Analytical expressions for the borehole seismic signatures excited by an explosive source buried in an elastic half‐space

Borehole guided waves that are excited by explosive sources outside of the borehole are important for interpreting borehole seismic surveys and for rock property inversion workflows. Borehole seismograms are typically modelled using numerical methods of wave propagation. In order to benchmark such numerical algorithms and partially to interpret the results of modelling, an analytical methodology is presented here to compute synthetic seismograms. The specific setup is a wavefield emanating from a monopole point source embedded within a homogeneous elastic medium that interacts with a fluid‐filled borehole and a free surface. The methodology assumes that the wavelength of the seismic signal is much larger than the borehole radius. In this paper, it is supposed that there is no poroelastic coupling between the formation and the borehole. The total wavefield solution consists of P, PP, and PS body waves; the surface Rayleigh wave; and the low‐frequency guided Stoneley wave (often referred as the tube wave) within the borehole. In its turn, the tube wave consists of the partial responses generated by the incident P‐wave and the reflected PP and PS body waves at the borehole mouth and by the Rayleigh wave, as well as the Stoneley wave eigenmode. The Mach tube wave, which is a conic tube wave, additionally appears in the Mach cone in a slow formation with the tube‐wave velocity greater than the shear one. The conditions of appearance of the Mach wave in a slow formation are formulated. It is shown that the amplitude of the Mach tube wave strongly depends on Poisson's ratio of the slow surrounding formation. The amplitude of the Mach tube wave exponentially decreases when the source depth grows for weakly compressible elastic media with Poisson's ratio close to 0.5 (i.e., saturated clays and saturated clay soils). Asymptotic expressions are also provided to compute the wavefield amplitudes for different combinations of source depth and source‐well offset. These expressions allow an approximate solution of the wavefield to be computed much faster (within several seconds) than directly computing the implicit integrals arising from the analytical formulation.     

Nature of the scattered seismic response from zones of random clusters of cavities and fractures in a massive rock

The scattering of elastic energy by random clusters of fractures and/or cavities in a massive rock is studied. The interpretation of the scattered seismic response reveals crucial information about the clusters of inhomogeneities (fractures/cavities), which may correspond to reservoirs. The study is based on a new two‐dimensional numerical‐modelling method that relaxes the constraints on the location and orientation of the inhomogeneities, accounts for inhomogeneities that have almost no volume but a finite surface area (fractures) and improves the accuracy of the calculation when the size of the inhomogeneities is comparable to the mesh size. It is shown that the nature of the seismic response of zones of diffuse fracturing and/or cavities is associated with the non‐uniformity of micro‐inhomogeneities in such zones; accumulations of these micro‐inhomogeneities are known as clusters. The relationship between the non‐uniformity of micro‐inhomogeneities and the strength of the seismic response has been established and measured. Considerable differences in the structure of the seismic response of zones of diffuse fracturing and diffuse cavities have been identified. Converted PS‐waves dominate in the scattered wavefield associated with fractures. This is explained, as the modelling results show, by a greater transparency of fluid‐filled fractures, which reduces the reflected energy of compressional waves. The wavefield associated with cavities is characterized by the predominance (in terms of strength) of compressional PP‐waves. The strength of converted PS‐waves in the scattered wavefields for both media is approximately the same. On the whole, according to the results of the modelling, the energy of the scattered response of fractured reservoirs is considerably less (about two times) than that of cavernous reservoirs.     

THEORETICAL REFLECTION SEISMOGRAMS FOR ELASTIC MEDIA*

Theoretical seismograms for an explosive source in a multilayered elastic medium are constructed by Fourier synthesis and plane wave superposition. The calculation scheme which builds up a reflection matrix layer by layer in the frequency and wave number domain allows the inclusion of attenuation and a choice of the level of internal multiples in each layer. Comparative calculations of theoretical seismograms for an elastic model and in the acoustic approximation, neglecting shear, show that the main differences arise at large offsets. The inclusion of shear waves leads to lower reflected P wave amplitudes at the end of the spread but only small amounts of converted phases.     

Complex frequency-shifted multi-axial perfectly matched layer for frequency-domain seismic wavefield simulation in anisotropic media

Seismic anisotropy has an important influence on seismic data processing and interpretation. Although the frequency-domain seismic wavefield simulation has a problem of solving the large scale linear sparse matrix due to the computational limitations, it has some advantages over the time-domain seismic wavefield simulation including efficient inversion using only a limited number of frequency components and easy implementation of multiple sources. To accurately simulate seismic wave propagation in the frequency domain, we also need to choose the absorbing boundary conditions to absorb artificial reflections from edges of the model as we do in the time domain. Compared with the classical boundary conditions including the perfectly matched layer and complex frequency-shifted perfectly matched layer, the complex frequency-shifted multi-axial perfectly matched layer has been proven to effectively suppress the unwanted reflections at grazing incidence and solve the instability problem in the time-domain seismic numerical modelling in anisotropic elastic media. In this paper, we propose to extend the complex frequency-shifted multi-axial perfectly matched layer absorbing boundary condition to the frequency-domain seismic wavefield simulation in anisotropic elastic media. To test the validity of our proposed algorithm, we compare the results (snapshots and seismograms) of the frequency-domain seismic wavefield simulation with those of the time-domain modelling. The model studies indicate that the complex frequency-shifted multi-axial perfectly matched layer absorbing boundary condition is stable in the frequency-domain seismic wavefield simulation in anisotropic media, and provides better absorbing performance than the complex frequency-shifted perfectly matched layer boundary condition.     

Visco‐acoustic prestack reverse‐time migration based on the time‐space domain adaptive high‐order finite‐difference method

It is important to include the viscous effect in seismic numerical modelling and seismic migration due to the ubiquitous viscosity in an actual subsurface medium. Prestack reverse‐time migration (RTM) is currently one of the most accurate methods for seismic imaging. One of the key steps of RTM is wavefield forward and backward extrapolation and how to solve the wave equation fast and accurately is the essence of this process. In this paper, we apply the time‐space domain dispersion‐relation‐based finite‐difference (FD) method for visco‐acoustic wave numerical modelling. Dispersion analysis and numerical modelling results demonstrate that the time‐space domain FD method has great accuracy and can effectively suppress numerical dispersion. Also, we use the time‐space domain FD method to solve the visco‐acoustic wave equation in wavefield extrapolation of RTM and apply the source‐normalized cross‐correlation imaging condition in migration. Improved imaging has been obtained in both synthetic and real data tests. The migration result of the visco‐acoustic wave RTM is clearer and more accurate than that of acoustic wave RTM. In addition, in the process of wavefield forward and backward extrapolation, we adopt adaptive variable‐length spatial operators to compute spatial derivatives to significantly decrease computing costs without reducing the accuracy of the numerical solution.     

低信噪比海底多分量地震数据波场分离方法

以多分量地震观测为基础,联合纵波和转换横波数据能更有效地估计地下介质的弹性和物性参数,提升地质构造成像与油气储层描述的精度.在海底多分量地震数据处理过程中,观测记录的上-下行波分解和P/S波分离可压制水层鸣震以及P与S波之间的串扰,对偏移成像和纵横波速度建模至关重要.但受海底环境、仪器与观测因素共同影响,许多海底多分量...     

Hydrothermal origin for sustained Long-Period (LP) activity at Campi Flegrei Volcanic Complex,Italy

We present a detailed analysis of the source properties of Long-Period (LP) signals recorded at Campi Flegrei Caldera (Italy) during the last (2005–2006) mini-uplift episode. Moment Tensor inversion via full-waveform modelling of broad-band seismograms indicates a crack-like source with a significant volumetric component. From auto-regressive modelling of the signal's tail we evaluate the dominant frequency and the attenuation factor of the oscillating source. Considering the acoustic properties of a fluid-filled crack, these values are consistent with the resonant oscillations of a crack filled by a water–gas mixture at variable gas–volume fraction. For these fluids, the crack size would be on the order of 40–420 m, a size range which is consistent with the spatial spreading of LP hypocenters. Analysis of temporally-correlated time series of seismological and geochemical data indicates that climaxing of LP activity was preceded by swarms of volcano-tectonic (VT) events and rapidly followed by a consistent increase of both thermal emissions and gas fluxes recorded at the surface (1 month — 2/3 days, respectively). Following these observations, we propose a conceptual model where VT activity increases permeability of the medium, thus favouring fluid mobility. As a consequence, the hydrothermal system experiences pressure perturbations able to trigger its resonant, LP oscillations.     

The dynamic response of a fluid‐filled borehole under a normal point load on the free surface

The dynamic response of a semi‐infinite fluid‐filled borehole embedded in an elastic half‐space under a concentrated normal surface load is analysed in the long‐wavelength limit. The solution of the problem is obtained with integral transforms in the form of a double integral with respect to the slowness and frequency. The partial P‐ and SV‐wave responses are further transformed to path integrals along Cagniard paths in the complex slowness plane. Unlike the traditional Cagniard‐de Hoop technique based on the Laplace transform of time dependence, this paper is based on the Fourier transform. The tube‐wave response is presented as a causal integral over a slowness range. The resultant representation in the time‐domain is suitable for the numerical evaluation of the complete response in the fluid‐filled borehole, especially at large distances. Asymptotic analysis of seismic phases arising in the borehole is performed on the basis of the obtained solution. The complete asymptotic wavefield consists in P‐ and SV‐waves, the Rayleigh wave and the low‐frequency Stoneley (tube) wave. Pressure synthetics obtained by the use of the asymptotic formulas are shown to be in good agreement with straightforward calculations.     

Elastic wave mode separation for tilted transverse isotropy media

Seismic waves propagate through the earth as a superposition of different wave modes. Seismic imaging in areas characterized by complex geology requires techniques based on accurate reconstruction of the seismic wavefields. A crucial component of the methods in this category, collectively known as wave‐equation migration, is the imaging condition that extracts information about the discontinuities of physical properties from the reconstructed wavefields at every location in space. Conventional acoustic migration techniques image a scalar wavefield representing the P‐wave mode, in contrast to elastic migration techniques, which image a vector wavefield representing both the P‐ and S‐waves. For elastic imaging, it is desirable that the reconstructed vector fields are decomposed into pure wave modes, such that the imaging condition produces interpretable images, characterizing, for example, PP or PS reflectivity. In anisotropic media, wave mode separation can be achieved by projection of the reconstructed vector fields on the polarization vectors characterizing various wave modes. For heterogeneous media, because polarization directions change with position, wave mode separation needs to be implemented using space‐domain filters. For transversely isotropic media with a tilted symmetry axis, the polarization vectors depend on the elastic material parameters, including the tilt angles. Using these parameters, we separate the wave modes by constructing nine filters corresponding to the nine Cartesian components of the three polarization directions at every grid point. Since the S polarization vectors in transverse isotropic media are not defined in the singular directions, e.g., along the symmetry axes, we construct these vectors by exploiting the orthogonality between the SV and SH polarization vectors, as well as their orthogonality with the P polarization vector. This procedure allows one to separate all three modes, with better preserved P‐wave amplitudes than S‐wave amplitudes. Realistic synthetic examples show that this wave mode separation is effective for both 2D and 3D models with strong heterogeneity and anisotropy.     

A comparison of field-line resonances observed at the Goose Bay and Wick radars

Previous observations with the Goose Bay HF coherent-scatter radar have revealed structured spectral peaks at ultra-low frequencies. The frequencies of these spectral peaks have been demonstrated to be extremely consistent from day to day. The stability of these spectral peaks can be seen as evidence for the existence of global magneto spheric cavity modes whose resonant frequencies are independent of latitude. Fieldline resonances occur when successive harmonics of the eigenfrequency of the magnetospheric cavity or waveguide match either the first harmonic eigenfrequency of the geomagnetic field lines or higher harmonics of this frequency. Power spectra observed at the SABRE VHF coherent-scatter radar at Wick, Scotland, during night and early morning are revealed to show similarly clearly structured spectral peaks. These spectral peaks are the result of local field-line resonances due to Alfvén waves standing on magnetospheric field lines. A comparison of the spectra observed by the Goose Bay and Wick radars demonstrate that the frequencies of the field-line resonances are, on average, almost identical, despite the different latitudinal ranges covered by the two radars. Possible explanations for the similarity of the signatures on the two radar systems are discussed.     

Source location using time‐reverse imaging

We present the chain of time‐reverse modeling, image space wavefield decomposition and several imaging conditions as a migration‐like algorithm called time‐reverse imaging. The algorithm locates subsurface sources in passive seismic data and diffractors in active data. We use elastic propagators to capitalize on the full waveforms available in multicomponent data, although an acoustic example is presented as well. For the elastic case, we perform wavefield decomposition in the image domain with spatial derivatives to calculate P and S potentials. To locate sources, the time axis is collapsed by extracting the zero‐lag of auto and cross‐correlations to return images in physical space. The impulse response of the algorithm is very dependent on acquisition geometry and needs to be evaluated with point sources before processing field data. Band‐limited data processed with these techniques image the radiation pattern of the source rather than just the location. We present several imaging conditions but we imagine others could be designed to investigate specific hypotheses concerning the nature of the source mechanism. We illustrate the flexible technique with synthetic 2D passive data examples and surface acquisition geometry specifically designed to investigate tremor type signals that are not easily identified or interpreted in the time domain.     

Data acquisition and pre-processing required for simultaneous P-SV inversion

The goal of seismic reflection surveys is the derivation of petrophysical subsurface parameters from surface measurements. Today's well established technique in data acquisition, as well as processing terms, is based on the acoustic approximation to the real world's wave propagation. In recent years a lot of work has been done to extend the technique to the elastic approximation. There was especially an important trend towards elastic inversion techniques operating on plane-wave seismograms, called simultaneous P-SV inversion (or short P-SV inversion) within this paper. Being still under investigation, some important aspects of P-SV inversion concerning data acquisition as well as pre-processing, should be pointed out. To fit the assumptions of P-SV inversion schemes, at least a two-dimensional picture of the reflected wavefield with vertical and in-line horizontal receivers has to be recorded. Moreover, the theoretical work done suggests that in addition to a survey with a compressional wave source, a second survey should be done using sources radiating vertically polarized shear waves, is needed. Finally, proper slant stacking must be performed to get plane-wave seismograms. The P/S separated plane-wave seismograms are then well prepared for feeding into the inversion algorithms. P/S separated planewave seismograms are then well prepared for feeding into the inversion algorithm.s In this paper, a tutorial overview of the data acquisition and pre-processing in accordance with the P-SV inversion philosophy is given and illustrated using synthetic seismograms. A judgement on the feasibility of the P-SV inversion philosophy must be left to ongoing research.     

基于改进BISQ机制的双相HTI介质波传播伪谱法模拟与特征分析

改进BISQ(Biot-Squirt)机制在不引入特征喷流长度的情况下,将含流体孔隙介质中Biot流动和喷射流动两种重要的力学机制有机地结合起来,且各相关参数具有明确物理意义和可实现性.本文将改进BISQ机制一维孔隙流体压力公式推广到三维具有水平对称轴横向各向同性介质(HTI介质)情况,结合裂缝各向异性理论,给出了基于改进BISQ机制的双相HTI介质模型及其二维三分量波传播方程,采用伪谱法求解该方程,进行了不同相界、不同频率以及双层地质结构情况下该类介质中波场的数值模拟与特征分析.数值模拟结果表明:伪谱法模拟精度高,压制网格频散效果好,可以得到高精度的波场快照和合成记录;基于改进BISQ机制的双相HTI介质模型兼具裂缝各向异性特征和孔隙弹性特征,其为从双相各向异性理论角度深入研究裂缝性储层的地震响应奠定了理论基础.     

2D acoustic‐elastic coupled waveform inversion in the Laplace domain

Although waveform inversion has been intensively studied in an effort to properly delineate the Earth's structures since the early 1980s, most of the time‐ and frequency‐domain waveform inversion algorithms still have critical limitations in their applications to field data. This may be attributed to the highly non‐linear objective function and the unreliable low‐frequency components. To overcome the weaknesses of conventional waveform inversion algorithms, the acoustic Laplace‐domain waveform inversion has been proposed. The Laplace‐domain waveform inversion has been known to provide a long‐wavelength velocity model even for field data, which may be because it employs the zero‐frequency component of the damped wavefield and a well‐behaved logarithmic objective function. However, its applications have been confined to 2D acoustic media. We extend the Laplace‐domain waveform inversion algorithm to a 2D acoustic‐elastic coupled medium, which is encountered in marine exploration environments. In 2D acoustic‐elastic coupled media, the Laplace‐domain pressures behave differently from those of 2D acoustic media, although the overall features are similar to each other. The main differences are that the pressure wavefields for acoustic‐elastic coupled media show negative values even for simple geological structures unlike in acoustic media, when the Laplace damping constant is small and the water depth is shallow. The negative values may result from more complicated wave propagation in elastic media and at fluid‐solid interfaces. Our Laplace‐domain waveform inversion algorithm is also based on the finite‐element method and logarithmic wavefields. To compute gradient direction, we apply the back‐propagation technique. Under the assumption that density is fixed, P‐ and S‐wave velocity models are inverted from the pressure data. We applied our inversion algorithm to the SEG/EAGE salt model and the numerical results showed that the Laplace‐domain waveform inversion successfully recovers the long‐wavelength structures of the P‐ and S‐wave velocity models from the noise‐free data. The models inverted by the Laplace‐domain waveform inversion were able to be successfully used as initial models in the subsequent frequency‐domain waveform inversion, which is performed to describe the short‐wavelength structures of the true models.     

THE EXACT SEISMIC RESPONSE OF AN OCEAN AND A N-LAYER CONFIGURATION*

The space-time acoustic wave motion generated by an impulsive monopole source is calculated with the aid of the Cagniard-de Hoop technique. Two configurations with plane interfaces are discussed: an air/fluid/solid configuration with the source and the receiver located in the fluid layer; and a stack of n fluid layers between two acoustic half-spaces where the source and the receiver are located in the upper half-space. Synthetic seismograms are generated for the pressure of the reflected wavefield, using the source signature of an airgun.     

长白山天池火山区的谐频事件

通过对长白山天池火山地区2002、2003和2005年夏季3期流动地震观测资料的频谱分析,发现火山口附近存在一种在频率域中形态比较特殊的地震事件,其频谱由1组等间隔的谱峰构成,峰值振幅随频率缓慢变化,形态与时间域中的谐波信号相似,我们把这种地震事件称为谐频事件。在3个夏季的流动观测中,共发现38个谐频事件,且这些事件大多与震群活动有关。分析表明,谐频地震频谱中的谐波现象与震源有关,可能是岩石破裂过程中,在特殊激发条件下,裂缝壁和裂缝内部岩浆或热液的压力扰动相互作用产生的。我们认为近年来长白山天池地震活动的突然增加和谐频事件的出现与深部岩浆的侵入活动有关     

Creation of a Digital Database for XXth Century Historical Earthquakes Occurred in the Iberian Area

—The problems of recovering the seismic information contained in the old seismograms through their digitization and processing by computer methods are discussed. We present the main principles of a simple manual technique for digitization of early seismic records of the Wiechert seismograph. Detrending of the zero-line slope, circular arc removal, smoothing and interpolation treatment of the digital data are made. The accuracy of the digitizing process is assessed and its reliability is tested by a comparison with automatically obtained digital data and their spectral amplitudes. The deconvolution of the seismograph response has allowed us to obtain the time variation of ground motion which is then contrasted with direct measurements of ground motion displacement amplitudes given in the old-time bulletins. We have created a digital database for historical earthquakes which occurred in the Iberian area during the period 1912–1940 and recorded by the Wiechert seismograph at the Geophysical Observatory of Toledo, Spain. It contains the following output data the digitized original records; the geometrically corrected and interpolated data; the time variation of ground motion; maximum amplitudes and corresponding periods; total duration of the seismic oscillations and amplitude spectra. We carry out magnitude estimates and give formulae for magnitude classification based on the signal duration and on the maximum ground displacement amplitude. We also perform seismic moment determinations by spectral analysis of waveforms and propose a new seismic moment-magnitude relation.     

Numerical modelling of interface scattering of seismic wavefield from a random rough interface in an acoustic medium: comparison between 2D and 3D cases

Seismic wavefield scattering from a statistically randomly rough interface in a multilayered piecewise homogeneous medium is studied in 3D. The influence of the surface roughness on the scattered wavefield is analysed numerically by using a finite‐difference operator in the acoustic domain. Since interface scattering in the real practical sense is a 3D physical phenomenon, we show in this work that the scattering response of a randomly rough interface is not the same in 3D situations as in the 2D cases described in some earlier works. For a given interface roughness height in 3D, an interface roughness height at least three times greater is required to produce an equivalent phase scattering effect in 2D situations, for a given correlation length of the interface roughness scale. Based on observations from spectral analysis, we show that scattering results principally in de‐phasing and frequency band‐limiting of the incident wavefront, the frequency band‐limiting properties being comparable to cases reported in the literature for absorption and thin‐layer filtering. The interface scattering phenomenon should be critically considered when using amplitude and phase information from seismic signal during inversion processes.     

部分饱和孔隙岩石中声波传播数值研究

利用基于Biot理论的孔隙弹性介质的高阶交错网格有限差分算法,模拟了具有随机分布特征的多种流体饱和岩石中声波在中心频率分别为25,50,75,100kHz时的声场特点. 对于一个由两种成分（气和水）饱和的岩石模型, 假设含不同流体的孔隙介质随机分布在不同的宏观区域,该区域尺度远小于计算的声波波长;组成模型的两种随机分布介质具有相同的固体骨架参数、渗透率和孔隙度,但分别被具有不同压缩性、密度和黏滞系数特性的水和气饱和. 计算和统计分析结果表明,在两种孔隙成分随机分布的部分饱和条件下纵波速度比较复杂,除骨架参数外,其变化主要依赖于中心频率、各种孔隙成分饱和度及饱和介质的速度. 比较该随机分布模型、Gassmann理论模型和White的“气包”模型,发现三种模型得到的纵波速度和衰减规律有较好的定性对应关系. 其次,按照这种随机计算模型的处理方法,本文还首次计算了一个三种流体成分充填饱和的例子,即岩石模型中的孔隙被水、油和气部分饱和,计算时保持模型含水饱和度不变而只改变含油和含气饱和度. 在这种计算条件下,纵波速度随中心频率呈增大的趋势但有起伏变化. 声场快照显示了各种转换波在多种孔隙成分充填（两种和三种孔隙成分）岩石中的声场特征,复杂的水-油-气界面的非均匀分布对声场有重要影响,纵波能量主要转换形成了较为复杂的多种慢纵波和横波.     

用于声波方程数值模拟的时间-空间域有限差分系数确定新方法

声波方程数值模拟已广泛应用于理论地震计算,同时构成了地震逆时偏移成像技术的基础.对于有限差分法而言,在满足一定的稳定性条件时,普遍存在着因网格化而形成的数值频散效应.如何有效地缓解或压制数值频散是有限差分方法研究的关键所在.为精确求解空间偏导数,相继发展了高阶差分格式优化方法和伪谱方法.近期,为更好地缓解数值频散,提出了时间-空间域有限差分方法,该方法采用了泰勒展开近似方法来确定有限差分格式系数,因而只能保证在一定的小范围内很好的拟合波场传播规律.为进一步压制数值频散效应,本文引入了时间-空间域特定波数点满足频散关系的方法,根据震源、波速和网格间距确定波数范围,同时考虑了多个传播角度,然后建立方程确定了相应的有限差分格式系数,使得差分系数能在更大范围符合波场传播规律.通过频散分析和正演模拟,验证了本文方法的有效性.