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.     

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.     

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.     

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.     

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.     

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.     

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.     

基于编码解码思想的鬼波预测与压制方法

高分辨率的宽带地震勘探技术是最近几年海上油气地震勘探的热点问题,鬼波压制是其中的核心议题.石油工业界,除了提出各种压制鬼波的采集方式外,资料处理过程中压制鬼波的方法也在不断地推陈出新.源、检鬼波的存在使得反射子波的有效频带变窄,成像分辨率降低,且干扰后续的自由表面多次波压制、FWI等.不同于常规的鬼波压制模型,本文基于编码与解码理论框架,用编码建立起鬼波预测模型,在Bayes反演框架下建立起解码估计一次波、从而压制鬼波的方法.基于此鬼波预测模型及相应反演理论的鬼波压制方法对鬼波的压制更为彻底.理论模型数据与实际资料测试结果验证了本文提出的理论框架和方法技术的有效性与优越性.     

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.     

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.     

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.     

Scattered ground‐roll attenuation using model‐driven interferometry

Scattered ground roll is a type of noise observed in land seismic data that can be particularly difficult to suppress. Typically, this type of noise cannot be removed using conventional velocity‐based filters. In this paper, we discuss a model‐driven form of seismic interferometry that allows suppression of scattered ground‐roll noise in land seismic data. The conventional cross‐correlate and stack interferometry approach results in scattered noise estimates between two receiver locations (i.e. as if one of the receivers had been replaced by a source). For noise suppression, this requires that each source we wish to attenuate the noise from is co‐located with a receiver. The model‐driven form differs, as the use of a simple model in place of one of the inputs for interferometry allows the scattered noise estimate to be made between a source and a receiver. This allows the method to be more flexible, as co‐location of sources and receivers is not required, and the method can be applied to data sets with a variety of different acquisition geometries. A simple plane‐wave model is used, allowing the method to remain relatively data driven, with weighting factors for the plane waves determined using a least‐squares solution. Using a number of both synthetic and real two‐dimensional (2D) and three‐dimensional (3D) land seismic data sets, we show that this model‐driven approach provides effective results, allowing suppression of scattered ground‐roll noise without having an adverse effect on the underlying signal.     

Three‐dimensional controlled‐source electromagnetic modelling with a well casing as a grounded source: a hybrid method of moments and finite element scheme

Steel well casings in or near a hydrocarbon reservoir can be used as source electrodes in time‐lapse monitoring using grounded line electromagnetic methods. A requisite component of carrying out such monitoring is the capability to numerically model the electromagnetic response of a set of source electrodes of finite length. We present a modelling algorithm using the finite‐element method for calculating the electromagnetic response of a three‐dimensional conductivity model excited using a vertical steel‐cased borehole as a source. The method is based on a combination of the method of moments and the Coulomb‐gauged primary–secondary potential formulation. Using the method of moments, we obtain the primary field in a half‐space due to an energized vertical steel casing by dividing the casing into a set of segments, each assumed to carry a piecewise constant alternating current density. The primary field is then substituted into the primary–secondary potential finite‐element formulation of the three‐dimensional problem to obtain the secondary field. To validate the algorithm, we compare our numerical results with: (i) the analytical solution for an infinite length casing in a whole space, excited by a line source, and (ii) a three‐layered Earth model without a casing. The agreement between the numerical and analytical solutions demonstrates the effectiveness of our algorithm. As an illustration, we also present the time‐lapse electromagnetic response of a synthetic model representing a gas reservoir undergoing water flooding.     

Modified image algorithm to simulate seismic channel waves in 3D tunnel model with rugged free surfaces

The existence of rugged free‐surface three‐dimensional tunnel conditions in the coal seams, caused either by geological or mining processes, will inevitably influence wave propagation characteristics when the seismic waves go through the coal mines. Thus, a modified image algorithm has been developed to account for seismic channel waves propagating through this complicated topography with irregular free surfaces. Moreover, the seismic channel waves commonly exhibit damped and dispersive signatures, which is not only because of their own unique sandwich geometry of rock–coal–rock but also because of the viscoelastic behavior of coal. Considering the complexity of programming in three‐dimensional tunnel models with rugged free surfaces, an optimized vacuum grid search algorithm, enabling to model highly irregular topography and to compute efficiently, is also proposed when using high‐order staggered finite‐difference scheme to simulate seismic channel wave propagations in viscoelastic media. The numerical simulations are implemented to investigate the accuracy and stability of the method and the impact of coal's viscoelastic behavior on seismic channel wave propagation characteristics. The results indicate that the automatic vacuum grid search algorithm can be easily merged into high‐order staggered finite‐difference scheme, which can efficiently be applied to calculate three‐dimensional tunnel models with rugged free surfaces in the viscoelastic media. The simulation also suggests that the occurrence of a three‐dimensional tunnel with free surfaces has a remarkable influence on the seismic channel wave propagation characteristics and elastic energy distribution.     

Seismic channel edge detection using 3D shearlets—a study on synthetic and real channelised 3D seismic data

Automatic feature detection from seismic data is a demanding task in today's interpretation workstations. Channels are among important stratigraphic features in seismic data both due to their reservoir capability or drilling hazard potential. Shearlet transform as a multi‐scale and multi‐directional transformation is capable of detecting anisotropic singularities in two and higher dimensional data. Channels occur as edges in seismic data, which can be detected based on maximizing the shearlet coefficients through all sub‐volumes at the finest scale of decomposition. The detected edges may require further refinement through the application of a thinning methodology. In this study, a three‐dimensional, pyramid‐adapted, compactly supported shearlet transform was applied to synthetic and real channelised, three‐dimensional post‐stack seismic data in order to decompose the data into different scales and directions for the purpose of channel boundary detection. In order to be able to compare the edge detection results based on three‐dimensional shearlet transform with some famous gradient‐based edge detectors, such as Sobel and Canny, a thresholding scheme is necessary. In both synthetic and real data examples, the three‐dimensional shearlet edge detection algorithm outperformed Sobel and Canny operators even in the presence of Gaussian random noise.     

Experimental study on the performance of an azimuthal acoustic receiver sonde for a downhole tool

A new azimuthal acoustic receiver sonde with a body and corresponding circuits was designed for a downhole tool. The 64‐sensor receiver sonde holds eight receiver stations that can be combined into at least 64 three‐sensor receiver subarrays. As a result, the receiver sonde can use different sensor combinations instead of different transducer types to produce multiple modes, including a phased azimuthal reception mode and conventional monopole, dipole, and quadruple modes. Laboratory measurements were conducted to study the performance of the azimuthal acoustic receiver sonde for a downhole tool, and the experimental results indicate that the receiver sonde provides a consistent reception performance. Individual sensors receive similar time‐domain waveforms, and their corresponding frequency bands and sensitivities are consistent within the measurement errors of around 5%. The direction of the reception main lobe is approximately parallel to its exterior normal direction. In addition, a receiver subarray with three sensors receives waveforms that have higher energy and narrower beamwidths. For individual sensors, the angular width of the dominant reception lobe is 191.3^° on average, whereas that of the individual receiver subarrays is approximately 52.1^° on average. The amplitude of the first arrival received by the receiver subarray centred at the primary sensor directly pointing to the source is approximately 2.2 times the average amplitude of the first arrivals received by the other receiver subarrays in the same receiver station. Thus, the maximum amplitude of the waveforms received by the receiver subarrays can be used to determine the direction of the incident waves. This approach represents a promising method for determining the reflector azimuth for acoustic reflection logging and three‐dimensional acoustic logging.     

Differential evolution with subpopulations for high‐dimensional seismic inversion

Seismic inversion has drawn the attention of researchers due to its capability of building an accurate earth model. Such a model will need to be discretised finely, and the dimensions of the inversion problem will be very high. In this paper, we propose an efficient differential evolution algorithm and apply it to high‐dimensional seismic inversion. Our method takes into account the differences among individuals, which are disregarded in conventional differential evolution methods, resulting to a better balance between exploration and exploitation. We divide the entire population into three subpopulations and propose a novel mutation strategy with two phases. Furthermore, we optimise the crossover operator by applying the components having the best objective function values into the crossover operator. We embed this strategy into a cooperative coevolutionary differential evolution and propose a new differential evolution algorithm referred to as a differential evolution with subpopulations. Then, we apply our scheme to both synthetic and field data; the results of high‐dimensional seismic inversion have shown that the proposed differential evolution with subpopulations achieves faster convergence and a higher‐quality solution for seismic inversion.     

基于逆散射级数法的鬼波压制方法

鬼波问题是影响海上地震资料分辨率和保真度提高的最重要因素之一.详细论述了逆散射级数理论和逆散射级数法鬼波压制原理,说明了逆散射级数方法进行鬼波压制理论的完善性和对鬼波描述的精确性.实现了基于逆散射级数理论的鬼波压制方法,方法以波动方程和Lippmann-Schwinger方程为基础,在频率-波数-波数域内构造与鬼波相关的压制算子,在不需要对地下介质作任何假设条件下实现地震数据驱动鬼波压制,并通过改善消除鬼波的压制算子,提高算法的稳定性.资料处理试验与处理结果分析表明,基于逆散射级数鬼波压制方法能在实现鬼波压制的同时较好保留有效反射波的信息,从而补偿地震资料低频损失和提高地震数据的保真度.数据处理试验还表明,研究方法能对低信噪比的地震资料进行有效的鬼波压制处理.建立了基于逆散射级数鬼波压制处理流程.     

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.