RELATED PROPERTIES OF MINIMUM-PHASE AND ZERO-PHASE TIME FUNCTIONS *

In this paper properties of the discrete zero-phase time function are derived and compared with related properties of the discrete minimum-phase time function. The two-sided minimum-length signal is introduced and it is derived that, for any given amplitude spectrum, the two-sided minimum-length signal and the signal with zero-phase spectrum are identical signals. A comparison is made between the one-sided minimum-length signal (minimum-phase signal) and the two-sided minimum-length signal (zero-phase signal). A computational scheme is discussed which determines the zero-phase correspondent of a given signal. A method is proposed to compute zero-phase least-square inverse filters. The efficiency of minimum-phase and zero-phase least-square inverse filters is shown on signals with different phase properties. A criterion is derived which determines whether a symmetric time function has the zero-phase property. The close relationship with the minimum-phase criterion is discussed. Finally the relationship between signal length and resolving power is illustrated on numerical examples.     

Doubly Stochastic Earthquake Source Model: “Omega-Square” Spectrum and Low High-Frequency Directivity Revealed by Numerical Experiments

Since its formulation in 1967–1970, the classical ω ^?2 model of earthquake source spectrum awaits a consistent theoretical foundation. To obtain one, stochastic elements are incorporated both into the final structure of the fault and into the mode of rupture propagation. The main components of the proposed “doubly stochastic” model are: (1) the Andrews’s concept, that local stress drop over a fault is a random self-similar field; (2) the concept of rupture with running slip pulse, after Heaton; (3) the hypothesis that a rupture front is a tortuous, multiply connected (“lacy”) fractal polyline that occupies a strip of finite width close to the slip-pulse width; and (4) the assumption that the propagation distance of fault-guided, mostly Rayleigh waves from a failing spot on a fault is determined by the slip-pulse width. Waveforms produced by this model are determined based on the fault asperity failure model after Das and Kostrov. Properties of the model are studied by numerical experiments. At high frequency, simulated source spectra behave as ω ^?2, and acceleration spectra are flat. Their level, at a given seismic moment and rms stress drop, is inversely related to the relative width of the slip pulse. When this width is relatively low, a well-defined second corner frequency (lower cutoff of acceleration spectrum) is seen. The model shows clear dependence of propagation-related directivity on frequency. Between the first and the second corner frequency, amplitude spectra are strongly enhanced for the forward direction; whereas, above the second corner frequency, directivity is significantly reduced. Still, it is not inhibited totally, suggesting incomplete incoherence of the simulated radiator at high frequencies.     

基于Chebyshev自褶积组合窗的有限差分算子优化方法

有限差分法广泛应用于地震波数值模拟、成像和波形反演中,差分数值解的精度直接影响着地震成像和反演的效果.因为有限差分算子可以通过截断伪谱法的空间褶积序列得到,而截断窗函数的属性影响有限差分算子逼近微分算子的精度.具体地讲,窗函数的幅值响应的主瓣和旁瓣决定了有限差分算子逼近的精度,主瓣越窄,旁瓣衰减越大,则有限差分算子逼近微分算子的精度越高,更好地压制数值频散.基于此认识,本文提出了一种基于Chebyshev自褶积组合窗截断逼近的有限差分算子优化方法.Chebyshev自褶积组合窗的主瓣较窄,且旁瓣衰减大,其可通过只调节三个参数,更直观和可视化地控制主瓣和旁瓣的形状,改变有限差分算子逼近微分算子的精度;该窗函数截断逼近的有限差分算子不仅有较大的谱覆盖范围,而且精度误差波动较小,这表明低阶的差分算子可以达到高阶算子的精度,且逼近误差更稳定;从经济上来讲,将有效地减少模拟计算花费,提高计算效率.     

A procedure to reduce side lobes of reflection wavelets: A contribution to low frequency information

Side lobes of the wavelets arise from the lack of low frequency content in a reflection wavelet. They tend to increase the time span of an individual reflection event and interfere with the other primary reflections or side lobes. Furthermore, their trace-by-trace consistency may produce pseudo-reflections and may cause misinterpretations of the side lobes as weak reflections.A procedure in order to improve the low frequency content of the seismic traces by suppressing the side lobe amplitudes based on the complex trace envelope is proposed. Using the average energies of the seismic trace and its envelope, the polarity table of the trace is obtained and used to correct the phase of the envelope. The resultant trace is termed “side lobe reduced (SLR) trace”. The method can be applied to the stack or migrated seismic data by a trace-by-trace basis. The only required parameter of the method is the moving average operator length which is used to calculate average energies of the input traces. In general, shorter operator lengths yield better results when the dominant frequency of the input increases.Results from synthetics and real seismic data sets show that the procedure improves the low frequency components of the input trace and side lobes in the output SLR trace are significantly suppressed. The method may be considered as a seismic amplitude attribute, which aids the interpreter to obtain the true seismic signature of the geological formations by removing the side lobes of the wavelet and restoring the low frequency components if the lower frequencies of deeper reflections are of primary concern.     

Synthesis of accelerograms compatible with the Chinese GB 50011-2001 design spectrum via harmonic wavelets： artificial and historic records

A versatile approach is employed to generate artificial accelerograms which satisfy the compatibility criteria prescribed by the Chinese aseismic code provisions GB 50011-2001. In particular, a frequency dependent peak factor derived by means of appropriate Monte Carlo analyses is introduced to relate the GB 50011 -2001 design spectrum to a parametrically defined evolutionary power spectrum (EPS). Special attention is given to the definition of the frequency content of the EPS in order to accommodate the mathematical form of the aforementioned design spectrum. Further, a one-to-one relationship is established between the parameter controlling the time-varying intensity of the EPS and the effective strong ground motion duration. Subsequently, an efficient auto-regressive moving-average (ARMA) filtering technique is utilized to generate ensembles of non-stationary artificial accelerograms whose average response spectrum is in a close agreement with the considered design spectrum. Furthermore, a harmonic wavelet based iterative scheme is adopted to modify these artificial signals so that a close matching of the signals' response spectra with the GB 50011-2001 design spectrum is achieved on an individual basis. This is also done for field recorded accelerograms pertaining to the May, 2008 Wenchuan seismic event. In the process, zero-phase high-pass filtering is performed to accomplish proper baseline correction of the acquired spectrum compatible artificial and field accelerograms. Numerical results are given in a tabulated format to expedite their use in practice.     

利用张家口地震台体应变观测资料检测地球自由振荡

在保证低频自由振荡信号分辨率,又不对高频自由振荡信号产生抑制效应的前提下,利用张家口地震台体应变观测资料,采用功率谱密度估计方法,获得2011年3月11日日本9.0级大地震激发的₀S₂-₀S₇₄基频球型振荡和17个谐频球型振荡（₃S₂、₅S₃、₂S₁₀、₂S₁₂、₃S₉、₁₁S₁、₇S₁₀、₅S₁₃、₄S₁₈、₅S₁₄、₁₄S₄、₄S₂₄、₁S₃₈、₇S₁₈、₁₄S₈、₉S₁₉、₅S₃₀）,并与地球初步参考模型（PREM）的理论自由振荡周期进行对比,发现与实测振荡周期基本一致。     

基于三元伪随机编码的冲击夯可控震源控制系统设计

冲击夯可控震源具有移动方便、质量轻、输出力大等优点,在城市工程勘察以及中浅层地震勘探等领域具有一定的应用前景.其激励信号主要基于二元伪随机编码技术,由于旁瓣效应导致相关干扰严重、地震记录信噪比低等问题,制约了冲击夯震源的推广应用.本文针对传统控制方法的不足,开展了基于三元伪随机的冲击夯可控震源编码技术和编码匹配控制方法研究,并在此基础上设计和实现了相应的控制系统.野外实验结果表明:相比于二元伪随机编码控制方法,三元伪随机编码控制方法得到的地震子波的主旁瓣比提高了4.04 dB;震源信号穿透力强,在测线远端处能量约为30磅锤击震源的100倍,约为二元伪随机方法的4倍;单炮地震记录中干扰抑制能力强,信噪比显著提升,子波频带宽,提高了分辨率,在一定程度上提高了地震勘探效果.     

Frequency-specified EOF analysis and its application to Pacific decadal oscillation

A frequency-specified empirical orthogonal function (FSEOF) analysis is proposed in this study. The aim of FSEOF is to specify a prescribed-band of frequency in leading principal components with less information losing at the ends of the data, thus well characterizing the signals of interest. The FSEOF can well capture prescribed variability in leading modes, and has intrinsic merits in resolving frequency-related modes, especially those associated with low frequency oscillations. An application of the FSEOF to the tropical and northern Pacific sea surface temperature shows that this new method can successfully separate Pacific decadal oscillation (PDO) mode from the El Niño-Southern oscillation mode, and clearly detect all regime shifts of PDO in the past century.     

三维随钻反射声波成像测井的数值模拟

采用有限差分方法对基于圆弧片状声源和接收器的三维随钻反射声波成像测井进行模拟,研究了反射信号的幅度、相位等参数随方位和源距的变化规律,着重分析了利用该方法在水平井中对地层界面进行探测的可行性.研究结果表明,钻铤的存在使得圆弧片状声源能够向固定方位辐射声场,其主瓣三分贝角宽窄,旁瓣级低,向目的方位辐射的纵波场的幅度约为传统环状声源的0.6倍,适用于三维随钻反射声波成像测井;对于本文计算的井孔模型,反射波信号约为井孔导波信号的1/100;随着源距的增加,反射纵波幅度逐渐减小,转换波(P-SV、SV-P)的幅度先增加后减小,反射SV波的幅度增加,建议在实际应用中,选择合适源距的波形进行处理,并对其他非目的波动进行压制,以期获得更好的成像效果.本文模拟了在水平井中对地层上下界面进行探测的例子,结果显示,反射波纵波信号有较好的方位分辨率,能够准确获得井外波阻抗不连续界面的方位,而且对上、下界面的成像互不影响.     

The lobes of lava flows on Earth and Olympus Mons,Mars

The lobate distal margins of lava flows provide a useful source of morphological information on the rheology of the lava if the lobes are assumed to represent the arrest of free-flowing isothermal Bingham fluids on a slope. The widths of lobes are a more useful practical index than lobe thicknesses because they are about an order of magnitude larger and can be more accurately measured from aerial photographs and other remote images. Lobes do not suffer from the changes in morphology that channels undergo during the course of eruptions. A terrestrial data set of flow lobe and ancillary measurements from lavas throughout the range alkali olivine basalt to rhyolite shows some features that are predicted by the isothermal Bingham fluid model. These are correlation of width and thickness over more than two orders of magnitude and essentially no correlation of aspect ratio with slope. There is a positive correlation of lobe width with silica content of the lava. From a data set of measurements on lava flow lobes from the Martian volcano Olympus Mons the mean value of aspect ratio (0.07) was found to be significantly less than that for the terrestrial data set (0.19). Higher general levels of effusion rate on Olympus Mons are probably the factor responsible. After normalisation, lobe widths on Olympus Mons are found to be largely equivalent to those expected for terrestrial flows with andesitic/basaltic silica contents.     

Source characterisation of low frequency events at Stromboli and Vulcano Islands (Isole Eolie Italy)

The discussion about the source of low frequency events generally wrecorded on active volcanoes is still open and needs deeper understanding of the phenomena involved in their generation. Most of the models view such a phenomenon as a source effect (oscillation of volcanic fluids in conduits or cracks), although a different explanation as a path or site effect exists. In the present paper we analysed 26 seismic signals recorded at Vulcano and 60 at Stromboli in order to put some constraints on the functional shape of the recorded signals. They evidence all the characteristics of the low frequency events. The spectral analysis reveals sharp peaks in the range 0.5–4 Hz, while the cepstra suggest that the signals are composed by a two-sine kind function. This suggestion is confirmed by the two-dimensional projections of the reconstructed phase space. The correlation dimension of the attractor is very close to 3 for both the volcanoes confirming the existence of a toroidal structure in the phase space. This implies that we can suggest as a model for the low frequency events source a physical mechanism very similar to a Duffing oscillator or any other quasiperiodic one. In particular in the cases of the analysed volcanoes we recognise two independent oscillations.     

强震动记录H/V谱比法计算处理的若干关键环节

强震动记录H/V谱比法自提出以来,已广泛应用于地震工程各研究领域中。但对数据处理的2个关键环节——Taper预处理及傅氏谱平滑未有详细研究。因此,本文针对强震动记录H/V谱比法计算涉及的重要数据处理过程,对四川地区19个强震动台站在汶川地震余震中获取的642组强震动记录开展研究。研究实例表明:S波H/V谱比振幅在周期 < 1s时高于全时程,论证计算H/V谱比时截取S波窗口的必要性;S波窗口的截断会引起傅里叶振幅谱的边瓣效应,若不加以处理,将显著影响低频部分H/V谱比结果,Taper预处理对于消除这种截断误差具有良好效果;在兼顾平滑效果及卓越周期识别准确度的基础上,通过不同带宽的Parzen窗试算,认为0.5Hz带宽宜用于傅里叶H/V谱比曲线平滑。     

基于递归高通滤波的经验模态分解及其在地震信号分析中的应用

将地震信号分解成包含频谱互不重叠的单主周期的分量有利于地震信号的分析.分析了经验模态分解(EMD)中模态混叠的内在原因和已有的解决方法,梳理了解决模态混叠的思路框架,进而提出了一种新的基于输入递归高通滤波的EMD算法.首先用递归高通滤波器将信号预分解成频率由高到低的多个分量,实现信号的等价带通滤波,再用EMD对各带通分量按频率高低逐级递归筛分,获得完备的经验模态分量.通过合成信号和地震信号的仿真实验表明,该算法较好地克服了模态混叠,获得了频谱互不重叠的单主周期分量,并成功用于震相分离和分析,为地震信号分析提供了一种新思路.     

全球地震灾害发展趋势综述

基于EM-DAT（OFDA/CRED）国际灾害数据库及美国地质勘探局（USGS）给出的数据,提取全球1970—2018年干旱、地震、极端温度、极端气候、洪水、滑坡、火山活动、火灾和块体运动9种自然灾害的相关数据,并进行综合分析,着重分析死亡人数和经济损失。分析结果表明,21世纪以来地震灾害造成的损失最大。此外,2000—2017年全球重大地震尤其是9次特大地震的分析结果显示,可有效减轻地震灾害损失的措施至少包括建立地震预警机制、建设韧性城乡、建立完善的风险排查机制。     

GPR spectral analysis for clay content evaluation by the frequency shift method

A recent approach relates the shift of the frequency peak of the Ground Penetrating Radar (GPR) spectrum with the increasing of the moisture content in the soil. The weakness characterizing this approach is represented by the needs of high resolution signals, whereas GPR spectra are affected by low resolution. The novelty introduced by this work is twofold. First, we evidence that clay content information is present in the location where the maximum amplitude of the GPR spectra occurs. Then, we propose three super resolution methods, namely parabolic, triangular, and sinc-based interpolators, to further refine the location of the frequency peak. In fact, it is really important to be able to find this location quite precisely, to obtain accurate estimates of clay content. We show that the peak location can be found best through sinc-interpolation in the frequency domain of the measured data. Our experimental results confirm the effectiveness of the proposed approach to resolve a frequency shift in the GPR spectrum, even for a small amount of clay.     

基于AR模型的相干函数有效频段范围的确定

目前人们在进行地震动相干函数模型参数的拟合时,选取的频段范围存在很大差异,而确定有效的频段范围对相干函数模型拟合结果的合理性很重要。本文利用AR模型(Autoregressive Model,自回归模型)计算地震动的功率谱,提出了根据功率谱"信噪比(SNR)"确定相干函数有效频段范围的方法。本文的信噪比中的"噪",专指AR模型中的激励白噪声,用于衡量AR模型中某一频率地震动功率谱与激励白噪声功率谱之间的比例。定义信噪比SNR=0时对应的频率为有效频段的最高频率,大于最高频率的频率成分,被当作是地震波中的随机成分,可以不考虑地震动的相关性。采用这一方法,对SMART-1第45次地震记录的不同台站间距下的地震波进行了功率谱估计,根据信噪比确定出了有效频段范围,并计算了相应的相干函数,结果表明此方法是可行的。     

Coda pattern and multipath propagation of Rayleigh waves at NORSAR

The coda of Rayleigh waves from fifteen earthquakes recorded at the Norwegian Seismic Array (NORSAR) have been analyzed in wavenumber space at periods of 40 and 20 sec. The power at 40 sec drops off faster vs. time, which reduces the probability of interference between events. On the other side, the capability of the array to resolve signals under various conditions is better at 20 sec. Since also the frequency distribution of signal power varies, one cannot determine any specific frequency as generally having the best signal/interference ratio. The detection problem is also complicated by considerable multipath propagation, which is most severe at 20 sec. Multipath arrivals with as much as 40–60° azimuthal deviation are frequently identified. Travel path solutions for different events are proposed, and usually the rays have been found to be refracted or reflected at continental boundaries. An atmospheric nuclear explosion from Lop Nor has been used to illustrate these various aspects of the problem of detecting one Rayleigh wave in the presence of another.     

Seismic low-frequency-based calculation of reservoir fluid mobility and its applications

Low frequency content of seismic signals contains information related to the reservoir fluid mobility. Based on the asymptotic analysis theory of frequency-dependent reflectivity from a fluid-saturated poroelastic medium, we derive the computational implementation of reservoir fluid mobility and present the determination of optimal frequency in the implementation. We then calculate the reservoir fluid mobility using the optimal frequency instantaneous spectra at the low-frequency end of the seismic spectrum. The methodology is applied to synthetic seismic data from a permeable gas-bearing reservoir model and real land and marine seismic data. The results demonstrate that the fluid mobility shows excellent quality in imaging the gas reservoirs. It is feasible to detect the location and spatial distribution of gas reservoirs and reduce the non-uniqueness and uncertainty in fluid identification.     

广义S变换域有色噪声与信号识别方法

为研究广义S变换域有色噪声与信号识别问题,首先推导白噪声在S变换和广义S变换下平均功率谱的统计规律,白噪声的平均功率谱与频率呈线性关系. 然后从理论上定性分析一般的有色噪声功率谱的分布特性,得出在广义S变换域有色噪声的功率谱服从自由度为2的χ2分布的规律, 并用Monte Carle方法进行了验证. 在上述工作基础上,本文提出了利用噪声和有效信号统计特性的差别,在广义S变换域中区分噪声和信号的方法,并用模型数据证明了方法的有效性.     

Evidence for gas influence on volcanic seismic signals recorded at Stromboli

The meaning of the large variety of seismic waveforms showing different frequencies associated with volcanic activity is still uncertain. No definitive model for source dynamics has been proposed yet. At present, seismic models explaining the origin of the spectral content of the seismic signal are mainly linked to geometrical features of the volcanic conduit and to resonant effects induced by pressure fluctuations in a fluid-filled conduit. Such models assume the physical system to be in a steady state over a long interval of time. At Stromboli, the seismicity produced by each of the three active vents is not stable and can suddenly change in time. Therefore, the application of stable resonator models appears to be unwarranted.On the basis of infrared image analyses, atmospheric pressure, and seismic wavefield signals, we show that different frequency contents and different explosive styles occur at Stromboli at the same time at different vents. Moreover, we give evidence to support the idea that seismicity and explosivity are both controlled by a variable gas flow regime released during explosions at the top of the magma column. We have recognized two main pressure regimes, controlling the explositivity at Stromboli: one is impulsive, short and possibly produced by a gas accumulation beneath a cap rock; the other has an intermittent regime feature, and lasts longer. We demonstrate how the first one generates a monochromatic low-frequency wavefield, while the second shows a high-frequency spectrum where the frequency content depends on pressure fluctuations and on pressure gradient. We suggest different pressure growth and gas flow in the magma as the common source for both explosive style and seismic wavefield.