Improved structural interpretation of legacy 3D seismic data from Karee platinum mine (South Africa) through the application of novel seismic attributes

Seismic detection of faults, dykes, potholes and iron-rich ultramafic pegmatitic bodies is of great importance to the platinum mining industry, as these structures affect safety and efficiency. The application of conventional seismic attributes (such as instantaneous amplitude, phase and frequency) in the hard-rock environment is more challenging than in soft-rock settings because the geology is often complex, reflections disrupted and the seismic energy strongly scattered. We have developed new seismic attributes that sharpen seismic reflections, enabling additional structural information to be extracted from hard-rock seismic data. The symmetry attribute is based on the invariance of an object with respect to transformations such as rotation and reflection; it is independent of the trace reflection amplitude, and hence a better indicator of the lateral continuity of thin and weak reflections. The reflection-continuity detector attribute is based on the Hilbert transform; it enhances the visibility of the peaks and troughs of the seismic traces, and hence the continuity of weak reflections. We demonstrate the effectiveness of these new seismic attributes by applying them to a legacy 3D seismic data set from the Bushveld Complex in South Africa. These seismic attributes show good detection of deep-seated thin (∼1.5 m thick) platinum ore bodies and their associated complex geological structures (faults, dykes, potholes and iron-rich ultramafic pegmatites). They provide a fast, cost-effective and efficient interpretation tool that, when coupled with horizon-based seismic attributes, can reveal structures not seen in conventional interpretations.     

Water‐bottom multiple attenuation by Kirchhoff extrapolation

Despite being less general than 3D surface‐related multiple elimination (3D‐SRME), multiple prediction based on wavefield extrapolation can still be of interest, because it is less CPU and I/O demanding than 3D‐SRME and moreover it does not require any prior data regularization. Here we propose a fast implementation of water‐bottom multiple prediction that uses the Kirchhoff formulation of wavefield extrapolation. With wavefield extrapolation multiple prediction is usually obtained through the cascade of two extrapolation steps. Actually by applying the Fermat’s principle (i.e., minimum reflection traveltime) we show that the cascade of two operators can be replaced by a single approximated extrapolation step. The approximation holds as long as the water bottom is not too complex. Indeed the proposed approach has proved to work well on synthetic and field data when the water bottom is such that wavefront triplications are negligible, as happens in many practical situations.     

Robust f‐x projection filtering for simultaneous random and erratic seismic noise attenuation

Linear prediction filters are an effective tool for reducing random noise from seismic records. Unfortunately, the ability of prediction filters to enhance seismic records deteriorates when the data are contaminated by erratic noise. Erratic noise in this article designates non‐Gaussian noise that consists of large isolated events with known or unknown distribution. We propose a robust f‐x projection filtering scheme for simultaneous erratic noise and Gaussian random noise attenuation. Instead of adopting the ?₂‐norm, as commonly used in the conventional design of f‐x filters, we utilize the hybrid ‐norm to penalize the energy of the additive noise. The estimation of the prediction error filter and the additive noise sequence are performed in an alternating fashion. First, the additive noise sequence is fixed, and the prediction error filter is estimated via the least‐squares solution of a system of linear equations. Then, the prediction error filter is fixed, and the additive noise sequence is estimated through a cost function containing a hybrid ‐norm that prevents erratic noise to influence the final solution. In other words, we proposed and designed a robust M‐estimate of a special autoregressive moving‐average model in the f‐x domain. Synthetic and field data examples are used to evaluate the performance of the proposed algorithm.     

Low-rank seismic denoising with optimal rank selection for hankel matrices

Based on the fact that the Hankel matrix representing clean seismic data is low rank, low-rank approximation methods have been widely utilized for removing noise from seismic data. A common strategy for real seismic data is to perform the low-rank approximations for small local windows where the events can be approximately viewed as linear. This raises a fundamental question of selecting an optimal rank that best captures the number of events for each local window. Gavish and Donoho proposed a method to select the rank when the noise is independent and identically distributed. Gaussian matrix by analysing the statistical performance of the singular values of the Gaussian matrices. However, such statistical performance is not available for noisy Hankel matrices. In this paper, we adopt the same strategy and propose a rule that computes the number of singular values exceed the median singular value by a multiplicative factor. We suggest a multiplicative factor of 3 based on simulations which mimic the theories underlying Gavish and Donoho in the independent and identically distributed Gaussian setting. The proposed optimal rank selection rule can be incorporated into the classical low-rank approximation method and many other recently developed methods such as those by shrinking the singular values. The low-rank approximation methods with optimally selected rank rule can automatically suppress most of the noise while preserving the main features of the seismic data in each window. Experiments on both synthetic and field seismic data demonstrate the superior performance of the proposed rank selection rule for seismic data denoising.     

A genetic algorithm for filter design to enhance features in seismic images

We present a novel method to enhance seismic data for manual and automatic interpretation. We use a genetic algorithm to optimize a kernel that, when convolved with the seismic image, appears to enhance the internal characteristics of salt bodies and the sub‐salt stratigraphy. The performance of the genetic algorithm was validated by the use of test images prior to its application on the seismic data. We present the evolution of the resulting kernel and its convolved image. This image was analysed by a seismic interpreter, highlighting possible advantages over the original one. The effects of the kernel were also subject to an automatic interpretation technique based on principal component analysis. Statistical comparison of these results with those from the original image, by means of the Mann‐Whitney U‐test, proved the convolved image to be more appropriate for automatic interpretation.     

Retrieving virtual reflection responses at drill‐bit positions using seismic interferometry with drill‐bit noise

In the field of seismic interferometry, researchers have retrieved surface waves and body waves by cross‐correlating recordings of uncorrelated noise sources to extract useful subsurface information. The retrieved wavefields in most applications are between receivers. When the positions of the noise sources are known, inter‐source interferometry can be applied to retrieve the wavefields between sources, thus turning sources into virtual receivers. Previous applications of this form of interferometry assume impulsive point sources or transient sources with similar signatures. We investigate the requirements of applying inter‐source seismic interferometry using non‐transient noise sources with known positions to retrieve reflection responses at those positions and show the results using synthetic drilling noise as source. We show that, if pilot signals (estimates of the drill‐bit signals) are not available, it is required that the drill‐bit signals are the same and that the phases of the virtual reflections at drill‐bit positions can be retrieved by deconvolution interferometry or by cross‐coherence interferometry. Further, for this case, classic interferometry by cross‐correlation can be used if the source power spectrum can be estimated. If pilot signals are available, virtual reflection responses can be obtained by first using standard seismic‐while‐drilling processing techniques such as pilot cross‐correlation and pilot deconvolution to remove the drill‐bit signatures in the data and then applying cross‐correlation interferometry. Therefore, provided that pilot signals are reliable, drill‐bit data can be redatumed from surface to borehole depths using this inter‐source interferometry approach without any velocity information of the medium, and we show that a well‐positioned image below the borehole can be obtained using interferometrically redatumed reflection responses with just a simple velocity model. We discuss some of the practical hurdles that restrict the application of the proposed method offshore.     

Research Note: Frequency domain orthogonal projection filtration of surface microseismic monitoring data

We address the problem of increasing the signal-to-noise ratio during surface microseismic monitoring data processing. Interference from different seismic waves causes misleading results of microseismic event locations. Ground-roll suppression is particularly necessary. The standard noise suppression techniques assume regular and dense acquisition geometries. Many pre-processing noise suppression algorithms are designed for special types of noise or interference. To overcome these problems, we propose a novel general-purpose filtration method. The goal of this method is to amplify only the seismic waves that are excited in the selected target area and suppress all other signals. We construct a linear projector onto a frequency domain data subspace, which corresponds to the seismic emission of the target area. The novel filtration method can be considered an extension of the standard frequency–wavenumber flat wave filtration method for non-flat waves and arbitrary irregular receiver-position geometries. To reduce the effect of the uncertainty of the velocity model, we suggest using additional active shot data (typically the perforation shots), which provide static travel time corrections for the target area. The promising prospects of the proposed method are confirmed by synthetic and semi-synthetic data processing.     

由地震背景噪声提取介质衰减:衰减介质中的空间相干表示

传统基于地震背景噪声互相关的层析成像技术,主要利用了互相关函数的相位信息,即利用走时来反演地球介质的速度和各向异性特征.最近,开始有研究人员利用互相关函数的振幅信息提取介质的衰减.主要是将二维弹性情形下,互相关函数正比于第一类零阶贝塞尔函数J_0(k_0r)这一结论,通过引入指数衰减系数,直接推广到衰减介质情形,令衰减介质中背景噪声互相关函数类比于J_0(k_0r)·e~(-α(ω)r),以此来反演介质的衰减系数α.然而,在衰减介质中,互相关受源的方位平均的影响,这种简单的推广,可能无法提取可靠的衰减系数.本文基于平面波的叠加模型,研究不同的互相关定义和坐标选择下,衰减介质中两点间互相关函数的理论表达式.结果表明,在平面波叠加模型下,互相关函数的表达形式随着坐标原点的选择,并因而随着源分布的变化而变化,对不同的归一化因子,表达式也不尽相同.利用J_0(k_0r)·e~(-α(ω)r)的形式拟合背景噪声的观测数据得到的衰减比实际值偏小.     

Random noise attenuation via the randomized canonical polyadic decomposition

Tensor algebra provides a robust framework for multi-dimensional seismic data processing. A low-rank tensor can represent a noise-free seismic data volume. Additive random noise will increase the rank of the tensor. Hence, tensor rank-reduction techniques can be used to filter random noise. Our filtering method adopts the Candecomp/Parafac decomposition to approximates a N-dimensional seismic data volume via the superposition of rank-one tensors. Similar to the singular value decomposition for matrices, a low-rank Candecomp/Parafac decomposition can capture the signal and exclude random noise in situations where a low-rank tensor can represent the ideal noise-free seismic volume. The alternating least squares method is adopted to compute the Candecomp/Parafac decomposition with a provided target rank. This method involves solving a series of highly over-determined linear least-squares subproblems. To improve the efficiency of the alternating least squares algorithm, we uniformly randomly sample equations of the linear least-squares subproblems to reduce the size of the problem significantly. The computational overhead is further reduced by avoiding unfolding and folding large dense tensors. We investigate the applicability of the randomized Candecomp/Parafac decomposition for incoherent noise attenuation via experiments conducted on a synthetic dataset and field data seismic volumes. We also compare the proposed algorithm (randomized Candecomp/Parafac decomposition) against multi-dimensional singular spectrum analysis and classical prediction filtering. We conclude the proposed approach can achieve slightly better denoising performance in terms of signal-to-noise ratio enhancement than traditional methods, but with a less computational cost.     

A study of the geophysical response of distributed fibre optic acoustic sensors through laboratory‐scale experiments

In the past few years, distributed acoustic sensing has gained great interest in geophysics. This acquisition technology offers immense improvement in terms of efficiency when compared with current geophysical acquisition methods. However, the fundamentals of the measurement are still not fully understood because direct comparisons of fibre data with conventional geophysical sensors are difficult during field tests. We present downscaled laboratory experiments that enabled us to characterise the relationship between the signals recorded by conventional seismic point receivers and by distributed fibre optic sensors. Interrogation of the distributed optical fibre sensor was performed with a Michelson interferometer because this system is suited to compact test configurations, and it requires only a very simple data processing workflow for extracting the signal outputs. We show acoustic data that were recorded simultaneously by both the fibre optical interferometer and conventional three‐component accelerometers, thus enabling the comparison of sensor performance. We present results focused on the directionality of fibre measurements, on the amplitude variation with angle of incidence, and on the transfer function that allows accelerometer signals to be transformed into optical fibre signals. We conclude that the optical fibre response matches with the array of the displacement differences of the inline accelerometers deployed along the fibre length. Moreover, we also analysed the influence of various types of coupling and fibre cable coating on the signal responses, emphasising the importance of these parameters for field seismic acquisitions when using the distributed fibre optic technology.     

The estimation of spectra from time‐frequency transforms for use in attenuation studies

We introduce the signal dependent time–frequency distribution, which is a time–frequency distribution that allows the user to optimize the tradeoff between joint time–frequency resolution and suppression of transform artefacts. The signal‐dependent time–frequency distribution, as well as the short‐time Fourier transform, Stockwell transform, and the Fourier transform are analysed for their ability to estimate the spectrum of a known wavelet used in a tuning wedge model. Next, the signal‐dependent time–frequency distribution, and fixed‐ and variable‐window transforms are used to estimate spectra from a zero‐offset synthetic seismogram. Attenuation is estimated from the associated spectral ratio curves, and the accuracy of the results is compared. The synthetic consisted of six pairs of strong reflections, based on real well‐log data, with a modeled intrinsic attenuation value of 1000/Q = 20. The signal‐dependent time–frequency distribution was the only time–frequency transform found to produce spectra that estimated consistent attenuation values, with an average of 1000/Q = 26±2; results from the fixed‐ and variable‐window transforms were 24±17 and 39±10, respectively. Finally, all three time–frequency transforms were used in a pre‐stack attenuation estimation method (the pre‐stack Q inversion algorithm) applied to a gather from a North Sea seismic dataset, to estimate attenuation between nine different strong reflections. In this case, the signal‐dependent time‐frequency distribution produced spectra more consistent with the constant‐Q model of attenuation assumed in the pre‐stack attenuation estimation algorithm: the average L1 residuals of the spectral ratio surfaces from the theoretical constant‐Q expectation for the signal‐dependent time‐frequency distribution, short‐time Fourier transform, and Stockwell transform were 0.12, 0.21, and 0.33, respectively. Based on the results shown, the signal‐dependent time‐frequency distribution is a time–frequency distribution that can provide more accurate and precise estimations of the amplitude spectrum of a reflection, due to a higher attainable time–frequency resolution.     

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.     

裂缝、裂隙介质衰减频散研究

为研究裂缝、裂隙介质中波致流引起的衰减,将裂缝看作背景孔隙岩石中非常薄且孔隙度非常高的层状介质,并等价成White周期层状模型.分别考虑不同类型的裂隙和孔隙之间的挤喷流影响,结合改进的Biot方程,推导得到裂缝裂隙介质的刚度与频率的关系.当缝隙中饱含流体时,介质的衰减和速度频散受裂缝、孔隙之间和裂隙、孔隙之间流体流动的显著影响.在低频极限下,裂缝裂隙介质的性质由各向异性Gassmann理论和挤喷流模型获得;而在非常高的频率时,由于缝隙中的压力来不及达到平衡,波致流的影响可忽略.分析表明,裂隙密度主要影响波的衰减,而裂隙纵横比主要控制优势衰减频率和速度显著变化的频率范围;由于不同裂隙的衰减机制不同,衰减和速度频散大小有所差异,但基本趋势相同.

     

3D Marchenko applications: implementation and examples

We implement the 3D Marchenko equations to retrieve responses to virtual sources inside the subsurface. For this, we require reflection data at the surface of the Earth that contain no free-surface multiples and are densely sampled in space. The required 3D reflection data volume is very large and solving the Marchenko equations requires a significant amount of computational cost. To limit the cost, we apply floating point compression to the reflection data to reduce their volume and the loading time from disk. We apply the Marchenko implementation to numerical reflection data to retrieve accurate Green's functions inside the medium and use these reflection data to apply imaging. This requires the simulation of many virtual source points, which we circumvent using virtual plane-wave sources instead of virtual point sources. Through this method, we retrieve the angle-dependent response of a source from a depth level rather than of a point. We use these responses to obtain angle-dependent structural images of the subsurface, free of contamination from wrongly imaged internal multiples. These images have less lateral resolution than those obtained using virtual point sources, but are more efficiently retrieved.     

Three-parameter Radon transform in layered transversely isotropic media

Radon transform is a powerful tool with many applications in different stages of seismic data processing, because of its capability to focus seismic events in the transform domain. Three-parameter Radon transform can optimally focus and separate different seismic events, if its basis functions accurately match the events. In anisotropic media, the conventional hyperbolic or shifted hyperbolic basis functions lose their accuracy and cannot preserve data fidelity, especially at large offsets. To address this issue, we propose an accurate traveltime approximation for transversely isotropic media with vertical symmetry axis, and derive two versions of Radon basis functions, time-variant and time-invariant. A time-variant basis function can be used in time domain Radon transform algorithms while a time-invariant version can be used in, generally more efficient, frequency domain algorithms. Comparing the time-variant and time-invariant Radon transform by the proposed basis functions, the time-invariant version can better focus different seismic events; it is also more accurate, especially in presence of vertical heterogeneity. However, the proposed time-invariant basis functions are suitable for a specific type of layered anisotropic media, known as factorized media. We test the proposed methods and illustrate successful applications of them for trace interpolation and coherent noise attenuation.     

Detection of point scatterers using diffraction imaging and deep learning

Diffracted waves carry high-resolution information that can help interpreting fine structural details at a scale smaller than the seismic wavelength. However, the diffraction energy tends to be weak compared to the reflected energy and is also sensitive to inaccuracies in the migration velocity, making the identification of its signal challenging. In this work, we present an innovative workflow to automatically detect scattering points in the migration dip angle domain using deep learning. By taking advantage of the different kinematic properties of reflected and diffracted waves, we separate the two types of signals by migrating the seismic amplitudes to dip angle gathers using prestack depth imaging in the local angle domain. Convolutional neural networks are a class of deep learning algorithms able to learn to extract spatial information about the data in order to identify its characteristics. They have now become the method of choice to solve supervised pattern recognition problems. In this work, we use wave equation modelling to create a large and diversified dataset of synthetic examples to train a network into identifying the probable position of scattering objects in the subsurface. After giving an intuitive introduction to diffraction imaging and deep learning and discussing some of the pitfalls of the methods, we evaluate the trained network on field data and demonstrate the validity and good generalization performance of our algorithm. We successfully identify with a high-accuracy and high-resolution diffraction points, including those which have a low signal to noise and reflection ratio. We also show how our method allows us to quickly scan through high dimensional data consisting of several versions of a dataset migrated with a range of velocities to overcome the strong effect of incorrect migration velocity on the diffraction signal.     

海底地震仪的信号传递效果和噪声水平

单球式海底地震仪（以下简称OBS）由于其成本低、操作简便的优点在天然地震研究、人工地震探测中获得了广泛应用.本文首先分析多型进口和国产OBS在台湾海峡西部采集的地震数据,发现同一台OBS上的垂直向速度检波器（Z分量）的信噪比常显著低于压力检波器（H分量）,由于这两种检波器记录的都是海底的垂向振动信号,推测速度检波器的低信噪比更多的与仪器特性有关.然后从信号传递和噪声水平两方面分析影响速度检波器信噪比的因素：为检测速度检波器与OBS壳体的耦合效果,对某型宽频带OBS和陆上地震仪进行了同址同步观测试验,发现OBS的整机灵敏度有较大的差异;为分析速度检波器的水底噪声特征,以H分量记录作为基准,对比分析了同一台仪器不同站位的Z分量噪声水平,发现速度检波器在浅海区受到较大的次生干扰.本文指出OBS的内部耦合和水流次生干扰是至今尚未引起大家重视而又严重影响资料品质和多波探测成效的两个关键问题,这一研究结果对于改进OBS结构设计和制造工艺,以及OBS数据多分量处理方法研究有重要的参考意义.     

沙漠地区地震勘探随机噪声建模及其在噪声压制中的应用

随机噪声是影响地震勘探有效信号的主要因素,其存在大大降低了地震记录的信噪比.在噪声压制方法不断被改进的同时,对随机噪声特性进行研究,了解噪声的产生机制是对其进行压制的先决条件,目前对噪声的研究主要是特性研究以寻找规律性,对其进行定性定量的分析还比较少.本文根据塔里木沙漠地区实际采集环境,考虑到噪声的连续性给计算带来的不便,假设各类噪声源以点源的形式分布在检波器周围,依据相应理论确定各类噪声源的源函数,其激发的噪声经由波动方程传播,将随机噪声作为各类噪声源共同作用的综合波场,建立随机噪声的理论模型.通过分析不同种噪声对地震记录的影响,选取合适的滤波方法对其进行压制,实验结果表明,通过建立沙漠地区随机噪声的理论模型,为选择有效的滤波方法,提高地震记录信噪比起到理论指导作用.     

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.