from an introduction to the deghosting process, we present and compare two strategies to solve the latter. The first is an adaptive mechanism that adjusts the deghosting operator to compensate for 3D effects or errors in source/receiver depth measurement. This method does not include explicitly the crossline slowness component and is not affected by the sparse sampling in the same direction. The second method is an inversion‐type approach that does include the crossline slowness component in the algorithm and handles the 3D effects explicitly. Both synthetic and field data examples in wide azimuth acquisition settings are shown to compare the two strategies. Both methods provide satisfactory results.     

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.     

High-resolution frequency-domain Radon transform and variable-depth streamer data deghosting

Receiver ghost reflections adversely affect variable-depth streamer (VDS) data acquisition. In addition, the frequency notches caused by the interference between receiver ghosts and primary waves strongly affect seismic data processing and imaging. We developed a high-resolution Radon transform algorithm and used it to predict receiver ghosts from VDS data. The receiver ghost reflections are subtracted and removed from the raw data. We propose a forward Radon transform operator of VDS data in the frequency domain and, based on the ray paths of the receiver ghosts, we propose an inverse Radon transform operator. We apply the proposed methodology to model and field data with good results. We use matching and subtracting modules of commercially available seismic data processing software to remove the receiver ghosts. The frequency notches are compensated and the effective frequency bandwidth of the seismic data broadens.     

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.     

Marine,seabed, and land seismic equipment for broadband acquisition: a review

The broadband capabilities of marine, seabed, and land seismic equipment are reviewed with respect to both the source and the receiver sides. In marine acquisition, the main issue at both ends of the spectrum relates to ghosts occurring at the sea surface. Broadband deghosting requires towing at variable depth to introduce notch diversity or using new equipment like multi‐component and/or low‐noise streamers. As a result, a doubling of the bandwidth from about three to six octaves (2.5–200 Hz) has been achieved. Such improvement is not yet observed for seabed surveys in spite of deghosting being a standard process on the receiver side. One issue may be related to the coupling of the particle motion sensor, particularly at high frequencies. For land acquisition, progress came from the vibrators. New shakers and control electronics using broadband sweeps made it possible to add two more octaves to the low‐frequency signal (from 8 to 2 Hz). Whereas conventional 10 Hz geophones are still able to record such low frequencies, 5 Hz high gain geophones or digital accelerometers enhance them to keep the signal above the noise floor. On the high end of the bandwidth, progress is not limited by equipment specifications. Here, the issue is related to a low signal‐to‐noise ratio due to the strong absorption that occurs during signal propagation. To succeed in enlarging the bandwidth, these improved equipment and sweeps must be complemented by a denser spatial sampling of the wavefield by point–source and point–receiver acquisition.     

A probabilistic model for ghost delay time estimation based on recording geometry

In order to deconvolve the ghost response from marine seismic data, an estimate of the ghost operator is required. Typically, this estimate is made using a model of in‐plane propagation, i.e., the ray path at the receiver falls in the vertical plane defined by the source and receiver locations. Unfortunately, this model breaks down when the source is in a crossline position relative to the receiver spread. In this situation, in‐plane signals can only exist in a small region of the signal cone. In this paper, we use Bayes' theory to model the posterior probability distribution functions for the vertical component of the ray vector given the known source–receiver azimuth and the measured inline component of the ray vector. This provides a model for the ghost delay time based on the acquisition geometry and the dip of the wave in the plane of the streamer. The model is fairly robust with regard to the prior assumptions and controlled by a single parameter that is related to the likelihood of in‐plane propagation. The expected values of the resulting distributions are consistent with the deterministic in‐plane model when in‐plane likelihood is high but valid everywhere in the signal cone. Relaxing the in‐plane likelihood to a reasonable degree radically simplifies the shape of the expected‐value surface, lending itself for use in deghosting algorithms. The model can also be extended to other plane‐wave processing problems such as interpolation.     

Unified multi‐depth‐level field decomposition

Wavefield decomposition forms an important ingredient of various geophysical methods. An example of wavefield decomposition is the decomposition into upgoing and downgoing wavefields and simultaneous decomposition into different wave/field types. The multi‐component field decomposition scheme makes use of the recordings of different field quantities (such as particle velocity and pressure). In practice, different recordings can be obscured by different sensor characteristics, requiring calibration with an unknown calibration factor. Not all field quantities required for multi‐component field decomposition might be available, or they can suffer from different noise levels. The multi‐depth‐level decomposition approach makes use of field quantities recorded at multiple depth levels, e.g., two horizontal boreholes closely separated from each other, a combination of a single receiver array combined with free‐surface boundary conditions, or acquisition geometries with a high‐density of vertical boreholes. We theoretically describe the multi‐depth‐level decomposition approach in a unified form, showing that it can be applied to different kinds of fields in dissipative, inhomogeneous, anisotropic media, e.g., acoustic, electromagnetic, elastodynamic, poroelastic, and seismoelectric fields. We express the one‐way fields at one depth level in terms of the observed fields at multiple depth levels, using extrapolation operators that are dependent on the medium parameters between the two depth levels. Lateral invariance at the depth level of decomposition allows us to carry out the multi‐depth‐level decomposition in the horizontal wavenumber–frequency domain. We illustrate the multi‐depth‐level decomposition scheme using two synthetic elastodynamic examples. The first example uses particle velocity recordings at two depth levels, whereas the second example combines recordings at one depth level with the Dirichlet free‐surface boundary condition of zero traction. Comparison with multi‐component decomposed fields shows a perfect match in both amplitude and phase for both cases. The multi‐depth‐level decomposition scheme is fully customizable to the desired acquisition geometry. The decomposition problem is in principle an inverse problem. Notches may occur at certain frequencies, causing the multi‐depth‐level composition matrix to become uninvertible, requiring additional notch filters. We can add multi‐depth‐level free‐surface boundary conditions as extra equations to the multi‐component composition matrix, thereby overdetermining this inverse problem. The combined multi‐component–multi‐depth‐level decomposition on a land data set clearly shows improvements in the decomposition results, compared with the performance of the multi‐component decomposition scheme.     

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.     

Three‐dimensional inversion of towed streamer electromagnetic data

A towed streamer electromagnetic system capable of simultaneous seismic and electromagnetic data acquisition has recently been developed and tested in the North Sea. We introduce a 3D inversion methodology for towed streamer electromagnetic data that includes a moving sensitivity domain. Our implementation is based on the 3D integral equation method for computing responses and Fréchet derivatives and uses the re‐weighted regularized conjugate gradient method for minimizing the objective functional with focusing regularization. We present two model studies relevant to hydrocarbon exploration in the North Sea. First, we demonstrate the ability of a towed electromagnetic system to detect and characterize the Harding field, a medium‐sized North Sea hydrocarbon target. We compare our 3D inversion of towed streamer electromagnetic data with 3D inversion of conventional marine controlled‐source electromagnetic data and observe few differences between the recovered models. Second, we demonstrate the ability of a towed streamer electromagnetic system to detect and characterize the Peon discovery, which is representative of an infrastructure‐led shallow gas play in the North Sea. We also present an actual case study for the 3D inversion of towed streamer electromagnetic data from the Troll field in the North Sea and demonstrate our ability to image all the Troll West Oil and Gas Provinces and the Troll East Gas Province. We conclude that 3D inversion of data from the current generation of towed streamer electromagnetic systems can adequately recover hydrocarbon‐bearing formations to depths of approximately 2 km. We note that by obviating the need for ocean‐bottom receivers, the towed streamer electromagnetic system enables electromagnetic data to be acquired over very large areas in frontier and mature basins for higher acquisition rates and relatively lower cost than conventional marine controlled‐source electromagnetic methods.     

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.     

两种斜缆采集正演模拟及虚反射压制效果分析

斜缆采集是近些年发展起来的海上采集技术,主要为了压制虚反射,获得高品质的宽频地震资料。线形斜缆和弧形斜缆是目前最常用的斜缆类型,能够获取较多的高低频信息。针对这两种斜缆采集方式,通过对比不同采集参数的地震记录及其消除虚反射后的数据,发现弧形斜缆采集观测系统明显优于线形斜缆,不仅在波场模拟中表现出较好的特征,而且在虚反射消除的过程中,引入了较小的噪声,能够获得较高信噪比的地震资料。分析模型测试的结果,证明海上地震勘探中更适合采用弧形斜缆。      

Shallow virtual source redatuming by multi‐dimensional deconvolution

Recently, new on‐shore acquisition designs have been presented with multi‐component sensors deployed in the shallow sub‐surface (20 m–60 m). Virtual source redatuming has been proposed for these data to compensate for surface statics and to enhance survey repeatability. In this paper, we investigate the feasibility of replacing the correlation‐based formalism that undergirds virtual source redatuming with multi‐dimensional deconvolution, offering various advantages such as the elimination of free‐surface multiples and the potential to improve virtual source repeatability. To allow for data‐driven calibration of the sensors and to improve robustness in cases with poor sensor spacing in the shallow sub‐surface (resulting in a relatively high wavenumber content), we propose a new workflow for this configuration. We assume a dense source sampling and target signals that arrive at near‐vertical propagation angles. First, the data are preconditioned by applying synthetic‐aperture‐source filters in the common receiver domain. Virtual source redatuming is carried out for the multi‐component recordings individually, followed by an intermediate deconvolution step. After this specific pre‐processing, we show that the downgoing and upgoing constituents of the wavefields can be separated without knowledge of the medium parameters, the source wavelet, or sensor characteristics. As a final step, free‐surface multiples can be eliminated by multi‐dimensional deconvolution of the upgoing fields with the downgoing fields.