IMPROVED LOW-FREQUENCY DECAY ESTIMATION USING THE MULTITAPER SPECTRAL ANALYSIS METHOD1

Spectral analysis is one of the most ubiquitous signal processing tools used in exploration geophysics. Among many applications, it is used simply to look at the frequency content of seismic traces, to find notches, to estimate wavelets under the minimum-phase assumption, and to match broadband synthetic seismograms to seismic data. Seismic spectra exhibit very large dynamic ranges, particularly at low frequencies. Estimation of low-frequency decay is very important for accurate modelling. However, when using traditional spectral estimates incorporating smoothing windows, too much sidelobe energy leaks from high power into low power areas, spoiling our ability to estimate low-frequency spectral decay. The multitaper method of spectral analysis due to D. Thomson does not employ just a single window, but rather a set of orthogonal data tapers. It is possible to have much less sidelobe contamination, while maintaining a stable estimate. The trace is tapered by each of a subset of the orthogonal tapers, and a raw spectral estimate produced in each case. These are combined to produce a final spectral estimate. The technique can be made adaptive by applying different weights to the different raw spectra at different frequencies. A comparison of seismic spectral estimation using this multitaper technique with a traditional approach having the same analysis bandwidth and stability demonstrates the very different estimates of spectral decay in the areas of high dynamic range. The multitaper approach provides estimates with much reduced sidelobe leakage, and hence is a very appealing method for reflection seismology.     

Estimation of the seismic wavelet through homomorphic deconvolution and well log data: application on well-to-seismic tie procedure

Wavelet estimation and well-tie procedures are important tasks in seismic processing and interpretation. Deconvolutional statistical methods to estimate the proper wavelet, in general, are based on the assumptions of the classical convolutional model, which implies a random process reflectivity and a minimum-phase wavelet. The homomorphic deconvolution, however, does not take these premises into account. In this work, we propose an approach to estimate the seismic wavelet using the advantages of the homomorphic deconvolution and the deterministic estimation of the wavelet, which uses both seismic and well log data. The feasibility of this approach is verified on well-to-seismic tie from a real data set from Viking Graben Field, North Sea, Norway. The results show that the wavelet estimated through this methodology produced a higher quality well tie when compared to methods of estimation of the wavelet that consider the classical assumptions of the convolutional model.     

小波域叠前地震资料衰减参数定性估计方法

叠前地震资料中,高频分量和低频分量随传播距离的衰减特性不同.本文给出了一种在小波域定性估计叠前地震资料衰减参数的方法.该方法利用连续小波变换提取共反射点道集的高、低频分量,以低频分量和高频分量之差定性反映地震波的衰减.通过累加不同偏移距的衰减,提高了估计的稳定性;采用幅度归一化方法,降低了信号幅值对衰减参数估计的影响.将本文提出方法与常用的基于叠后地震资料衰减估计方法用于某油田的地震资料处理,结果表明,本文方法得到的衰减估计结果能够更好地反映油气的空间展布.     

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.     

POST-CRITICAL WAVELET ESTIMATION AND DECONVOLUTION1

Using synthetic data, it is demonstrated that the amplitude spectra of post-critical plane-wave components are stable and equal to the amplitude spectrum of the input wavelet (critical reflection theorem). Our analysis and physical explanation of the theorem are based only on amplitude versus offset arguments. The stability of the spectra in the post-critical region is directly related to a high amplitude post-critical reflection that dominates the trace in the slant-stack domain. The validity of the theorem for both the acoustic and elastic cases, its assumptions and limitations, are also examined with emphasis on applications for processing seismic reflection data. Based on the theorem, a deterministic procedure is developed (assuming minimum-phase properties) for wavelet estimation and subsequent deconvolution. We call this method Post-critical Deconvolution, which emphasizes reliance on post-critical reflection data. The performance of the method is shown with real data and the results are compared to those obtained with conventional deconvolution techniques.     

基于PSO的地震盲反褶积方法

本文基于地层反射系数非高斯的统计特性,在反褶积输出单位方差约束下,将反褶积输出的负熵表示为非多项式函数,作为盲反褶积的目标函数,然后采用粒子群算法优化目标函数寻找最佳反褶积算子,实现地震信号的盲反褶积.数值模拟和实际资料处理结果表明,与传统反褶积方法相比,本文方法同时适应于最小相位子波及混合相位子波的反褶积,能够更好地从地震数据中估计反射系数,有效拓宽地震资料的频谱,得到高分辨率的地震资料.     

基于保角变换的双谱域相位谱估计方法及其在地震子波估计中的应用(英文)

地震子波估计是地震资料处理与解释中的重要环节,它的准确与否直接关系到反褶积及反演等结果的好坏。高阶谱(双谱和三谱)地震子波估计方法是一类重要的、新兴的子波估计方法,然而基于高阶谱的地震子波估计往往因为高阶相位谱卷绕的原因,导致子波相位谱求解产生偏差,进而影响了混合相位子波估计的效果。针对这一问题,本文在双谱域提出了一种基于保角变换的相位谱求解方法。通过缩小傅里叶相位谱的取值范围,有效避免了双谱相位发生卷绕的情况,从而消除了原相位谱估计中双谱相位卷绕的影响。该方法与最小二乘法相位谱估计相结合,构成了基于保角变换的最小二乘地震子波相位谱估计方法,并与最小二乘地震子波振幅谱估计方法一起,应用到了地震资料混合相位子波估计中。理论模型和实际资料验证了该方法的有效性。同时本文将双谱域地震子波相位谱估计中保角变换的思想推广到三谱域地震子波相位谱估计中。     

Klauder wavelet removal before vibroseis deconvolution

The spiking deconvolution of a field seismic trace requires that the seismic wavelet on the trace be minimum phase. On a dynamite trace, the component wavelets due to the effects of recording instruments, coupling, attenuation, ghosts, reverberations and other types of multiple reflection are minimum phase. The seismic wavelet is the convolution of the component wavelets. As a result, the seismic wavelet on a dynamite trace is minimum phase and thus can be removed by spiking deconvolution. However, on a correlated vibroseis trace, the seismic wavelet is the convolution of the zero-phase Klauder wavelet with the component minimum-phase wavelets. Thus the seismic wavelet occurring on a correlated vibroseis trace does not meet the minimum-phase requirement necessary for spiking deconvolution, and the final result of deconvolution is less than optimal. Over the years, this problem has been investigated and various methods of correction have been introduced. In essence, the existing methods of vibroseis deconvolution make use of a correction that converts (on the correlated trace) the Klauder wavelet into its minimum-phase counterpart. The seismic wavelet, which is the convolution of the minimum-phase counterpart with the component minimum-phase wavelets, is then removed by spiking deconvolution. This means that spiking deconvolution removes both the constructed minimum-phase Klauder counterpart and the component minimum-phase wavelets. Here, a new method is proposed: instead of being converted to minimum phase, the Klauder wavelet is removed directly. The spiking deconvolution can then proceed unimpeded as in the case of a dynamite record. These results also hold for gap predictive deconvolution because gap deconvolution is a special case of spiking deconvolution in which the deconvolved trace is smoothed by the front part of the minimum-phase wavelet that was removed.     

基于物理小波的频谱分解方法及应用研究

在地震资料频谱分解中,采用匹配地震子波的物理小波,依据地震信号的特征,用振幅、能量衰减率、能量延迟时间及地震子波的中心频率等四类参数构造基本小波,把地震信号分解在小波域,高频分量能够得到精细的刻画.本文以物理小波变换为工具, 给出了该变换中的核函数的选择方法,进而提出了基于物理小波变换的频谱成像方法.我们将此方法用于海上某油田河流相储层的描述,并与常规软件中的小波变换频谱成像结果进行了对比, 结果表明,本文提出的方法更能精细地刻画地质事件.     

SEISMIC PHASE UNWRAPPING: METHODS,RESULTS, PROBLEMS1

Six known methods of seismic phase unwrapping (or phase restoration) are compared. All the methods tested unwrap the phase satisfactorily if the initial function is a simple theoretical wavelet. None of the methods restore the phase of a synthetic trace exactly. An initial validity test of the phase-unwrapping method is that the sum of the restored wavelet phase spectrum and the restored pulse-trace phase spectrum (assuming the convolutional model for the seismic trace) must be equal to the restored phase spectrum of the synthetic trace. Results show that none of the tested methods satisfy this test. Quantitative estimation of the phase-unwrapping accuracy by correlation analysis of the phase deconvolution results separated these methods, according to their efficiency, into three groups. The first group consists of methods using a priori wavelet information. These methods make the wavelet phase estimation more effective than the minimum-phase approach, if the wavelet is non-minimum-phase. The second group consists of methods using the phase increment Δø(Δω) between two adjacent frequencies. These methods help to decrease the time shift of the initial synthetic trace relative to the model of the medium. At the same time they degrade the trace correlation with the medium model. The third group consists of methods using an integration of the phase derivative. These methods do not lead to any improvement of the initial seismic trace. The main problem in the phase unwrapping of a seismic trace is the random character of the pulse trace. For this reason methods based on an analysis of the value of Δø(Δω) only, or using an adaptive approach (i.e. as Δω decreases) are not effective. In addition, methods based on integration of the phase derivative are unreliable, due to errors in numerical integration and differentiation.     

Bayesian frequency-domain blind deconvolution of ground-penetrating radar data

Enhancing the resolution and accuracy of surface ground-penetrating radar (GPR) reflection data by inverse filtering to recover a zero-phased band-limited reflectivity image requires a deconvolution technique that takes the mixed-phase character of the embedded wavelet into account. In contrast, standard stochastic deconvolution techniques assume that the wavelet is minimum phase and, hence, often meet with limited success when applied to GPR data. We present a new general-purpose blind deconvolution algorithm for mixed-phase wavelet estimation and deconvolution that (1) uses the parametrization of a mixed-phase wavelet as the convolution of the wavelet's minimum-phase equivalent with a dispersive all-pass filter, (2) includes prior information about the wavelet to be estimated in a Bayesian framework, and (3) relies on the assumption of a sparse reflectivity. Solving the normal equations using the data autocorrelation function provides an inverse filter that optimally removes the minimum-phase equivalent of the wavelet from the data, which leaves traces with a balanced amplitude spectrum but distorted phase. To compensate for the remaining phase errors, we invert in the frequency domain for an all-pass filter thereby taking advantage of the fact that the action of the all-pass filter is exclusively contained in its phase spectrum. A key element of our algorithm and a novelty in blind deconvolution is the inclusion of prior information that allows resolving ambiguities in polarity and timing that cannot be resolved using the sparseness measure alone. We employ a global inversion approach for non-linear optimization to find the all-pass filter phase values for each signal frequency. We tested the robustness and reliability of our algorithm on synthetic data with different wavelets, 1-D reflectivity models of different complexity, varying levels of added noise, and different types of prior information. When applied to realistic synthetic 2-D data and 2-D field data, we obtain images with increased temporal resolution compared to the results of standard processing.     

SIGNAL ADJUSTMENT OF VIBROSEIS AND IMPULSIVE SOURCE DATA*

In certain areas continuous Vibroseis profiling is not possible due to varying terrain conditions. Impulsive sources can be used to maintain continuous coverage. While this technique keeps the coverage at the desired level, for the processing of the actual data there is the problem of using different sources resulting in different source wavelets. In addition, the effect of the free surface is different for these two energy sources. The approach to these problems consists of a minimum-phase transformation of the two-sided Vibroseis data by removal of the anticipation component of the autocorrelation of the filtered sweep and a minimum-phase transformation of the impulsive source data by replacement of the recording filter operator with its minimum-phase correspondent. Therefore, after this transformation, both datasets show causal wavelets and a conventional deconvolution (spike or predictive) may be used. After stacking, a zero-phase transformation can be performed resulting in traces well suited for computing pseudo-acoustic impedance logs or for application of complex seismic trace analysis. The solution is also applicable to pure Vibroseis data, thereby eliminating the need for a special Vibroseis deconvolution. The processing steps described above are demonstrated on synthetic and actual data. The transformation operators used are two-sided recursive (TSR) shaping filters. After application of the above adjustment procedure, remaining signal distortions can be removed by modifying only the phase spectrum or both the amplitude and phase spectra. It can be shown that an arbitrary distortion defined in the frequency domain, i.e., a distortion of the amplitude and phase spectrum, is noticeable in the time section as a two-sided signal.     

Nonstationary deconvolution using maximum kurtosis optimization

Deconvolution is an essential step for high-resolution imaging in seismic data processing. The frequency and phase of the seismic wavelet change through time during wave propagation as a consequence of seismic absorption. Therefore, wavelet estimation is the most vital step of deconvolution, which plays the main role in seismic processing and inversion. Gabor deconvolution is an effective method to eliminate attenuation effects. Since Gabor transform does not prepare the information about the phase, minimum-phase assumption is usually supposed to estimate the phase of the wavelet. This manner does not return the optimum response where the source wavelet would be dominantly a mixed phase. We used the kurtosis maximization algorithm to estimate the phase of the wavelet. First, we removed the attenuation effect in the Gabor domain and computed the amplitude spectrum of the source wavelet; then, we rotated the seismic trace with a constant phase to reach the maximum kurtosis. This procedure was repeated in moving windows to obtain the time-varying phase changes. After that, the propagating wavelet was generated to solve the inversion problem of the convolutional model. We showed that the assumption of minimum phase does not reflect a suitable response in the case of mixed-phase wavelets. Application of this algorithm on synthetic and real data shows that subtle reflectivity information could be recovered and vertical seismic resolution is significantly improved.     

CONSIDERATIONS IN ESTIMATING THE MINIMUM-PHASE PROPERTIES OF SAMPLED DATA*

Analysis of the phase spectra from the signatures, impulse responses and other wavelets observed in seismic data leads to the construction of equivalent minimum-phase functions. The accuracy of such computations using digitally sampled data is questioned with special reference to Texas Instruments DFS IV and DFS V recording filters. Results vary with the lengths and sample rates of the time functions, and further errors may be introduced when implementing the Hilbert transform. Such problems are related to poor resolution in the low amplitude areas of the spectrum. Techniques for correction are described. With appropriate shaping a reasonably accurate phase spectrum may be computed for the minimum-phase function. The generation of minimum-phase wavelets within the processing sequence is briefly discussed.     

PHASE DISTORTION DUE TO ABSORPTION IN SEISMOGRAMS AND VSP*

Absorption of seismic energy in the earth reduces amplitudes and changes phases of the propagating seismic waves. Amplitudes are usually recovered according to an estimated exponential decay curve, while phase distortions are generally disregarded. Therefore, accurate processing of seismic data requires a careful investigation of the relationship between absorption and phases. In this paper a procedure is suggested to achieve this goal, and some related topics are worked out. A method is outlined for computing synthetic seismograms and vertical seismic profiles with phase distortion due to absorption. The algorithm works in the frequency domain, and it provides for absorption according to the usual model of exponential decay of amplitude with distance. The absorption coefficient is a linear function of frequency and is related to the quality factor Q of the rocks. Complex seismic velocities are introduced and minimum-phase delay due to absorption is assumed for all cases considered. Methods for estimating Q profiles from seismic well surveys and seismic data are described. Comparison between field and synthetic data shows the effectiveness and benefits of the procedure. Some applications of the method to phase distortion recovery and wavelet processing are presented.     

Improving the resolution of seismic traces based on the secondary time–frequency spectrum

The resolution of seismic data is critical to seismic data processing and the subsequent interpretation of fine structures. In conventional resolution improvement methods, the seismic data is assumed stationary and the noise level not changes with space, whereas the actual situation does not satisfy this assumption, so that results after resolution improvement processing is not up to the expected effect. To solve these problems, we propose a seismic resolution improvement method based on the secondary time–frequency spectrum. First, we propose the secondary time-frequency spectrum based on S transform (ST) and discuss the reflection coefficient sequence and time-dependent wavelet in the secondary time–frequency spectrum. Second, using the secondary time–frequency spectrum, we design a twodimensional filter to extract the amplitude spectrum of the time-dependent wavelet. Then, we discuss the improvement of the resolution operator in noisy environments and propose a novel approach for determining the broad frequency range of the resolution operator in the time–frequency–space domain. Finally, we apply the proposed method to synthetic and real data and compare the results of the traditional spectrum-modeling deconvolution and Q compensation method. The results suggest that the proposed method does not need to estimate the Q value and the resolution is not limited by the bandwidth of the source. Thus, the resolution of the seismic data is improved sufficiently based on the signal-to-noise ratio (SNR).     

Ground roll wave suppression based on wavelet frequency division and radial trace transform

Ground roll waves interfere with seismic data. The suppression of ground roll waves based on the division of wavelet frequencies considers the low-frequency characteristics of ground roll waves. However, this method will not be effective when the ground roll wave and the effective signal have the same frequency bands because of overlapping. The radial trace transform (RTT) considers the apparent velocity difference between the effective signal and the ground roll wave to suppress the latter, but affects the low-frequency components of the former. This study proposes a ground roll wave suppression method by combining the wavelet frequency division and the RTT based on the difference between the ground roll wave velocity and the effective signal and their energy difference in the wavelet domain, thus making full use of the advantages of both methods. First, we decompose the seismic data into different frequency bands through wavelet transform. Second, the RTT and low-cut filtering are applied to the low-frequency band, where the ground roll waves are appearing. Third, we reconstruct the seismic record without ground roll waves by using the inverse RTT and the remaining frequency bands. The proposed method not only improves the ground roll wave suppression, but also protects the signal integrity. The numerical simulation and real seismic data processing results suggest that the proposed method has a strong ability to denoise while preserving the amplitude.     

非稳态地震记录时变子波估计

地震子波估计是地震资料处理和解释中的一个关键问题,子波估计的可靠性会直接影响反褶积和反演的准确度.现有的子波估计方法分为确定型和统计型两种类型,本文通过结合这两类方法,利用确定型的谱分析法和统计型的偏度最大化方法,分别提取时变子波的振幅和相位信息,得到估计的时变子波.这种方法不需要对子波进行任何时不变或相位等的假设,具有对时变相位的估计能力.进而利用估计时变子波进行非稳态反褶积,提高地震记录的保真度,为精细储层预测和描述提供高质量的剖面.理论模型试算验证了方法的可行性,通过实际地震资料的处理应用,表明该方法能有效地提取出子波时变信息.     

基于双谱幅值和相位重构的地震子波提取

利用地震记录双谱中包含子波的幅值和相位信息，以及其超强的抗噪声干扰能力，采用一种基于双谱幅值和相位重构的地震子波提取方法，首先提取出子波幅值及相位信息，进而通过傅立叶反变换，使子波得以完全恢复.本文针对双谱相位重构递推公式，提出一种新的初值选取方法，使地震子波估计的稳定性得到了提高.仿真实验证实了该方法的可行性.