多次各向异性散射模式对S波能量密度包络曲线的影响

在多次各向异性散射理论的基础上,本文重新推导了方向性散射系数的球函数展开式.引入特征时间的概念,来定义震源处初始地震波脉冲宽度,并在地震波能量密度积分方程中引入任意给定频率的初始脉冲能量谱密度的解析表达.通过离散波数方法求解了修正的地震波能量密度积分方程.基于积分方程的数值解,研究了不同散射模式对S波能量密度包络曲线的影响.计算结果表明:随着震源距的增加,在S波到时之后,多次各向异性散射模式与多次各向同性散射模式合成的能量密度包络差异逐渐增大.其中通过多次前散射模式,我们可以得到不同震源距的尾波能量密度包络的同一衰减趋势,以及S波能量密度包络随着震源距的增加而出现的展宽现象.最后,利用美国内华达州Wells地震余震的台站记录验证了多次前散射模式的实用性与有效性.     

Modeling Full Seismogram Envelopes Using Radiative Transfer Theory with Born Scattering Coefficients

The equation of radiative transfer is used to model the transport of seismic energy in 2-D and 3-D acoustic random media. Monte-Carlo solutions of this equation using non-isotropic Born scattering coefficients are compared to three analytical solutions: Markov approximation, radiative transfer theory with isotropic scattering coefficients, and diffusion approximation. Additionally, we compare to finite differences solutions of the full wave equation in 2-D. We find a good correspondence of radiative transfer theory to Markov approximation for the case of multiple forward scattering. The comparison to radiative transfer theory with isotropic scattering coefficients, a model frequently used in data analysis, demonstrates that in the case of forward scattering the isotropic scattering model is not better than a diffusion approach. To compare radiative transfer theory with non-isotropic scattering coefficients to finite differences solutions of the full wave equation, the finite source duration and the bandpass filter process as well as the normalization of absolute amplitudes are explicitely taken into account. We find a good coincidence of both theories for scattering parameters, which are realistic for usual Earth crust. The theory correctly describes the unscattered direct wavefront, the envelope broadening caused by multiple forward scattering, as well as the late coda caused by multiple wide angle scattering. For strong scattering, which can be expected for very heterogeneous media such as strato volcanoes, the solutions of radiative transfer differ from the more complete solutions of the full wave equation.     

不同散射模式下S波包络合成

为揭示地震波在地壳小尺度非均匀介质中的散射过程,更准确地描述地震波的包络展宽现象,本文基于多次各向异性散射理论,采用离散波数法求解能量密度积分方程,选取高斯型自相关函数表征的散射模式,得到S波能量密度包络.基于此,本文首先分析了单次散射和多次散射在形成S波能量密度包络中的贡献规律;然后探讨了吸收系数和总散射系数对合成S...     

Seismic wave scattering inversion for fluid factor of heterogeneous media

Elastic wave inverse scattering theory plays an important role in parameters estimation of heterogeneous media. Combining inverse scattering theory, perturbation theory and stationary phase approximation, we derive the P-wave seismic scattering coefficient equation in terms of fluid factor, shear modulus and density of background homogeneous media and perturbation media. With this equation as forward solver, a pre-stack seismic Bayesian inversion method is proposed to estimate the fluid factor of heterogeneous media. In this method, Cauchy distribution is utilized to the ratios of fluid factors, shear moduli and densities of perturbation media and background homogeneous media, respectively. Gaussian distribution is utilized to the likelihood function. The introduction of constraints from initial smooth models enhances the stability of the estimation of model parameters. Model test and real data example demonstrate that the proposed method is able to estimate the fluid factor of heterogeneous media from pre-stack seismic data directly and reasonably.     

弹性波逆散射微扰论

本文将普遍声逆散射微扰论应用于弹性波层析成像问题,在Born变换下推出了以旋转角为补偿参数的各阶微扰重建公式,实现了对非均匀各向同性散射体内3个参数（质量密度ρ和两个Lamé系数λ,μ）的同时重建. 对于层析成像问题,在弹性波的传播过程中P波与SV波有耦合,但它们不会和SH波发生耦合,于是可以得到3个形式相对简单的标量方程. 在Born变换下,在散射波中引入微扰参数,将散射体的3个参数分别按该微扰参数展开,然后利用二维自由空间的Green函数分别得到散射的P波、SV波和SH波的积分表示. 最后,经一维傅氏变换后,得到Born变换下散射体3个参数的各阶微扰重建公式.     

Scattered Surface Wave Energy in the Seismic Coda

One of the many important contributions that Aki has made to seismology pertains to the origin of coda waves (Aki, 1969; Aki and Chouet, 1975). In this paper, I revisit Aki's original idea of the role of scattered surface waves in the seismic coda. Based on the radiative transfer theory, I developed a new set of scattered wave energy equations by including scattered surface waves and body wave to surface wave scattering conversions. The work is an extended study of Zeng et al. (1991), Zeng (1993) and Sato (1994a) on multiple isotropic-scattering, and may shed new insight into the seismic coda wave interpretation. The scattering equations are solved numerically by first discretizing the model at regular grids and then solving the linear integral equations iteratively. The results show that scattered wave energy can be well approximated by body-wave to body wave scattering at earlier arrival times and short distances. At long distances from the source, scattered surface waves dominate scattered body waves at surface stations. Since surface waves are 2-D propagating waves, their scattered energies should in theory follow a common decay curve. The observed common decay trends on seismic coda of local earthquake recordings particular at long lapse times suggest that perhaps later seismic codas are dominated by scattered surface waves. When efficient body wave to surface wave conversion mechanisms are present in the shallow crustal layers, such as soft sediment layers, the scattered surface waves dominate the seismic coda at even early arrival times for shallow sources and at later arrival times for deeper events.     

Coda wave analysis for distinguishing attenuation due to isotropic scattering from attenuation due to absorption

When the quality factorQ is taken into account in attenuation studies, it is necessary to know the relative losses of wave energy due to scattering and to anelastic absorption. The coda is the most important phenomenon now known which is related to elastic scattering of seismic waves. Utilizing coda, this study presents relationships which give theQ factors of the medium around the recording station and discriminate between attenuations arising from elastic scattering (under the assumption of isotropic scattering) and those arising from anelastic absorption. This work proposes a technique for separately determining the attenuation due to isotropic scattering and that due to absorption from the observed envelope of coda waves.     

地震波散射研究的新进展——第25届IASPEI大会S13专题报告会“地震波散射与衰减”简介

本文以IASPEI的“地震波的散射与衰减”专题报告会为主,评述了近几年在地震波散射方面的研究进展.述评所涉及的方面有:1.关于地震尾波的起源;2.大震前尾波包络的前兆性变化;3.地震尾波包络衰降的机理;4.区分散射和吸收的新方法;5.新领域的开拓和研究.     

Significant release of shear energy of the North Korean nuclear test on February 12, 2013

On February 12, 2013 the Democratic People’s Republic of Korea (DPRK) carried out an announced nuclear test, which was the third after tests conducted in 2006 and 2009. An important task in discriminating a man-made explosion and a natural tectonic earthquake is the analysis of seismic waveforms. To determine the isotropic and non-isotropic characteristics of the detonation source, I invert long-period seismic data for the full seismic moment tensor to match the observed seismic signals by synthetic waveforms based on a 3D Earth model. Here, I show that the inversion of long-period seismic data of the 2013 test reveals a clear explosive (isotropic) component combined with a significant release of shear energy by the double-couple part of the moment tensor. While the isotropic part of the nuclear test in 2009 was similar to that in 2013, the double-couple part was lower by a factor of 0.55 compared to the explosion in 2013. Moreover, the ratio of the isotropic seismic moments of the 2013 and 2009 nuclear tests is 1.4?±?0.1 and lower than published estimations of the yield ratio, which indicates the importance of considering the release of shear energy. The determined orientation of the double-couple fault plane is parallel to the dominating geologic fault structures NNE-SSW to NE-SW, but the calculated normal faulting mechanism does not correspond to the general tectonic strike-slip regime. Thus, explanations for the enhanced release of shear energy might be induced dip-slip motion pre-stressed by the previous test or near source damaging effects due to a changed containment of the nuclear explosion.     

地震波散射理论及应用研究综述

回顾了地震波散射的概念、研究历史及分类.对散射理论及应用研究成果进行了系统评述，特别对前人关于散射波数值模拟和应用研究的不足进行了总结：(1)观测系统设计不合理；(2)对散射波的特征研究缺乏系统性；(3)对复杂散射波场的识别方法没有进行系统研究；(4)适合散射成像的处理软件还有待开发.并介绍了作者关于地震散射波场特征数值模拟研究的初步成果.     

Analysis of fracture induced scattering of microseismic shear-waves

Fractures are pervasive features within the Earth’s crust and have a significant influence on the multi-physical response of the subsurface. The presence of coherent fracture sets often leads to observable seismic scattering enabling seismic techniques to remotely locate and characterise fracture systems. In this study, we confirm the general scale-dependence of seismic scattering and provide new results specific to shear-wave propagation. We do this by generating full waveform synthetics using finite-difference wave simulation within an isotropic background model containing explicit fractures. By considering a suite of fracture models having variable fracture density and fracture size, we examine the widening effect of wavelets due to scattering within a fractured medium by using several different approaches, such as root-mean-square envelope analysis, shear-wave polarisation distortion, differential attenuation analysis and peak frequency shifting. The analysis allows us to assess the scattering behavior of parametrised models in which the propagation direction is either normal or parallel to the fracture surfaces. The quantitative measures show strong observable deviations for fractures size on the order of or greater than the dominant seismic wavelength within the Mie and geometric scattering regime for both propagation normal and parallel to fracture strike. The results suggest that strong scattering is symptomatic of fractures having size on the same order of the probing seismic wave.     

再论地震数据偏移成像

利用地震波正向传播方程对属于波形线性反演问题近似求解方法的地震数据偏移成像进行重新推导,得到了适合散射地震数据的散射偏移成像方法和适合反射地震数据的反射偏移成像方法.以地震波传播的散射理论为出发点,首先根据描述一次散射波正向传播的线性方程研究建立散射地震数据的偏移成像方法理论;利用高频近似对产生散射波场的地下速度扰动函数的空间变化进行近似,推导出地下反射率函数,再由散射波传播方程推导出基于反射率函数的反射波传播方程,然后根据描述一次反射波正向传播的线性方程研究建立反射地震数据的偏移成像方法理论.本文指出和修正了Claerbout偏移成像方法中的不足,提出的地震数据偏移成像方法是对当前偏移成像方法理论的完善,使反射地震数据偏移成像具有了更坚实的数学物理理论基础,得到的偏移成像结果相位正确、位置准确、分辨率提高.     

Bayesian Markov chain Monte Carlo inversion for anisotropy of PP- and PS-wave in weakly anisotropic and heterogeneous media

A single set of vertically aligned cracks embedded in a purely isotropic background may be considered as a long-wavelength effective transversely isotropy (HTI) medium with a horizontal symmetry axis. The crack-induced HTI anisotropy can be characterized by the weakly anisotropic parameters introduced by Thomsen. The seismic scattering theory can be utilized for the inversion for the anisotropic parameters in weakly anisotropic and heterogeneous HTI media. Based on the seismic scattering theory, we first derived the linearized PP- and PS-wave reflection coefficients in terms of P- and S-wave impedances, density as well as three anisotropic parameters in HTI media. Then, we proposed a novel Bayesian Markov chain Monte Carlo inversion method of PP- and PS-wave for six elastic and anisotropic parameters directly. Tests on synthetic azimuthal seismic data contaminated by random errors demonstrated that this method appears more accurate, anti-noise and stable owing to the usage of the constrained PS-wave compared with the standards inversion scheme taking only the PP-wave into account.     

Microseismic Full Waveform Modeling in Anisotropic Media with Moment Tensor Implementation

Seismic anisotropy which is common in shale and fractured rocks will cause travel-time and amplitude discrepancy in different propagation directions. For microseismic monitoring which is often implemented in shale or fractured rocks, seismic anisotropy needs to be carefully accounted for in source location and mechanism determination. We have developed an efficient finite-difference full waveform modeling tool with an arbitrary moment tensor source. The modeling tool is suitable for simulating wave propagation in anisotropic media for microseismic monitoring. As both dislocation and non-double-couple source are often observed in microseismic monitoring, an arbitrary moment tensor source is implemented in our forward modeling tool. The increments of shear stress are equally distributed on the staggered grid to implement an accurate and symmetric moment tensor source. Our modeling tool provides an efficient way to obtain the Green’s function in anisotropic media, which is the key of anisotropic moment tensor inversion and source mechanism characterization in microseismic monitoring. In our research, wavefields in anisotropic media have been carefully simulated and analyzed in both surface array and downhole array. The variation characteristics of travel-time and amplitude of direct P- and S-wave in vertical transverse isotropic media and horizontal transverse isotropic media are distinct, thus providing a feasible way to distinguish and identify the anisotropic type of the subsurface. Analyzing the travel-times and amplitudes of the microseismic data is a feasible way to estimate the orientation and density of the induced cracks in hydraulic fracturing. Our anisotropic modeling tool can be used to generate and analyze microseismic full wavefield with full moment tensor source in anisotropic media, which can help promote the anisotropic interpretation and inversion of field data.     

长白山天池火山区S波包络展宽的特征

高频S波随着传播距离的增大其均方根(RMS)包络逐渐变宽,把这种现象称为S波的包络展宽现象。S波传播路径上随机分布的非均匀体对S波的多次前向散射和绕射作用是导致S波包络展宽现象的主要原因,因此可用S波的包络展宽现象来研究介质的非均匀性。采用S波包络峰值延时对S波包络展宽现象进行量化。S波包络峰值延时定义为S波初至与其RMS包络峰值最大值之间的时间差。文中对长白山天池火山区204个小震记录进行了S波包络展宽分析,研究发现长白山天池火山区小震S波包络展宽现象明显,S波包络峰值延时与震中距、频率呈正相关;运用统计学方法获取了长白山天池火山区不同频带下S波包络峰值延时与震中距之间的关系。研究结果对认识S波包络展宽的特征以及定量研究长白山天池火山区介质的非均匀性具有重要意义     

Intrinsic attenuation and scattering of shear waves in the lithosphere of Kamchatka

Records of small local Kamchatka earthquakes were processed using Multiple Lapse Time Window Analysis (MLTWA). The method makes use of normalized integrals of 3D seismic energy density in several windows applied to an earthquake record that has been put through a bandpass filter. The intrinsic attenuation and scattering properties of the earth were estimated by choosing parameters that provide the best agreement between experimental and theoretical integrals as functions of hypocentral distance. The theoretical normalized integrals as functions of distance were computed using an analytical solution to the equation of seismic energy transport based on a simple model of isotropic scattering for scalar seismic waves excited by an impulse point source in an earth that is uniform as to scattering and intrinsic attenuation. The resulting estimates of attenuation and scattering parameters are similar to those derived in other studies of Kamchatka, as well as of other continents: America (California, US), Europe (the Canary Is., Spain, and Italy), and Asia (Japan).     

地震波散射研究的若干重要进展

本文从地球介质的复杂性与非均匀性的普遍性以及地震波在其中的传播过程的复杂性出发,对地震波散射理论及方法研究的历史进行了简要的回顾,并对该领域从20世纪90年代以来的某些进展作了简要的介绍与评述.本文分两大部分进行阐述.(1)．历史回顾：简介并回顾了地震波散射理论几十年的发展历程、存在的问题及对解决这些问题的潜在的基本途径.(2)．20世纪90年代以来的若干进展：简要介绍了弱散射理论体系的形成及强散射问题研究的部分成果,提出了散射理论未来发展的可能方向之一,即在无近似的拟微局部分析理论的基础上,建立并发展可处理高度复杂的地球固体介质中地震波传播问题的地震波散射及全波理论.     

On the generation and decay of the long-period coda energy of large earthquakes

Seismic coda wave is the tail portion of the earthquake record after main arrivals. Studies on the coda usually focus on high-frequency data within several hours after regional events and attribute them to the scattering effect of the heterogeneities inside the earth. Here, we use records of seven large earthquakes at globally distributed seismic stations to examine the decay of long-period (100 s to 300 s) coda in the time window of 10,000 s to 140,000 s after the origin time and fit it with a statistical model. The geometric spreading effect in the estimated initial energy and a location-independent equivalent attenuation coefficient indicate that the long-period coda energy is less affected by the heterogeneity-induced scattering effect than that of shorter-period coda. The coda energy can reach the earth's inner core and can be explained by a 1D earth model, making it more effective for constraining the global attenuation model. It also has the potential to determine the magnitudes of large earthquakes and to explore the interior of planetary bodies.     

SH波作用下浅埋裂纹附近半圆形凸起的地震动

利用Green函数、复变函数及多极坐标法研究了浅埋裂纹附近的半圆形凸起地形对SH波的散射问题。首先求解出适合本问题的Green函数,即含有半圆形凸起的弹性半空间内任意一点承受时间谐和的出平面线源荷载作用时位移场的解答。然后,从半圆形凸起地形对SH波的散射问题出发,利用本问题的Green函数在基体内构造裂纹。最后给出了浅埋裂纹附近的半圆形凸起地形对SH波散射的位移场。通过算例讨论了裂纹对地表位移幅值的影响,结果表明裂纹在一定情况下具有减震作用。     

随机弹性介质中地震波散射衰减分析(英文)

地震波衰减一直是许多学科研究的热点,因为可以反映介质的特性。导致地震波衰减的因素很多,如:传播过程中由于能量扩散导致的几何衰减,固体岩石内部晶粒间相对滑移导致的摩擦衰减,岩石结构不均匀引起的地震波散射衰减。本文主要从统计的观点出发,通过多次数值模拟的方法研究纵波散射在随机弹性介质中所引发的衰减。首先用随机理论建立了二维空间随机弹性介质模型,然后用错格伪谱法的数值方法模拟了波在随机介质中的传播,再通过波场中虚拟检波器的记录,用谱比法估计了弹性波在随机介质中的散射衰减。不同非均匀程度随机弹性介质中的数值结果表明:介质不均匀程度越高,散射衰减越大;在散射体尺寸小于波长的前提下,不同散射体尺寸的计算结果说明:散射体尺寸越大,弹性波衰减越明显。最后提出了一种不均匀孔隙介质中流体流动衰减的方法。通过对随机孔隙介质中地震波的总衰减和散射衰减分别进行了计算,并定量得出了随机孔隙介质中流体流动衰减,结果表明:在实际地震频段下,当介质不均匀尺度101米量级时,散射衰减比流体流动衰减要大,散射衰减是地震波在实际不均匀岩石孔隙介质中衰减的主要原因。