An application of the autoregressive extrapolation technique to enhance deconvolution results: a 2D marine data example

Interpreting a post‐stack seismic section is difficult due to the band‐limited nature of the seismic data even post deconvolution. Deconvolution is a process that is universally applied to extend the bandwidth of seismic data. However, deconvolution falls short of this task as low and high frequencies of the deconvolved data are either still missing or contaminated by noise. In this paper we use the autoregressive extrapolation technique to recover these missing frequencies, using the high signal‐to‐noise ratio (S/N) portions of the spectrum of deconvolved data. I introduce here an algorithm to extend the bandwidth of deconvolved data. This is achieved via an autoregressive extrapolation technique, which has been widely used to replace missing or corrupted samples of data in signal processing. This method is performed in the spectral domain. The spectral band to be extrapolated using autoregressive prediction filters is first selected from the part of the spectrum that has a high signal‐to‐noise ratio (S/N) and is then extended. As there can be more than one zone of good S/N in the spectrum, the results of prediction filter design and extrapolation from three different bands are averaged. When the spectrum of deconvolved data is extended in this way, the results show higher vertical resolution to a degree that the final seismic data closely resemble what is considered to be a reflectivity sequence of the layered medium. This helps to obtain acoustic impedance with inversion by stable integration. The results show that autoregressive spectral extrapolation highly increases vertical resolution and improves horizon tracking to determine continuities and faults. This increase in coherence ultimately yields a more interpretable seismic section.     

Using the Wiener–Levinson algorithm to suppress ground-roll

In land seismic surveys, the seismic data are mostly contaminated by ground-roll noise, high amplitude and low frequency. Since the ground-roll is coherent with reflections and depends on the source, the spectral band of seismic signal and ground-roll always overlap, which can be clearly seen in the spectral domain. So, separating them in time or frequency domain commonly causes waveform distortions and information missing due to cut-off effects. Therefore, the combination of these factors leads to search for alternative filtering methods or processes. We applied the conventional Wiener–Levinson algorithm to extract ground-roll from the seismic data. Then, subtracting it from the seismic data arithmetically performs the ground-roll suppression. To set up the algorithm, linear or nonlinear sweep signals are used as reference noise trace. The frequencies needed in creating a reference noise trace using analytical sweep signal can be approximately estimated in spectral domain. The application of the proposed method based on redesigning of Wiener–Levinson algorithm differs from the usual frequency filtering techniques since the ground-roll is suppressed without cutting signal spectrum. The method is firstly tested on synthetics and then is applied to a shot data from the field. The result obtained from both synthetics and field data show that the ground-roll suppression in this way causes no waveform distortion and no reduction of frequency bandwidth of the data.     

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.     

OPTIMUM DIGITAL FILTERING AND INVERSE FILTERING IN THE FREQUENCY DOMAIN*

Two distinct filters are developed in the frequency domain which represent an attempt to increase the resolution of fine structure contained in the signal whilst keeping the expected filtered noise energy within reasonable bounds. A parameter termed the White Noise Amplification is defined and used together with a measure of the deconvolved pulse width in order to provide a more complete characterisation of the filters. Each of the two main types of frequency domain filters discussed varies in properties with respect to a single adjustable parameter. This may be contrasted with a time domain Wiener filter which in general has three variables: length, delay and an adjustable noise parameter or weight. The direct frequency domain analogue of the Wiener filter is termed a gamma-Fourier filter, and is shown to have properties which span the range from those of a spiking filter with zero least square error at one extreme, to those of a matched filter at the other extreme of its variable parameter's range. The second type of filter considered—termed the modulated Gaussian filter—is similarly shown to be a perfect spiking filter at one extreme of its parameter range, but adopts the properties of an output energy filter at the other extreme.     

基于核函数主分量的维纳滤波方法研究

针对强随机噪声地震资料背景下经典维纳滤波方法在信号的保幅及高维数据空间求解过程中产生病态矩阵的问题,提出利用核函数主分量维纳滤波压制强地震勘探随机噪声.首先利用线性核函数将地震信号映射到特征空间,再通过主分量分析方法提取地震数据主分量进行数据降维,并得到核主分量维纳滤波因子,从而进行核主分量维纳滤波（K-WPC）.正演仿真及对实际地震资料处理表明,该方法对随机噪声有较好的压制作用,保幅效果也令人满意.     

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.     

利用经验格林函数谱比法估计2013年芦山地震序列的应力降

本文以芦山地震余震为例,分析了基于强震动观测记录的经验格林函数（EGF）谱比法估计地震的拐角频率和应力降的可行性。首先给出能够可靠估计地震拐角频率和应力降的经验格林函数谱比曲线的质量标准;然后利用其估算出17次M_L3.8—5.4芦山强余震的拐角频率;最后,参考其它研究给出的地震矩震级,计算出地震应力降。结果显示,芦山强余震的拐角频率主要介于1.0—2.0 Hz之间,应力降平均值为9.98 MPa,且地震应力降表现出明显的震级相关性。      

最小二乘支持向量回归滤波系统性能分析

支持向量机(Support Vector Machine: SVM)一直作为机器学习方法在统计学习理论基础上被研究和发展,本文从信号与系统的角度出发,证明了平移不变核最小二乘支持向量机(Least Squares SVM: LS-SVM)是一个线性时不变系统.以Ricker子波核为例,探讨了不同参数对最小二乘支持向量回归(Least Squares Support Vector Regression: LS-SVR)滤波器频率响应特性的影响,这些参数的不同选择相应地控制着滤波器通带上升沿的陡峭性、通带的中心频率、通带带宽以及信号能量的衰减,即滤波器长度越长通带的上升沿越陡,核参数值越大通带的中心频率越高,且通带带宽越宽,正则化参数值越小,通带带宽越窄(但通带中心频率基本保持恒定),有效信号幅度衰减越严重.合成地震记录的仿真实验结果表明,Ricker子波核LS-SVR滤波器在处理地震勘探信号的应用中,滤波性能优于径向基函数(Radial Basic Function: RBF)核LS-SVR滤波器以及小波变换滤波和Wiener滤波方法.     

Optimum pilot sweep

The successful application of high-resolution seismic methods requires evaluating each element in the seismic system and ensuring that each part of the system contributes optimally to the success of the method. Unfortunately, unlike data processing, seismic signal generation is not carefully optimized. The purpose of our study was to optimize the source signal in order to better coordinate field operations with subsequent data processing to achieve their common objective. We developed an iterative method for a rational frequency distribution of the energy of a seismic source. The method allows the optimum amplitude spectrum of a source signal to be calculated, thus providing the best data quality at the end of the processing. We assume that the source signal is affected by a total transfer function, by the reflectivity function of a target interval, and by ambient noise, whose characteristics, if not known, can be estimated or measured in practice. The transfer function includes data processing other than the correlation stage and the final trace-optimizing filter. The variance of a reflectivity estimate is considered to be a measure of the data quality and improvement of the characteristic corresponds to a decrease in the variance. For this reason, a constrained Wiener deconvolution filter is used as the final trace-optimizing filter. It not only minimizes the variance of a reflectivity estimate but also ensures a specific signal-to-noise ratio. The method is made feasible by following the Vibroseis technique, primarily because of the versatility of the technique in controlling the signal spectrum. With the optimum amplitude spectrum obtained, the corresponding optimum pilot sweep can be readily calculated. Examples using synthetic data are presented to illustrate the method.     

Application of autoregressive extrapolation to the cross-borehole tomography

Autoregressive (AR) extrapolation of travel-time data is tested using several synthetic tomography examples using a cross-borehole geometry. Earlier studies have shown crossborehole tomography using travel-times can have reduced resolution because of the limitations on ray coverage. We apply AR extrapolation to partial travel-time data and then compare the tomographic inversions using the full data and the extrapolated data. Both the overall patterns of the extended data and the tomographic reconstructions with the extended data show that AR extrapolation can effectively extend the synthetic crossborehole tomographic data to a broader coverage and can improve the cross-hole reconstruction images.     

Fine structure of microwave emission in the 25 August 1999 event and its association with the magnetic field fine structure

A study is made of the initial stage of the 25 August 1999, event using high time-resolution microwave observations, as well as the data from the Siberian Solar Radio Telescope and Yohkoh/SXT/HXT. Microwave emission revealed fine structures with a typical time scale of about 1 s with a frequency drift 1 GHz/s, and structures with a typical time scale of less than 0.1 s with a frequency drift 10 GHz/s. Emission bands with a slower frequency drift are generated by energetic electrons subjected to the cyclotron resonance condition. This slower frequency drift is a consequence of a change in plasma density caused by the coalescence of magnetic structures with a typical size of the order of 10⁸ cm, while the emission with a faster drift is generated by beams of energetic electrons generating Cherenkov resonance emission. The energetic electron beams are produced as a result of the interaction of magnetic structures 10⁶–10⁷ cm in size.     

数据重构提高τ-p变换的精度

地震数据采样密度及近远道数据不足时,常规τ-p变换算法易出现假频和端点效应,影响τ-p变换的精度,进而影响地震资料处理的效果。本文对τ-p变换算法进行了改进,在τ-p变换前,使用F-K域道内插和道集外推的方法重构地震数据,通过加密地震数据和外推近远道数据的方式改善了τ-p变换效果。理论模型试算和实际数据证实,改进后的τ-p变换方法具有可靠性高、压制假频和端点效应等优点。      

New constraints on the seismic history of the Castrovillari fault in the Pollino gap (Calabria, southern Italy)

The Pollino Range area represents the mostprominent gap in seismicity within thesouthern Apennines. Geomorphic andtrenching investigations along theCastrovillari fault indicate that thisnormal fault is a major seismogenic faultwithin the southern part of this gap. Atleast four surface-faulting earthquakeshave occurred on this fault since latePleistocene age. Radiocarbon dating coupledwith historical consideration set thetime of the most recent earthquake as mostlikely to be between 530 A.D. and 900 A.D.,with the possible widest interval of530–1100 A.D. No evidence for this eventhas been found in the historical records,although its age interval falls within thetime spanned by the seismic catalogues.Slip per event ranges between 0.5 and1.6 m, with a minimum rupture length of13 km. These values suggest a M 6.5–7.0 forthe paleoearthquakes. The minimum long-termvertical slip rate obtained from displacedgeomorphic features is of 0.2–0.5 mm/yr. Avertical slip-rate of about 1 mm/yr is alsoinferred from trenching data. Theinter-event interval obtained from trenchdata ranges between 940 and 7760 years(with the young part of the intervalpossibly more representative; roughly940–3000 years). The time elapsed since themost recent earthquake ranges between aminimum of 900–1100 and a maximum of 1470years. The seismic behavior of this faultappears to be consistent with that of othermajor seismogenic faults of thecentral-southern Apennines. The Pollinocase highlights the fact thatgeological investigations represent apotentially useful technique tocharacterize the seismic hazard of `silent' areas for which adequate historical andseismological data record are notavailable.     

Spectral classification methods in monitoring small local events by the Israel seismic network

We use the dense Israel Seismic Network (ISN) to discriminate between low magnitude earthquakes and explosions in the Middle East region. This issue is important for CTBT monitoring, especially when considering small nuclear tests which may be conducted under evasive conditions. We explore the performance of efficient discriminants based on spectral features of seismograms using waveforms of 50 earthquakes and 114 quarry and underwater blasts with magnitudes 1.0–2.8, recorded by ISN short-period stations at distances up to 200 km. The single-station spectral ratio of the low and high-frequency seismic energy shows an overlap between explosions and earthquakes. After averaging over a subnet of stations, the resolving power is enhanced and the two classes of events are separated. Different frequency bands were tested; the (1–3 Hz)/(6–8 Hz) ratio provided the best discriminant performance. We also estimated normalized r.m.s. spectral amplitudes in several sequential equal frequency windows within the 1–12 Hz band and applied multiparametric automatic classification procedures (Linear Discrimination Function and Artificial Neural Network) to the amplitudes averaged over a subnetwork. A leave-one-out test showed a low rate of error for the multiparametric procedures. An innovative multi-station discriminant is proposed, based on spectral modulation associated with ripple-firing in quarry blasts and with the bubbling effect in underwater explosions. It utilizes a distinct azimuth-invariant coherency of spectral shapes for different stations in the frequency range (1–12 Hz). The coherency is measured by semblance statistics commonly used in seismic prospecting for phase correlation in the time domain. After modification, the statistics applied to the network spectra provided event separation. A new feature of all the above mentioned procedures is that they are based on smoothed (0.5 Hz window), instrument-corrected FFT spectra of the whole signal; they are robust to the accuracy of onset time estimation and, thus well suited to automatic event identification.     

Correlation of seismic activity and fumarole temperature at the Mt. Merapi volcano (Indonesia) in 2000

In this paper we present densely sampled fumarole temperature data, recorded continuously at a high-temperature fumarole of Mt. Merapi volcano (Indonesia). These temperature time series are correlated with continuous records of rainfall and seismic waveform data collected at the Indonesian–German multi-parameter monitoring network. The correlation analysis of fumarole temperature and precipitation data shows a clear influence of tropical rain events on fumarole temperature. In addition, there is some evidence that rainfall may influence seismicity rates, indicating interaction of meteoric water with the volcanic system. Knowledge about such interactions is important, as lava dome instabilities caused by heavy-precipitation events may result in pyroclastic flows. Apart from the strong external influences on fumarole temperature and seismicity rate, which may conceal smaller signals caused by volcanic degassing processes, the analysis of fumarole temperature and seismic data indicates a statistically significant correlation between a certain type of seismic activity and an increase in fumarole temperature. This certain type of seismic activity consists of a seismic cluster of several high-frequency transients and an ultra-long-period signal (<0.002 Hz), which are best observed using a broadband seismometer deployed at a distance of 600 m from the active lava dome. The corresponding change in fumarole temperature starts a few minutes after the ultra-long-period signal and simultaneously with the high-frequency seismic cluster. The change in fumarole temperature, an increase of 5 °C on average, resembles a smoothed step. Fifty-four occurrences of simultaneous high-frequency seismic cluster, ultra-long period signal and increase of fumarole temperature have been identified in the data set from August 2000 to January 2001. The observed signals appear to correspond to degassing processes in the summit region of Mt. Merapi.     

MIGRATION IN TERMS OF SPATIAL DECONVOLUTION*

The relationship between two finite-difference schemes (15° and 40°) and the Kirchhoff summation approach is discussed by using closed form solutions of Claerbout's approximate versions of the wave equation. Forward extrapolation is presented as a spatial convolution procedure for each frequency component. It is shown that downward extrapolation can be considered as a wavelet deconvolution procedure, the spatial wavelet being given by the wave theory. Using this concept, a three-dimensional model for seismic data is proposed. The advantages of downward extrapolation in the space-frequency domain are discussed. Finally, it is derived that spatial sampling imposes an upper limit on the aperture and a lower limit on the extrapolation step.     

Scaling relations for seismic events induced by mining

The values of seismic moment andS-wave corner frequency from 1575 seismic events induced in South African, Canadian, Polish, and German underground mines were collected to study their scaling relations. The values ofP-wave corner frequency from 649 events were also available. Seismic moments of these events range from 5*10³ to 2*10¹⁵ N·m (moment magnitude is from –3.6 to 4.1), theS-wave corner frequency ranges from 0.7 to 4438 Hz, and theP-wave corner frequency is between 5 and 4010 Hz. The slope of a regression line between the logarithm ofS- andP-wave corner frequencies is equal to one, and the corner frequencies ofP waves are higher than those ofS waves on the average by about 25 percent. In studies of large and moderate earthquakes it has been found that stress drop is approximately independent of the seismic moment, which means that seismic moment is inversely proportional to the third power of corner frequency. Such a behavior was confirmed for most of the data considered here. A breakdown in the similarity betwen large and small events seems to occur for the events with moment magnitude below –2.5. The average values of seismic moment referred to the same range of corner frequency, however, are vastly different in various mining areas.     

地震低频伴影的数值模拟与应用

Strong low-frequency energy beneath a hydrocarbon reservoir is called a seismic low-frequency shadow and can be used as a hydrocarbon indicator （Tarter et al., 1979） bu the physical mechanism of the observed low-frequency shadow is still unclear. To stud） the mechanism, we performed seismic numerical simulation of geological models with a hydrocarbon-bearing zone using the 2-D diffusive-viscous wave equation which car effectively model the characteristics of velocity dispersion and transform the seismic dat~ centered in a target layer slice within a time window to the time-frequency domain by usinl time-frequency signal analysis and sort the frequency gathers to common frequency cubes. Then, we observe the characteristics of the seismic low-frequency shadow in the common frequency cubes. The numerical simulations reveal that the main mechanism of seismic lowfrequency shadows is attributed to high attenuation of the medium to high seismic frequency components caused by absorption in the hydrocarbon-filled reservoir. Results from a practical example of seismic low-frequency shadows show that it is possible to identify the reservoir by the low-frequency shadow with high S/N seismic data.     

基于频率搬移的地震资料约束测井资料外推

于地震资料本身频带有限的特性,导致在利用地震资料作为约束条件进行测井资料外推时存在奇异性. 文中利用通信中常用的频率搬移技术,将频带有限的地震资料转化成一种频带拓宽的伪超分辨率资料来控制测井资料的外推,从而解决地震资料约束下的测井资料外推技术中的奇异性问题. 并利用同相轴自动追踪和时频分析技术,解决子波时变的问题,实现沿地层自适应地外推测井资料. 对实际资料的测井速度和反射系数外推结果表明, 此法具有较好的应用前景.     

On the frequency distribution of interoccurrence times of earthquakes

The distributions of discrete frequency, N, versus interoccurrence time, t (in days), of M 7 earthquakes in the Taiwan region during the 1900–1994 period, M 6 earthquakes in the north-south seismic belt of China during the 1900–1990 period, and M 5.5 earthquakes in Southern California, U.S.A., during the 1914–1995 period are studied through two statistical models (gamma function and exponential function). Results show that both the exponential function and gamma function can describe the distributions. However, the former is more appropriate than the latter. This indicates that the three time series of earthquakes have a significant component of Poisson processes, even though the tectonic conditions, the fault distributions and the size of the three seismic regions are different.