基于分数阶小波域GSM模型的地震信号随机噪声压制方法

地震信号中的随机噪声是一种干扰波,严重降低了地震信号的信噪比,并影响着资料的后续处理和分析.本文根据地震信号中有效信号和随机噪声的差异,结合分数阶B样条小波变换与高斯尺度混合模型提出了一种地震信号随机噪声压制方法.首先利用分数阶B样条小波变换将含噪地震信号映射到最优分数阶小波时频域内,然后对各小波子带系数分别建立高斯尺度混合模型,由贝叶斯方法估计出源地震信号小波系数,最后使用分数阶B样条小波逆变换重构得到降噪后的地震信号.利用本文方法对合成地震记录和实际地震信号进行降噪处理,实验结果表明本文方法能够有效地压制地震信号中的随机噪声,并且较好地保留了有效信号.     

基于粒子群优化算法的叠前角道集子波反演

本文探讨了粒子群优化(PSO)算法在叠前地震角道集子波反演中的应用.在基本最优PSO算法的基础上,提出了对粒子更新速度进行平滑滤波的改进最优粒子群算法.由于代表子波的粒子的维数较大,如果粒子的各维元素相互独立,将导致粒子速度更新紊乱,影响搜索速度.通过对粒子速度进行三点均值滤波,加强了单个粒子各维元素的相互联系,并防止了粒子速度逃逸,使粒子更快地向有利于最优解的位置收敛.该方法应用于叠前角道集子波的反演中,取得了较好的子波反演效果,证明了本文方法的有效性.     

小波尺度域含气储层地震波衰减特征

黏弹性衰减因子Q的可靠估计可通过Q反褶积来提高地震资料的分辨率并有助于振幅分析. 本文从小波理论出发,结合地震波在黏弹性介质中的传播方程,推导出小波尺度域地震波能量衰减公式. 能量衰减公式具有下列性质：（1）Q值越大,能量衰减得越慢;Q值越小,能量衰减越严重;（2）尺度越小,信号中保留的能量越少;（3）对于脉冲源来说在理想的无衰减介质(即Q趋近于∞)中传播时,信号在不同尺度内的能量相同. 利用尺度能量公式,可从反射地震资料中直接估计品质因子Q（即衰减因子）,也可以提取不同尺度的能量衰减剖面作为储层描述的属性参数,用来进行岩性识别和指示气藏,与经典的谱比法相比,避免了谱比法所面临的双时窗问题以及进行谱估计的窗选择问题. 理论模型试验表明了本文方法的正确性和有效性.     

L1 norm optimal solution match processing in the wavelet domain

Greater attention has been paid to vintage-merge processing of seismic data and extracting more valuable information by the geophysicist. A match filter is used within many important areas such as splicing seismic data, matching seismic data with different ages and sources, 4-D seismic monitoring, and so on. The traditional match filtering method is subject to many restrictions and is usually difficult to overcome the impact of noise. Based on the traditional match filter, we propose the wavelet domain L1 norm optimal matching filter. In this paper, two different types of seismic data are decomposed to the wavelet domain, different detailed effective information is extracted for L1-norm optimal matching, and ideal results are achieved. Based on the model test, we find that the L1 norm optimal matching filter attenuates the noise and the waveform, amplitude, and phase coherence of result signals are better than the conventional method. The field data test shows that, with our method, the seismic events in the filter results have better continuity which achieves the high precision seismic match requirements.     

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.     

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。     

Applications of Savitzky-Golay Filter for Seismic Random Noise Reduction

This article utilizes Savitzky–Golay (SG) filter to eliminate seismic random noise. This is a novel method for seismic random noise reduction in which SG filter adopts piecewise weighted polynomial via leastsquares estimation. Therefore, effective smoothing is achieved in extracting the original signal from noise environment while retaining the shape of the signal as close as possible to the original one. Although there are lots of classical methods such as Wiener filtering and wavelet denoising applied to eliminate seismic random noise, the SG filter outperforms them in approximating the true signal. SG filter will obtain a good tradeoff in waveform smoothing and valid signal preservation under suitable conditions. These are the appropriate window size and the polynomial degree. Through examples from synthetic seismic signals and field seismic data, we demonstrate the good performance of SG filter by comparing it with the Wiener filtering and wavelet denoising methods.     

基于带状混合矩阵ICA实现地震盲反褶积

基于对地震反褶积本质上是一个盲过程的认识,引入高阶统计学盲源分离技术——独立分量分析（ICA）实现地震盲反褶积.在无噪声假设条件下,利用地震记录时间延迟矩阵和地震子波带状褶积矩阵,将地震褶积模型转化为一般线性混合ICA模型,采用FastICA算法,将带状性质作为先验信息,实现所谓带状ICA算法（B\|ICA）,得到个数与子波算子长度相等的多个估计反射系数序列和估计子波序列,最后利用褶积模型提供的附加信息从中优选出最佳的反射系数序列及相应的地震子波.模型数据和实际二维地震道数值算例表明：对于统计性反褶积,在不对反射系数作高斯白噪假设,不对子波作最小相位假设的所谓“全盲”条件下,基于ICA方法（反射系数非高斯分布,地震子波非最小相位）可以较好解决地震盲反褶积问题,是基于二阶统计特性的地震信号统计性反褶积方法的提升,具有可行性和应用前景.     

CORRECTING FOR COLOURED PRIMARY REFLECTIVITY IN DECONVOLUTION1

Statistical deconvolution, as it is usually applied on a routine basis, designs an operator from the trace autocorrelation to compress the wavelet which is convolved with the reflectivity sequence. Under the assumption of a white reflectivity sequence (and a minimum-delay wavelet) this simple approach is valid. However, if the reflectivity is distinctly non-white, then the deconvolution will confuse the contributions to the trace spectral shape of the wavelet and reflectivity. Given logs from a nearby well, a simple two-parameter model may be used to describe the power spectral shape of the reflection coefficients derived from the broadband synthetic. This modelling is attractive in that structure in the smoothed spectrum which is consistent with random effects is not built into the model. The two parameters are used to compute simple inverse- and forward-correcting filters, which can be applied before and after the design and implementation of the standard predictive deconvolution operators. For whitening deconvolution, application of the inverse filter prior to deconvolution is unnecessary, provided the minimum-delay version of the forward filter is used. Application of the technique to seismic data shows the correction procedure to be fast and cheap and case histories display subtle, but important, differences between the conventionally deconvolved sections and those produced by incorporating the correction procedure into the processing sequence. It is concluded that, even with a moderate amount of non-whiteness, the corrected section can show appreciably better resolution than the conventionally processed section.     

Seismic refraction traveltime inversion for static corrections in a glaciated shield rock environment: a case study

A traveltime inversion technique is applied to model the upper ∼40 m of the subsurface of a glaciated shield rock area in order to calculate static corrections for a multi-azimuth multi-depth walk-away vertical seismic profile and a surface seismic reflection profile. First break information from a seismic refraction survey is used in conjunction with a ray-tracing program and an iterative damped least-squares inversion algorithm to create a two-dimensional model of the subsurface. The layout of the seismic survey required crooked seismic lines and substantial gaps in the source and receiver coverage to be accounted for. Additionally, there is substantial topographical variation and a complex geology consisting of glaciofluvial sediment and glacial till overlying a crystalline bedrock. The resolution and reliability of the models is measured through a parameter perturbation technique, normalized χ² values, root means square traveltime residuals and comparison to known geology.     

Application of wavelet‐based multi‐model Kalman filters to real‐time flood forecasting

This paper presents the application of a multimodel method using a wavelet‐based Kalman filter (WKF) bank to simultaneously estimate decomposed state variables and unknown parameters for real‐time flood forecasting. Applying the Haar wavelet transform alters the state vector and input vector of the state space. In this way, an overall detail plus approximation describes each new state vector and input vector, which allows the WKF to simultaneously estimate and decompose state variables. The wavelet‐based multimodel Kalman filter (WMKF) is a multimodel Kalman filter (MKF), in which the Kalman filter has been substituted for a WKF. The WMKF then obtains M estimated state vectors. Next, the M state‐estimates, each of which is weighted by its possibility that is also determined on‐line, are combined to form an optimal estimate. Validations conducted for the Wu‐Tu watershed, a small watershed in Taiwan, have demonstrated that the method is effective because of the decomposition of wavelet transform, the adaptation of the time‐varying Kalman filter and the characteristics of the multimodel method. Validation results also reveal that the resulting method enhances the accuracy of the runoff prediction of the rainfall–runoff process in the Wu‐Tu watershed. Copyright © 2004 John Wiley & Sons, Ltd.     

230Th/234U and 14C dating of a lowstand coral reef beneath the insular shelf off Irabu Island, Ryukyus, southwestern Japan

Abstract   High-resolution seismic reflection profiles delineated the distribution of mound-shaped reflections, which were interpreted as reefs, beneath the insular shelf western off Irabu Island, Ryukyus, southwestern Japan. A sediment core through one of the mounded structures was recovered from the sea floor at a depth of −118.2 m by offshore drilling and was dated by radiometric methods. The lithology and coral fauna of the core indicate that the mounded structure was composed of coral–algal boundstone suggesting a small-scaled coral reef. High-precision α-spectrometric ²³⁰Th/²³⁴U dating coupled with calibrated accelerator mass spectrometric ¹⁴C ages of corals obtained reliable ages of this reef ranging from 22.18 ± 0.63 to 30.47 ± 0.98 ka. This proves that such a submerged reef was formed during the lowstand stage of marine oxygen isotope stages 3–2. The existence of low-Mg calcite in the aragonitic coral skeleton of 22.18 ± 0.63 ka provides evidence that the reef had once been exposed by lowering of the relative sealevel to at least −126 m during the last glacial maximum in the study area. There is no room for doubt that a coral reef grew during the last glacial period on the shelf off Irabu Island of Ryukyus in the subtropical region of western Pacific.     

一种自适应增益限的反Q滤波

地层的Q吸收会造成地震波振幅衰减、相位畸变,分辨率和信噪比明显降低.反Q滤波可消除由于地层Q吸收造成的振幅衰减和相位畸变,从而提高地震资料的分辨率;但反Q滤波振幅补偿的数值不稳定性问题会严重降低地震资料的信噪比,并产生很多假象.截止频率法和稳定因子法反Q滤波振幅补偿方法虽可控制数值非稳定性问题,但振幅补偿函数的增益限为一个时不变的常数,且与地震数据动态范围无关,其经常会压制深层地震波的高频成分,反而降低地震资料的分辨率;因此,本文在研究截止频率法和稳定因子法的基础上,结合地震数据的动态范围对地震记录分辨率的影响,提出了一种自适应增益限的反Q滤波振幅补偿方法,其增益限和稳定因子都是时变的,且都自适应于地震数据有效频带的截止频率.合成数据和实际数据试算表明,本文的自适应增益限的反Q滤波方法可恢复地震信号有效频带范围内的能量,且能较好地控制数值非稳定性问题,最终获得高分辨率和高信噪比的地震数据.     

消除探地雷达数据的子波衰减和频散的反滤波方法

消除探地雷达数据的子波衰减和频散可以很好地提高探地雷达的勘探深度和勘探分辨率.常用的消除探地雷达数据的子波衰减和频散方法为反Q滤波方法.该方法需要利用地下介质的Q参数,但是正确求取地下介质的Q参数很困难.针对这一问题,本文提出了一种消除探地雷达数据的子波衰减和频散的反滤波方法.该方法以地下介质反射系数是随机数为前提,利用地下介质等效滤波器具有最小相位这个特性,通过求取等效滤波器的振幅谱来求取等效滤波器的反滤波器.最后,利用该反滤波器对探地雷达数据进行反滤波,实现消除探地雷达数据的子波衰减和频散.     

L1 norm inversion method for deconvolution in attenuating media

In order to perform a good pulse compression, the conventional spike deconvolution method requires that the wavelet is stationary. However, this requirement is never reached since the seismic wave always suffers high‐frequency attenuation and dispersion as it propagates in real materials. Due to this issue, the data need to pass through some kind of inverse‐Q filter. Most methods attempt to correct the attenuation effect by applying greater gains for high‐frequency components of the signal. The problem with this procedure is that it generally boosts high‐frequency noise. In order to deal with this problem, we present a new inversion method designed to estimate the reflectivity function in attenuating media. The key feature of the proposed method is the use of the least absolute error (L1 norm) to define both the data and model error in the objective functional. The L1 norm is more immune to noise when compared to the usual L2 one, especially when the data are contaminated by discrepant sample values. It also favours sparse reflectivity when used to define the model error in regularization of the inverse problem and also increases the resolution, since an efficient pulse compression is attained. Tests on synthetic and real data demonstrate the efficacy of the method in raising the resolution of the seismic signal without boosting its noise component.     

WAVELET ESTIMATION USING THE MULTITAPER METHOD1

An accurate estimate of the seismic wavelet on a seismic section is extremely important for interpretation of fine details on the section and for estimation of acoustic impedance. In the absence of well-control, the recognized best approach to wavelet estimation is to use the technique of multiple coherence analysis to estimate the coherent signal and its amplitude spectrum, and thence construct the seismic wavelet under the minimum-phase assumption. The construction of the minimum-phase wavelet is critically dependent on the decay of the spectrum at the low-frequency end. Traditional methods of cross-spectral estimation, such as frequency smoothing using a Papoulis window, suffer from substantial side-lobe leakage in the areas of the spectrum where there is a large change of power over a relatively small frequency range. The low-frequency end of the seismic spectrum (less than 4 Hz) decays rapidly to zero. Side-lobe leakage causes poor estimates of the low-frequency decay, resulting in degraded wavelet estimates. Thomson's multitaper method of cross-spectral estimation which suffers little from side-lobe leakage is applied here, and compared with the result of using frequency smoothing with the Papoulis window. The multitaper method seems much less prone to estimating spuriously high coherences at very low frequencies. The wavelet estimated by the multitaper approach from the data used here is equivalent to imposing a low-frequency roll-off of some 48 dB/oct (below 3.91 Hz) on the amplitude spectrum. Using Papoulis smoothing the equivalent roll-off is only about 36 dB/oct. Thus the multitaper method gives a low-frequency decay rate of the amplitude spectrum which is some 4 times greater than for Papoulis smoothing. It also gives more consistent results across the section. Furthermore, the wavelet obtained using the multi-taper method and seismic data only (with no reference to well data) has more attractive physical characteristics when compared with a wavelet extracted using well data, than does an estimate using traditional smoothing.     

Properties of an improved Gabor wavelet transform and its applications to seismic signal processing and interpretation

This paper presents an analytical study of the complete transform of improved Gabor wavelets (IGWs), and discusses its application to the processing and interpretation of seismic signals. The complete Gabor wavelet transform has the following properties. First, unlike the conventional transform, the improved Gabor wavelet transform (IGWT) maps time domain signals to the time-frequency domain instead of the time-scale domain. Second, the IGW’s dominant frequency is fixed, so the transform can perform signal frequency division, where the dominant frequency components of the extracted sub-band signal carry essentially the same information as the corresponding components of the original signal, and the subband signal bandwidth can be regulated effectively by the transform’s resolution factor. Third, a time-frequency filter consisting of an IGWT and its inverse transform can accurately locate target areas in the time-frequency field and perform filtering in a given time-frequency range. The complete IGW transform’s properties are investigated using simulation experiments and test cases, showing positive results for seismic signal processing and interpretation, such as enhancing seismic signal resolution, permitting signal frequency division, and allowing small faults to be identified.     

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.     

An efficient and self‐adaptive approach for Q value optimization

The time‐invariant gain‐limit‐constrained inverse Q‐filter can control the numerical instability of the inverse Q‐filter, but it often suppresses the high frequencies at later times and reduces the seismic resolution. To improve the seismic resolution and obtain high‐quality seismic data, we propose a self‐adaptive approach to optimize the Q value for the inverse Q‐filter amplitude compensation. The optimized Q value is self‐adaptive to the cutoff frequency of the effective frequency band for the seismic data, the gain limit of the inverse Q‐filter amplitude compensation, the inverse Q‐filter amplitude compensation function, and the medium quality factor. In the processing of the inverse Q‐filter amplitude compensation, the optimized Q value, corresponding gain limit, and amplitude compensation function are used simultaneously; then, the energy in the effective frequency band for the seismic data can be recovered, and the seismic resolution can be enhanced at all times. Furthermore, the small gain limit or time‐variant bandpass filter after the inverse Q‐filter amplitude compensation is considered to control the signal‐to‐noise ratio, and the time‐variant bandpass filter is based on the cutoff frequency of the effective frequency band for the seismic data. Synthetic and real data examples demonstrate that the self‐adaptive approach for Q value optimization is efficient, and the inverse Q‐filter amplitude compensation with the optimized Q value produces high‐resolution and low‐noise seismic data.