基于非平稳相似性系数的构造导向滤波及断层检测方法

不连续地质体（如断层）的自动检测一直以来都是叠后地震数据解释中的关键问题之一,尤其在三维情况中尤为重要.然而,大多数边缘检测和相干算法都对随机噪声很敏感,随机噪声衰减是叠后地震数据解释的另一个主要问题.针对构造保护去噪和断层检测问题,本文基于非平稳相似性系数完善一种构造导向滤波方法并且提出一种自动断层检测方法,形成了一套匹配的处理技术.该构造导向滤波既能够有效地衰减随机噪声又可以很好地保护地震资料中的断层等信息不被破坏,增强地震剖面中弯曲、倾斜同相轴的连续性.根据地震数据局部倾角走向,利用相邻道构建当前地震道的预测,通过预测道的叠加得到参考道,计算预测道与参考道之间的非平稳相似性系数可以设计出数据驱动的加权中值滤波.另一方面,预测道与原始道之间的非平稳相似性系数能够用于带有断层指示性的相干分析.这两种方法都基于构造预测和非平稳相似性系数,但是使用不同的调节参数和处理方案.理论模型和实际数据的处理结果证明了本文提出构造导向滤波和断层检测方法的有效性.     

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.     

局部相关加权中值滤波技术及其在叠后随机噪声衰减中的应用

随机噪声的衰减和同相轴连续性的提高可以极大地改善地震资料解释的精度.本文提出一种新的滤波技术,既能够有效地衰减随机噪声又可以很好地保护地震资料中的断层等信息不被破坏,增强地震剖面中弯曲、倾斜同相轴的连续性.该方法结合新的加权中值滤波技术和两种构造信息保护滤波策略,实现基于预测数据体和基于倾角走向的加权中值滤波.通过设计...     

HORIZONTAL STACKING AND MULTICHANNEL FILTERING APPLIED TO COMMON DEPTH POINT SEISMIC DATA*

The common depth point method of shooting in oil exploration provides a series of seismic traces which yield information about the substrata layers at one location. After normal moveout and static corrections have been applied, the traces are combined by horizontal stacking, or linear multichannel filtering, into a single record in which the primary reflections have been enhanced relative to the multiple reflections and random noise. The criterion used in optimum horizontal stacking is to maximize the signal to noise power ratio, where signal refers to the primary reflection sequence and noise includes the multiple reflections. It is shown when this criterion is equivalent to minimizing the mean square difference between the desired signal (primary reflection sequence) and the weighted horizontally stacked traces. If the seismic traces are combined by multichannel linear filtering, the primary reflection sequence will have undergone some phase and frequency distortion on the resulting record. The signal to noise power ratio then becomes less meaningful a criterion for designing the optimum linear multichannel filter, and the mean square criterion is adopted. In general, however, since more a priori information about the seismic traces is required to design the optimum linear multichannel filter than required for the optimum set of weights of the horizontal stacking process, the former will be an improvement over the latter. It becomes evident that optimum horizontal stacking is a restricted form of linear multichannel filtering.     

HORIZONTAL STACKING AND MULTICHANNEL FILTERING APPLIED TO COMMON DEPTH POINT SEISMIC DATA*

The common depth point method of shooting in oil exploration provides a series of seismic traces which yield information about the substrata layers at one location. After normal moveout and static corrections have been applied, the traces are combined by horizontal stacking, or linear multichannel filtering, into a single record in which the primary reflections have been enhanced relative to the multiple reflections and random noise. The criterion used in optimum horizontal stacking is to maximize the signal to noise power ratio, where signal refers to the primary reflection sequence and noise includes the multiple reflections. It is shown when this criterion is equivalent to minimizing the mean square difference between the desired signal (primary reflection sequence) and the weighted horizontally stacked traces. If the seismic traces are combined by multichannel linear filtering, the primary reflection sequence will have undergone some phase and frequency distortion on the resulting record. The signal to noise power ratio then becomes less meaningful a criterion for designing the optimum linear multichannel filter, and the mean square criterion is adopted. In general, however, since more a priori information about the seismic traces is required to design the optimum linear multichannel filter than required for the optimum set of weights of the horizontal stacking process, the former will be an improvement over the latter. It becomes evident that optimum horizontal stacking is a restricted form of linear multichannel filtering.     

Seismic directional random noise suppression by radial‐trace time–frequency peak filtering using the Hurst exponent statistic

Radial‐trace time–frequency peak filtering filters a seismic record along the radial‐trace direction rather than the conventional channel direction. It takes the spatial correlation of the reflected events between adjacent channels into account. Thus, radial‐trace time–frequency peak filtering performs well in denoising and enhancing the continuity of reflected events. However, in the seismic record there is often random noise whose energy is concentrated in certain directions; the noise in these directions is correlative. We refer to this kind of random noise (that is distributed randomly in time but correlative in the space) as directional random noise. Under radial‐trace time–frequency peak filtering, the directional random noise will be treated as signal and enhanced when this noise has same direction as the signal. Therefore, we need to identify the directional random noise before the filtering. In this paper, we test the linearity of signal and directional random noise in time using the Hurst exponent. The time series of signals with high linearity lead to large Hurst exponent value; however, directional random noise is a random series in time without a fixed waveform and thus its linearity is low; therefore, we can differentiate the signal and directional random noise by the Hurst exponent values. The directional random noise can then be suppressed by using a long filtering window length during the radial‐trace time–frequency peak filtering. Synthetic and real data examples show that the proposed method can remove most directional random noise and can effectively recover the reflected events.     

Dip‐adaptive singular‐value decomposition filtering for seismic reflection enhancement

We present a singular value decomposition (SVD) filtering method for the enhancement of coherent reflections and for attenuation of noise. The method is applied in two steps. First normal move‐out (NMO) correction is applied to shot or CMP records, with the purpose of flattening the reflections. We use a spatial SVD filter with a short sliding window to enhance coherent horizontal events. Then the data are sorted in common‐offset panels and the local dip is estimated for each panel. The next SVD filtering is performed on a small number of traces and a small number of time samples centred around the output sample position. Data in a local window are corrected for linear moveout corresponding to the dips before SVD. At the central time sample position, we sum over the dominant eigenimages of a few traces, corresponding to SVD dip filtering. We illustrate the method using land seismic data from the Tacutu basin, located in the north‐east of Brazil. The results show that the proposed method is effective and is able to reveal reflections masked by ground‐roll and other types of noise.     

Random noise attenuation using a structure-oriented weighted singular value decomposition

Singular value decomposition (SVD) is a useful method for random noise suppression in seismic data processing. A structure-oriented SVD (SOSVD) approach which incorporates structure prediction to the SVD filter is effcient in attenuating noise except distorting seismic events at faults and crossing points. A modified SOSVD approach using a weighted stack, called structure-oriented weighted SVD (SOWSVD), is proposed. In this approach, the SVD filter is used to attenuate noise for prediction traces of a primitive trace which are produced via the plane-wave prediction. A weighting function related to local similarity and distance between each prediction trace and the primitive trace is applied to the denoised prediction traces stacking. Both synthetic and field data examples suggest the SOWSVD performs better than the SOSVD in both suppressing random noise and preserving the information of the discontinuities for seismic data with crossing events and faults.

     

Simulations of non‐stationary frequency content and its importance to seismic assessment of structures

To verify the importance of the non‐stationary frequency characteristic of seismic ground motion, a joint time–frequency analysis technique of time signals, called chirplet‐based signal approximation, is developed to extract the non‐stationary frequency information from the recorded data. The chirplet‐based signal approximation is clear in concept, similar to Fourier Transform in mathematical expressions but with different base functions. Case studies show that the chirplet‐based signal approximation can represent the joint time–frequency variation of seismic ground motion quite well. Both the random models of uniform modulating process and evolutionary process are employed to generate artificial seismic waves. The joint time–frequency modulating function in the random model of evolutionary process is determined by chirplet‐based signal approximation. Finally, non‐linear response analysis of a SODF system and a frame structure is performed based on the generated artificial seismic waves. The results show that the non‐stationary frequency characteristic of seismic ground motion can significantly change the non‐linear response characteristics of structures, particularly when a structure goes into collapse phase under seismic action. It is concluded that non‐stationary frequency characteristic of seismic ground motion should be considered for the assessment of seismic capacity of structures. Copyright © 2002 John Wiley & Sons, Ltd.     

Application of wavelet theory to identify yielding in seismic response of bi‐linear structures

The time–frequency and the time‐scale analysis methods are used in this paper to identify the dynamic characteristics of non‐linear seismic response of structural systems with single degree of freedom (SDOF) and multiple degrees of freedom (MDOF). Based on the floor acceleration response time histories of bi‐linear SDOF and MDOF structures, the current study compares the results of system identification using the short‐time Fourier transform (STFT), continuous wavelet transform (CWT) and discrete wavelet transform (DWT) methods. The aim is to identify the frequency variations and the time at on‐set of yielding and unloading of a bi‐linear structural system during seismic response. The results demonstrate that the CWT method is better than the STFT method in both time and frequency resolutions, and that the DWT method is the best at detecting the time at on‐set of yielding and unloading. Combining the results of CWT and DWT methods therefore provides accurate information of both frequency variations and yielding time in non‐linear seismic response. To alleviate the problems associated with noise‐contaminated signals, e.g. seismic response data recorded on site, the study suggests that low‐pass filtering be carried out before applying the DWT method to decompose the signals into multiple levels of details. Copyright © 2001 John Wiley & Sons, Ltd.     

Suppression of near‐surface scattered body‐to‐surface waves: a steerable and nonlinear filtering approach

We present an approach based on local‐slope estimation for the separation of scattered surface waves from reflected body waves. The direct and scattered surface waves contain a significant amount of seismic energy. They present great challenges in land seismic data acquisition and processing, particularly in arid regions with complex near‐surface heterogeneities (e.g., dry river beds, wadis/large escarpments, and karst features). The near‐surface scattered body‐to‐surface waves, which have comparable amplitudes to reflections, can mask the seismic reflections. These difficulties, added to large amplitude direct and back‐scattered surface (Rayleigh) waves, create a major reduction in signal‐to‐noise ratio and degrade the final sub‐surface image quality. Removal of these waves can be difficult using conventional filtering methods, such as an filter, without distorting the reflected signal. The filtering algorithm we present is based on predicting the spatially varying slope of the noise, using steerable filters, and separating the signal and noise components by applying a directional nonlinear filter oriented toward the noise direction to predict the noise and then subtract it from the data. The slope estimation step using steerable filters is very efficient. It requires only a linear combination of a set of basis filters at fixed orientation to synthesize an image filtered at an arbitrary orientation. We apply our filtering approach to simulated data as well as to seismic data recorded in the field to suppress the scattered surface waves from reflected body waves, and we demonstrate its superiority over conventional techniques in signal preservation and noise suppression.     

压制空间非平稳地震勘探随机噪声的ROAD径向时频峰值滤波算法

径向时频峰值滤波算法是一种有效保持低信噪比地震勘探记录中反射同相轴的随机噪声压制方法,但该算法对空间非平稳地震勘探随机噪声压制效果不理想.本文研究空间非平稳地震勘探随机噪声,即各道噪声功率不同的地震勘探随机噪声,其在径向滤波轨线上表征近似脉冲噪声,在径向时频峰值滤波过程中干扰相邻道滤波结果.为了减小空间非平稳随机噪声的影响,本文提出一种基于绝对级差统计量(ROAD)的径向时频峰值滤波随机噪声压制方法.该方法首先根据径向轨线上信号的绝对级差统计量检测空间非平稳地震勘探随机噪声,然后结合局部时频峰值滤波和径向时频峰值滤波压制地震勘探记录中的随机噪声.将ROAD径向时频峰值滤波方法应用于合成记录和实际共炮点地震记录,结果表明ROAD径向时频峰值滤波方法可以压制空间非平稳地震勘探随机噪声且不损害有效信号,有效抑制随机噪声空间非平稳对滤波结果的影响.与径向时频峰值滤波相比,ROAD径向时频峰值滤波方法更适用于空间非平稳地震勘探随机噪声压制.     

Incorporation of a Non-linear Image Filtering Technique for Noise Reduction in Seismic Data

Seismic noise is a fundamental part of seismic data which cannot be avoided when conducting any seismic survey. It consists of coherent and random noise. Noise removal or filtering is one of the major concerns in the field of seismic processing. In this paper, we introduce an image filtering technique based on a detection-estimation algorithm for Gaussian and random noise removal in seismic data, namely the trilateral filter, based on a statistic called rank-ordered absolute differences. The non-linear and adaptive behaviour of this filter makes it very robust in the presence of random and coherent noise, in addition to its computational simplicity and its ability to automatically identify noise in data. We have modified the strategy of trilateral filtering by adapting the rank-ordered absolute differences formula in order to extract the signal component. We have successfully used this filter for the removal of surface waves and random spiky noise from synthetic and field data. Results are very encouraging and show the superiority of this filter compared with other filters, particularly when used recursively.     

Erratic noise suppression using iterative structure‐oriented space‐varying median filtering with sparsity constraint

Erratic noise often has high amplitudes and a non‐Gaussian distribution. Least‐squares–based approaches therefore are not optimal. This can be handled better with non–least‐squares approaches, for example based on Huber norm which is computationally expensive. An alternative method has been published which involves transforming the data with erratic noise to pseudodata that have Gaussian distributed noise. It can then be attenuated using traditional least‐squares approaches. This alternative method has previously been used in combination with a curvelet transform in an iterative scheme. In this paper, we introduce a median‐filtering step in this iterative scheme. The median filter is applied following the slope direction of the seismic data to maximally preserve the energy of useful signals. The new method can suppress stronger erratic noise compared with the previous iterative method, and can better deal with random noise compared with the single‐step implementation of the median filter. We apply the proposed robust denoising algorithm to a synthetic dataset and two field data examples and demonstrate its advantages over three different noise attenuation algorithms.     

Non‐parametric–parametric model for random uncertainties in non‐linear structural dynamics: application to earthquake engineering

This paper deals with the transient response of a non‐linear dynamical system with random uncertainties. The non‐parametric probabilistic model of random uncertainties recently published and extended to non‐linear dynamical system analysis is used in order to model random uncertainties related to the linear part of the finite element model. The non‐linearities are due to restoring forces whose parameters are uncertain and are modeled by the parametric approach. Jayne's maximum entropy principle with the constraints defined by the available information allows the probabilistic model of such random variables to be constructed. Therefore, a non‐parametric–parametric formulation is developed in order to model all the sources of uncertainties in such a non‐linear dynamical system. Finally, a numerical application for earthquake engineering analysis is proposed concerning a reactor cooling system under seismic loads. Copyright © 2003 John Wiley & Sons, Ltd.     

Time‐frequency seismic data de‐noising

Marine seismic data are always affected by noise. An effective method to handle a broad range of noise problems is a time‐frequency de‐noising algorithm. In this paper we explain details regarding the implementation of such a method. Special emphasis is given to the choice of threshold values, where several different strategies are investigated. In addition we present a number of processing results where time‐frequency de‐noising has been successfully applied to attenuate noise resulting from swell, cavitation, strumming and seismic interference. Our seismic interference noise removal approach applies time‐frequency de‐noising on slowness gathers (τ?p domain). This processing trick represents a novel approach, which efficiently handles certain types of seismic interference noise that otherwise are difficult to attenuate. We show that time‐frequency de‐noising is an effective, amplitude preserving and robust tool that gives superior results compared to many other conventional de‐noising algorithms (for example frequency filtering, τ?p or fx‐prediction). As a background, some of the physical mechanisms responsible for the different types of noise are also explained. Such physical understanding is important because it can provide guidelines for future survey planning and for the actual processing.     

Spatially constrained attenuation compensation in the mixed domain

Seismic attenuation compensation is a spectrum-broadening technique for enhancing the resolution of non-stationary seismic data. The single-trace attenuation compensation algorithms ignore the prior information that the seismic reflection events are generally continuous along seismic traces, thus, the compensated result may have poor spatial continuity and low signal-to-noise ratio. To address this problem, we extend the single-trace approaches to the multi-trace algorithms and furthermore propose a multi-trace attenuation compensation with a spatial constraint. The frequency-space prediction filters are the key to construct this spatial regularization. We test the effectiveness of the proposed spatially constrained attenuation compensation algorithm by applying both synthetic and field data examples. Synthetic data tests indicate that the proposed multi-trace attenuation compensation approach can provide a better compensated result than single-trace attenuation compensation algorithm in terms of suppressing noise amplification and guaranteeing structural continuities. Field data applications further confirm its stability and practicality to improve seismic resolution.     

Inversion-based data-driven time-space domain random noise attenuation method

Conventional time-space domain and frequency-space domain prediction filtering methods assume that seismic data consists of two parts, signal and random noise. That is, the so-called additive noise model. However, when estimating random noise, it is assumed that random noise can be predicted from the seismic data by convolving with a prediction error filter. That is, the source-noise model. Model inconsistencies, before and after denoising, compromise the noise attenuation and signal-preservation performances of prediction filtering methods. Therefore, this study presents an inversion-based time-space domain random noise attenuation method to overcome the model inconsistencies. In this method, a prediction error filter (PEF), is first estimated from seismic data; the filter characterizes the predictability of the seismic data and adaptively describes the seismic data’s space structure. After calculating PEF, it can be applied as a regularized constraint in the inversion process for seismic signal from noisy data. Unlike conventional random noise attenuation methods, the proposed method solves a seismic data inversion problem using regularization constraint; this overcomes the model inconsistency of the prediction filtering method. The proposed method was tested on both synthetic and real seismic data, and results from the prediction filtering method and the proposed method are compared. The testing demonstrated that the proposed method suppresses noise effectively and provides better signal-preservation performance.     

EFFICIENT MULTICHANNEL FILTERING OF SEISMIC DATA1

Multichannel filters are used to eliminate coherent noise from surface seismic data, for wavefield separation from VSP stacks, and for signal enhancement. Their success generally depends on the choice of the filter parameters and the domain of application. Multichannel filters can be applied to shots (monitors), common-receiver traces, CDP traces and stacked sections. Cascaded applications in these domains are currently performed in the seismic industry for better noise suppression and for signal enhancement. One-step shot-domain filtering is adequate for some applications. However, in practice, cascaded applications in shot-and common-receiver domains usually give better results when the S/N ratio is low. Multichannel filtering after stacking (especially after repeated applications in shot and/or receiver domains) may create undesirable results such as artificial continuations, or smearing and smoothing of small features such as small throw faults and fine stratigraphic details. Consequently, multichannel filtering after stacking must be undertaken with the utmost care and occasionally only as a last resort. Multichannel filters with fan-shaped responses (linear moveout filters) should be applied after NMO correction. These are the filters commonly used in the seismic industry where they have such names as velocity filters, moveout filters, f-k filters and coherency filters. Filtering before NMO correction may result in break-up and flattening especially of those shallow reflection events with relatively higher curvatures and diffractions. NMO correction is needed prior to wavefield separation from VSP stacks for the same practical reasons outlined above whenever source-receiver offsets are involved. Creation of artificial lineup and smearing at the outputs of multichannel filters is presently the common practical concern. Optimum multichannel filters with well-defined pass, reject and transition bands overcome the latter problems when applied before stacking and after NMO correction. The trace dimension of these filters must be kept small to avoid such lineups and the smoothing of small structures. Good results can be obtained with only five traces, but seven traces seems to be a better compromise both in surface and well seismic applications. The so-called f-k filtering and τ-p domain filtering are no exceptions to the above practical considerations. Residual static computations after multichannel filtering also need special consideration. Since multichannel filtering improves spatial continuity, residual static algorithms using local correlation, i.e. nonsurface-consistent algorithms, may be impractical especially after multichannel filtering.     

Performance‐based design using structural optimization

A new methodology for seismic design is proposed based on structural optimization with performance‐based constraints. Performance‐based criteria are introduced for the seismic design of new buildings. These criteria are derived from the National Guidelines for Seismic Rehabilitation of Buildings (Reference [19], Federal Emergency Management Agency (FEMA), ‘NHERP Guidelines for seismic rehabilitation of buildings’, Report Nos 273 and 274, Washington, DC, 1997) for retrofitting existing structures. The proposed design methodology takes into account the non‐linear behaviour of the structure. The goal is to incorporate in the design the actual performance levels of the structure, i.e. how much reserve capacity the structure has in an earthquake of a given magnitude. The optimal design of the structure minimizes the structural cost subjected to performance constraints on plastic rotations of beams and columns, as well as behavioural constraints for reinforced concrete frames. Uncertainties in the structural period and in the earthquake excitation are taken into account using convex models. The optimization routine incorporates a non‐linear analysis program and the procedure is automated. The proposed methodology leads to a structural design for which the levels of reliability (performance levels) are assumed to be quantifiable. Furthermore, the entire behaviour of the structure well into the non‐linear range is investigated in the design process. Copyright © 2000 John Wiley & Sons, Ltd.