IMPULSE RESPONSE MODELS FOR NOISY VIBROSEIS† DATA*

A new method of Vibroseis deconvolution has been recently proposed by the authors. This discussion describes the effects of noise on the application of this method. The initial deconvolution step involves estimating the spectrum of the Vibroseis wavelet by homomorphic filtering. It is shown that noise causes problems with phase estimation. Hence, the Vibroseis wavelet is assumed to be zero phase. Examples demonstrate that zero phase cepstral filtering is a robust wavelet estimation approach for noisy data. The second step of the deconvolution method forms an impulse response model by a spectral extension method. Although this step can improve the resolution of seismic arrivals, it must be applied with caution in view of the deleterious effects of noise.     

THE PHASE PROPERTY OF A FINITE REALIZATION OF RANDOM NOISE AND ITS INFLUENCE ON DECONVOLUTION *

A finite realization of a discrete random noise process may be considered as a one-sided energy signal. Its phase property can then be described by means of the center position. The samples of such a realization are the components of a random signal vector and the center position is therefore a random variable. A statistical analysis shows that the expected value of the center position equals half the time duration of the realization. This implies that the Z-transform of the realization may be expected to have an equal number of poles and zeros inside and outside the unit circle. The standard deviation from the expected value of the center position is shown to depend on the time duration of the realization and on the autocorrelation of the process. It follows that, for processes that can be described by the convolution of a white series and a disturbance wavelet, the center position is independent of the phase property of the wavelet. A conclusion based on these results is that the homomorphic technique of wavelet estimation through cepstrum stacking must give questionable outcomes. Another conclusion is that the super-position of a realization of random noise on a minimum phase wavelet will in general give a mixed phase resulting signal. It is pointed out that schemes for the derivation of deconvolution filters do not take account of this phenomenon.     

Multiple suppression by 2D filtering in the parabolic τ–p domain: a wave-equation-based method1

The filter for wave-equation-based water-layer multiple suppression, developed by the authors in the x-t, the linear τ-p, and the f-k domains, is extended to the parabolic τ-2 domain. The multiple reject areas are determined automatically by comparing the energy on traces of the multiple model (which are generated by a wave-extrapolation method from the original data) and the original input data (multiples + primaries) in τ-p space. The advantage of applying the data-adaptive 2D demultiple filter in the parabolic τ-p domain is that the waves are well separated in this domain. The numerical examples demonstrate the effectiveness of such a dereverberation procedure. Filtering of multiples in the parabolic τ-p domain works on both the far-offset and the near-offset traces, while the filtering of multiples in the f-k domain is effective only for the far-offset traces. Tests on a synthetic common-shot-point (CSP) gather show that the demultiple filter is relatively immune to slight errors in the water velocity and water depth which cause arrival time errors of the multiples in the multiple model traces of less than the time dimension (about one quarter of the wavelet length) of the energy summation window of the filter. The multiples in the predicted multiple model traces do not have to be exact replicas of the multiples in the input data, in both a wavelet-shape and traveltime sense. The demultiple filter also works reasonably well for input data contaminated by up to 25% of random noise. A shallow water CSP seismic gather, acquired on the North West Shelf of Australia, demonstrates the effectiveness of the technique on real data.     

基于小波包和峰度赤池信息量准则的P波震相自动识别方法

基于小波包变换和峰度赤池信息量准则(AIC), 提出了一种新的自动识别P波震相的综合方法, 即小波包-峰度AIC方法． 首先对由加权长短时窗平均比(STA/LTA)法粗略确定的P波到时前后3 s的记录进行小波包三尺度的分解与重构, 分别计算每个尺度重构信号的峰度AIC曲线并将其叠加, 叠加曲线的最小值则为P波震相到时; 然后对原始地震记录进行有限冲激响应自适应滤波以提高信噪比和识别精度; 最后将小波包-峰度AIC方法应用到合成理论地震图及实际地震记录的P波初至自动识别中. 结果表明: 初至清晰度对识别精度的影响比信噪比对其影响更大; 与单独使用加权STA/LTA方法和峰度AIC法相比, 小波包-峰度AIC法具有更强的抗噪能力, 识别精度更高; 当初至清晰时, 小波包-峰度AIC法自动识别与人工识别的P波到时平均绝对差值为(0.077±0.075) s．      

Stratigraphic filtering of SH waves in a spherical,layered earth

We present a derivation of the formula for filtering a transmitted SH wavelet by shortperiod multiples in a spherically layered Earth. We use a continuous, rather than a discrete formulation and regard the impedance and the velocity as random variables. The mean shear displacement represents the propagating wavelet as modified by short-period multiples. Standard procedures and approximations Lead to the dispersion relation of the mean displacement. To describe the stratigraphic filtering we introduce a complex quantityF such that a wavelet which has travelled a time T is modified by the filter exp {iFT}. The impact of the higher angular harmonic modes is shown to produce a relative enhancement of those modes over the low angular harmonic modes due to fluctuations in the shear-wave propagation velocity. Numerical estimates indicate that the sizes of the apparent attenuation of the mean field and the time delay introduced by the short-period multiples sit squarely in the regime where they produce a nonnegligible distortion of the SH modes of propagation in both phase and amplitude.     

Using wavelet‐domain adaptive filtering to improve signal‐to‐noise ratio of nuclear magnetic resonance log data from tight gas sands

In tight gas sands, the signal‐to‐noise ratio of nuclear magnetic resonance log data is usually low, which limits the application of nuclear magnetic resonance logs in this type of reservoir. This project uses the method of wavelet‐domain adaptive filtering to denoise the nuclear magnetic resonance log data from tight gas sands. The principles of the maximum correlation coefficient and the minimum root mean square error are used to decide on the optimal basis function for wavelet transformation. The feasibility and the effectiveness of this method are verified by analysing the numerical simulation results and core experimental data. Compared with the wavelet thresholding denoise method, this adaptive filtering method is more effective in noise filtering, which can improve the signal‐to‐noise ratio of nuclear magnetic resonance data and the inversion precision of transverse relaxation time T₂ spectrum. The application of this method to nuclear magnetic resonance logs shows that this method not only can improve the accuracy of nuclear magnetic resonance porosity but also can enhance the recognition ability of tight gas sands in nuclear magnetic resonance logs.     

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

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

逆子波域消除多次波方法研究

SRMA（与表面相关多次波的衰减）算法包含预测和相减两步.相减算法中,当多次波与反射波同相轴相交时,如何有效减去多次波、保留反射波,是面临的主要问题.通过分析非正交性对滤波器（逆子波）的影响,可以证明：逆子波因非正交性产生的误差呈近似的高斯分布.在此基础上,本文提出了在逆子波域（单道自适应相减滤波的滤波算子的集合）,利用其误差的概率分布特征,对逆子波进行估计,用逆子波的估计对逆子波进行校正来消除多次波的方法.其步骤为：首先用SRMA方法预测出表面多次波,并对每一单炮进行单道自适应相减,得到逆子波,形成逆子波域;其次,在逆子波域采用中值滤波,提取接近真实逆子波的逆子波估计;第三,在逆子波域用逆子波估计对畸变的逆子波进行校正;最后采用校正后的逆子波来衰减多次波.通过简单模型和SMARRT模型的测试,该方法不仅能够有效减去多次波,而且在相交的区域,能够保持反射波同相轴的连续性并恢复其正确的振幅.     

利用基于子波估计的频谱校正方法提高Q值估计精度(英文)

用Q值刻画的地震衰减在地震信号处理和解释中具有很广泛的应用。利用反射地震资料进行Q值估计需要解决地震子波和反射系数序列耦合的问题。从反射地震资料中去除反射系数序列的影响,这个过程称为频谱校正。本文提出了一种基于子波估计的求取Q值的方法,进而设计了一个反Q滤波器。该方法利用反射地震资料的高阶统计量进行子波估计,并利用所估计子波实现频谱校正。我们利用合成数据实验给出了质心频移法与频谱比法这两种常用的Q值估计方法在不同参数设置下的性能。人工合成数据和实际数据处理表明,利用本文提出的方法进行频谱校正后,可以得到可靠的Q值估计。经过反Q滤波,地震数据的高频部分得到了有效地恢复。     

A COMPARISON BETWEEN WIENER FILTERING,KALMAN FILTERING,AND DETERMINISTIC LEAST SQUARES ESTIMATION*

The least squares estimation procedures used in different disciplines can be classified in four categories:

• a. Wiener filtering,
• b. b. Autoregressive estimation,
• c. c. Kalman filtering,
• d. d. Recursive least squares estimation.

The recursive least squares estimator is the time average form of the Kalman filter. Likewise, the autoregressive estimator is the time average form of the Wiener filter. Both the Kalman and the Wiener filters use ensemble averages and can basically be constructed without having a particular measurement realisation available. It follows that seismic deconvolution should be based either on autoregression theory or on recursive least squares estimation theory rather than on the normally used Wiener or Kalman theory. A consequence of this change is the need to apply significance tests on the filter coefficients. The recursive least squares estimation theory is particularly suitable for solving the time variant deconvolution problem.     

A first arrival detection method for low SNR microseismic signal

Most of the microseismic signals have low signal-to-noise ratio (SNR) due to the strong background noise, which makes it difficult to locate the first arrival time. Both accuracy and stability of conventional methods are poor in this situation. To overcome this problem, here we proposed a new method based on the adaptive Morlet wavelet and principal component analysis process in wavelet coefficients matrix. The three components of microseismic signal make it possible to extract the features in wavelet coefficients domain. Then the reconstructed signal from weighted features presents an obvious first arrival. Tests on synthetic signals and real data provide a solid evidence for its feasibility in low SNR microseismic signal.     

Deep learning for P-wave arrival picking in earthquake early warning

Fast and accurate P-wave arrival picking significantly affects the performance of earthquake early warning(EEW)systems.Automated P-wave picking algorithms used in EEW have encountered problems of falsely picking up noise,missing P-waves and inaccurate P-wave arrival estimation.To address these issues,an automatic algorithm based on the convolution neural network(DPick)was developed,and trained with a moderate number of data sets of 17,717 accelerograms.Compared to the widely used approach of the short-term average/long-term average of signal characteristic function(STA/LTA),DPick is 1.6 times less likely to detect noise as a P-wave,and 76 times less likely to miss P-waves.In terms of estimating P-wave arrival time,when the detection task is completed within 1 s,DPick′s detection occurrence is 7.4 times that of STA/LTA in the 0.05 s error band,and 1.6 times when the error band is 0.10 s.This verified that the proposed method has the potential for wide applications in EEW.     

Ricker子波视主频的变化对混沌振子检测效果的影响

针对地震勘探资料中存在加性强随机噪声干扰,已经提出用混沌振子系统处理的方法技术.为完善该方法,需要研究诸如地震勘探同相轴完整程度、组成同相轴的地震子波变化等对系统检测效果的影响.本文以Ricker子波模拟地震子波,研究Ricker子波视主频变化的相应检测效果.研究结果：随着Ricker子波视主频的升高,检测SNR逐渐变差,在高频部分SNR的变化明显比低频部分缓慢;在通常地震勘探频率范围内,混沌振子系统检测SNR有可能部分补偿由于地震波传播引起的幅度降低;为检测由畸变子波构成的同相轴提供一定的可能.     

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

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

基于重构激发信号的电磁式可控震源相关检测参考信号方法研究

针对电磁式可控震源地震数据的相关检测,研究发现,在地下结构复杂、基板-大地耦合不佳时,常规方法——基于震源控制信号或基板附近信号作为参考信号检测得到的地震记录中,存在子波到时误差和虚假多次波问题.本文分析了上述问题的理论原因,并提出基于重构激发信号的相关检测参考信号方法(Correlation Detection Reference Signal Based on the Reconstructed Excitation Signal,CDRSBRES).首先,利用直达波与其他地震波到时不一致的特点,从震源基板附近信号中分离、提取直达波.然后,利用直达波重构震源激发信号并作为参考信号对地震数据进行相关检测.最后,应用谱白化技术提高检测结果质量.数值模拟研究表明,重构激发信号与理想激发信号的相关系数为0.9869,达到高度线性相关,CDRSBRES方法检测的地震记录在子波到时和波形特征上均与模型相符.随后,在某金属矿区开展了可控震源对比实验.与液压式可控震源MiniVib T15000检测结果相比,电磁式可控震源PHVS 500的检测结果中:基于震源控制信号的检测结果存在子波到时误差约0.012s,对应垂向精度误差约11.16m;基于基板附近信号的检测结果部分区域出现虚假多次波,信噪比降低;而CDRSBRES方法的检测结果子波到时误差约0.001s,对应垂向精度误差约0.93m,波形特征一致,相同区域无虚假多次波.综上,本方法适用于电磁式可控震源地震数据的高精度检测,尤其对于地下结构复杂区域的高分辨率地震勘探具有重要意义.     

ON ERRORS OF FIT AND ACCURACY IN MATCHING SYNTHETIC SEISMOGRAMS AND SEISMIC TRACES*

A synthetic seismogram that closely resembles a seismic trace recorded at a well may not be at all reliable for, say, stratigraphic interpretation around the well. The most accurate synthetic seismogram is, in general, not the one that displays the smallest errors of fit to the trace but the one that best estimates the noise on the trace. If the match is confined to a short interval of interest or if the seismic reflection wavelet is allowed to be unduly long, there is considerable danger of forcing a spurious fit that treats the noise on the trace as part of the seismic reflection signal instead of making a genuine match with the signal itself. This paper outlines tests that allow an objective and quantitative evaluation of the accuracy of any match and illustrates their application with practical examples. The accuracy of estimation is summarized by the normalized mean square error (NMSE) in the estimated reflection signal, which is shown to be (/n)(P_N/P_S) where P_S/P_N is the signal-to-noise power ratio and n is the spectral smoothing factor. That is, the accuracy varies directly with the ratio of the power in the signal (taken to be the synthetic) to that in the noise on the seismic trace, and the smoothing acts to improve the accuracy of the predicted signal. The construction of confidence intervals for the NMSE is discussed. Guidelines for the choice of the spectral smoothing factor n are given. The variation of wavelet shape due to different realizations of the noise component is illustrated, and the use of confidence intervals on wavelet phase is recommended. Tests are described for examining the normality and stationarity of the errors of fit and their independence of the estimated reflection signal.     

COHERENCY WEIGHTING—AN EFFECTIVE APPROACH TO THE SUPPRESSION OF LONG LEG MULTIPLES*

Long leg multiples can be suppressed by a method which provides an alternative to weighted common-depth-point stacking and multichannel stacking filtering. The suppression is achieved by coherency weighting whereby the time-dependent weighting factor decreases as the semblance of the multiple reflections increases. The algorithm of the method is described. Its efficiency is discussed in relation to the input data and results of its application to marine seismic data are presented. For practical application, the stacking velocity of the multiples has to be known. As the process is based on stacking velocities, different types of multiples can be handled, for instance water-bottom multiples or internal multiples. The parameter analysis shows that the degree of multiple suppression can easily be controlled by adapting the parameters of the procedure to the field conditions. During the suppression of multiples, the primaries are saved according to the moveout differences between the two. The non-linear behaviour of the process causes signal suppression and distortion effects, which have to be corrected by AGC normalization and low-pass filtering. Among the various applications available, only the suppression of long leg water-bottom multiples is treated here. The results show that their suppression on the basis of moveout differences is efficient even when standard length streamers are used in regions with water depth of up to 1500 m and more, if the stacking velocity of the primaries is about 10 to 20% higher than that of the multiples. Even if those parts of the primaries which are masked by the multiples are suppressed in the individual common-depth-point gathers by the procedure, the remaining primaries in the AGV stacked section are largely uncovered by the multiple suppression.     

PSEUDO-DIAGRAPHIES DE VITESSE EN OFFSHORE PROFOND*

Pseudo-velocity-logs are tentative determinations of subsurface velocity variations with depth, using both information of seismic amplitude and reflection curvature. A rigorous theoretical method would consist in

• a) deconvolving the seismic traces to remove the filtering effects of the ground and of the recording equipment
• b) demultiplying the deconvolved traces by a complete desynthesization with convergence criteria
• c) computing the velocities.

While this method works with synthetic examples, it is not generally applicable to field cases, one of the reasons being the poor reliability of desynthesization in the presence of noise. The present method is a compromise between a rigorous and a practical process: the complete desynthesization is not performed; deconvolution and demultiplication are done by more classical techniques using real amplitudes; absolute velocities are determined to fit both the reflection coefficients and the rms velocities. It leads to pseudovelocity-logs, accurate enough to show lithologic variations, smoothed enough to preserve the signal/noise ratio. Examples are shown of Flexichoc profiles recorded in 2500 m (8000–9000 feet) deep areas of the Mediterranean Sea. Pseudo-velocity-logs show 1000 m (3000 feet) of a velocity-increasing-with-depth Plio-pleistocene marl formation, overlying Miocene evaporites. Intercalations of high and low-velocity layers in the evaporites seem to indicate vertical facies variations. The Pseudo-velocity-log, associated with other lithologic determination processes, should become a geological tool for deep offshore exploration.     

PARTIAL COHERENCE MATCHING OF SYNTHETIC SEISMOGRAMS WITH SEISMIC TRACES*

A crucial step in the use of synthetic seismograms is the estimation of the filtering needed to convert the synthetic reflection spike sequence into a clearly recognizable approximation of a given seismic trace. In the past the filtering has been effected by a single wavelet, usually found by trial and error, and evaluated by eye. Matching can be made more precise than this by using spectral estimation procedures to determine the contribution of primaries and other reflection components to the seismic trace. The wavelet or wavelets that give the least squares best fit to the trace can be found, the errors of fit estimated, and statistics developed for testing whether a valid match can be made. If the composition of the seismogram is assumed to be known (e.g. that it consists solely of primaries and internal multiples) the frequency response of the best fit wavelet is simply the ratio of the cross spectrum between the synthetic spike sequence and the seismic trace to the power spectrum of the synthetic spike sequence, and the statistics of the match are related to the ordinary coherence function. Usually the composition cannot be assumed to be known (e.g. multiples of unknown relative amplitude may be present), and the synthetic sequence has to be split into components that contribute in different ways to the seismic trace. The matching problem is then to determine what filters should be applied to these components, regarded as inputs to a multichannel filter, in order to best fit the seismic trace, regarded as a noisy output. Partial coherence analysis is intended for just this problem. It provides fundamental statistics for the match, and it cannot be properly applied without interpreting these statistics. A useful and concise statistic is the ratio of the power in the total filtered synthetic trace to the power in the errors of fit. This measures the overall goodness-of-fit of the least squares match. It corresponds to a coherent (signal) to incoherent (noise) power ratio. Two limits can be set on it: an upper one equal to the signal-to-noise ratio estimated from the seismic data themselves, and a lower one defined from the distribution of the goodness-of-fit ratios yielded by matching with random noise of the same bandwidth and duration as the seismic trace segment. A match can be considered completely successful if its goodness-of-fit reaches the upper limit; it is rejected if the goodness-of-fit falls below the lower one.