Studies of coda using array and three-component processing

The application of standard array processing techniques to the study of coda presents difficulties due to the design criteria of these techniques. Typically the techniques are designed to analyze isolated, short arrivals with definite phase velocity and azimuth and have been useful in the frequency range around 1 Hz. Coda is long in time and may contain waves of different types, phase velocities and azimuths. Nonetheless, it has proved possible to use or adapt array methods to answer two questions: what types of waves are present in coda and where are they scattered? Most work has been carried out on teleseismicP coda; work on local coda has lagged due to lack of suitable data and the difficulties of dealing with high frequencies. The time domain methods of beamforming and Vespagram analysis have shown that there is coherent energy with a high phase velocity comparable toP orPP in teleseismicP coda. These methods can detect this “coherent” coda because it has a fairly definite phase velocity and the same, or close to, azimuth as firstP orPP. This component must consist ofP waves and is either scattered near the source, or reflected in the mantle path as apdpP or precursorPP reflection. The Fourier transform method of the frequency-wavenumber spectrum has been adapted by integrating around circles of constant phase velocity (constant total wavenumber) to produce the wavenumber spectrum, which shows power as a function of wavenumber, or phase velocity. For teleseismicP coda, wavenumber spectra demonstrate that there is a “diffuse” coda of shear,Lg or surface waves scattered from teleseismicP near the receiver. Wavenumber spectra also suggest that the coherent coda is produced by near-source scattering in the crust, not mantle reflection, since it is absent or weak for deep-focus events. Crustal earthquakes have a very strong coherent component of teleseismic coda, suggesting scattering from shear to teleseismicP near the source. Three-component analysis of single-station data has shown the presence of off-azimuth arrivals and may lead to the identification of waves scattered from a single scatterer.     

Scattering objects in the lower mantle beneath northeastern China observed with a short-period seismic array

Precursor and coda portions of short-period PcP waves (reflected P wave from the core-mantle boundary, CMB) recorded at J-array stations in Japan were analyzed in order to extract weak scattered signals originating from small-scale heterogeneities in the lowermost mantle beneath northeastern China. Two nuclear explosions at Lop Nor in China detonated on 21 May 1992 (Mb=6.5) and 8 June 1996 (Mb=5.9) were used for our analysis.Three-dimensional grids above the CMB were defined in the area around the PcP bounce points beneath northeastern China to calculate theoretical travel times of scattered waves which propagate from the sources to each grid point and arrive at each station based on the IASP91 model. Subsequently the waveforms were aligned with respect to the theoretical travel times and the semblance (an amplitude dependent measure of coherency) was calculated for each grid point. In order to obtain a more accurate travel time correction, we applied a cross correlation method to PcP waveforms in order to reduce picking error of the PcP onset time. A cross convolution method was also applied so that the two events could be analyzed simultaneously without using unstable deconvolutions.We could identify regions with relative high semblance values in semblance contour maps at about 200 and 375 km above the CMB. Stacking waveforms with respect to the theoretical travel times for the grid points with relative high semblance values indicate coherent wavelets originating at those grid points, that is, they correspond to scattered waves originating from small-scale heterogeneities in the lowermost mantle. Our results indicate the existence of small-scale scattering objects in the D″ layer, especially in the depth range of 200 and 375 km above the CMB beneath northeastern China. Considering recent tomographic images of high velocity anomalies in this area, these scattering objects could be fragments of old oceanic crusts which have subducted through the lower mantle and have accumulated in the D″ layer beneath northeastern China.     

接收函数的克希霍夫２D偏移方法

本文将地震反射资料成像的Kirchhoff偏移方法引入到接收函数成像研究，提出了一种接收函数的Kirchhoff偏移方法，以适应介质速度的横向变化，提高接收函数成像的精度和分辨率. 模型检验表明，与传统的水平分层的共转换点偏移叠加方法相比，Kirchhoff偏移方法能够实现转换波的有效归位，消除水平分层共转换点偏移叠加造成的假象. 一个很重要的现象是，倾斜或弯曲界面的成像明显受控于远震的入射方向，其成像精度的提高有赖于不同方向接收函数的联合成像.     

Small-scale heterogeneities below the Lanzhou CTBTO seismic array,from seismic wave field fluctuations

Seismic wave field fluctuations below Lanzhou Comprehensive Test Ban Treaty Organization seismic array are determined and interpreted to describe the scattering characteristics of the crust beneath the northeastern margin of Qinghai–Tibet plateau in China. The frequency-dependent intensities of the mean and fluctuation wave fields are analyzed for 21 deep (206–632 km depth) teleseismic events. The observed wave field fluctuations in the frequency range 0.5–2.5 Hz can be explained by the scattering of the teleseismic P wave front at random media-type structures. The stable and narrow range of the fluctuation parameters from these teleseismic events indicates evidence for scattered seismic phases which are generated inside the crust. The reasonable structural models contain heterogeneities with 1–3% velocity fluctuations and 2.4–8.2 km correlation lengths in the crust with 53 km thickness.     

Numerical-analytical interfacing in two dimensions with applications to modeling NTS seismograms

A new method for interfacing numerical and integral techniques allows greater flexibility in seismic modeling. Specifically, numerical calculations in laterally varying structure are interfaced with analytic methods that enable propagation to great distances. Such modeling is important for studying situations containing localized complex regions not easily handled by analytic means. The calculations involved are entirely two-dimensional, but the use of an appropriate source in combination with a filter applied to the resulting seismograms produces synthetic seismograms which are point-source responses in three dimensions. The integral technique is called two-dimensional Kirchhoff because its form is similar to the classical three-dimensional Kirchhoff. Data from Yucca Flat at the Nevada Test Site are modeled as a demonstration of the usefulness of the new method. In this application, both local and teleseismic records are modeled simultaneously from the same model with the same finite-difference run. This application indicates the importance of locally scattered Rayleigh waves in the production of teleseismic body-wave complexity and coda.     

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.     

远震体波有限破裂过程反演敏感性测试及其在汶川地震上的应用

本文利用远震P和SH波反演得到2008年5月12日汶川大地震(M_W=7.9)的一系列有限破裂模型。使用一种基于小波变换的模拟退火非线性反演方法, 我们将主断层划分成若干个子断层, 在反演时同时确定每个子断层上的滑移量、 滑动角、 上升时间(rise time)以及平均破裂速度。我们首先根据一个假定的破裂模型生成理论地震图, 将该理论地震数据作为输入进行反演, 对该有限破裂反演方法进行了一系列测试, 以验证反演对断层倾角、 平均破裂速度、 最大破裂深度等参数的敏感性。然后我们采用4个不同倾角的断层面来对汶川地震远震体波记录进行反演。结果表明, 若对只在一个断层面上模拟该地震, 30°倾角是个较为合适的值。反演的结果还表明, 此次地震有两个主要的能量释放区域, 并且主断层面存在倾角变化的可能性。在将来的研究中, 可以结合GPS, InSAR测地学以及强震等数据, 来对强震的破裂过程做更细致的研究。     

海拉尔CTBTO地震台阵下方小尺度非均匀体研究

利用国际禁核组织在海拉尔布设的小孔径地震台阵的16个深远地震波资料,分离出了P波波场中不相干的尾波.频率域中对波场扰动的研究表明,在0.5～3.0 Hz的频率范围内,观测到的波场扰动可以利用P波在随机介质中的散射进行解释.不同远震事件得到的稳定结果表明,在该台阵下方34 km厚的地壳和110 km厚的岩石层中可能存在相关长度为2.0～7.4 km的散射体.     

Model-independent Travel-time Attributes for 2-D, Finite-offset Multicoverage Reflections

— In this paper, we provide a 5-parameter stacking formula to transform 2-D prestack data into a particular common-offset section. This requires the knowledge of the near-surface velocity only and it is expected that ray theory holds to describe primary reflections. The earth model can be arbitrarily inhomogeneous. The new stacking approach can be viewed as a generalization of the 3-parameter common-reflection-surface (CRS) stack, by which 2-D multicoverage data are stacked into a simulated zero-offset section. The new 5-parameter formula can handle P-P, P-S and S-S reflections.     

Far field elastodynamic Born scattering revisited

This paper summarizes part of an ongoing feasibility study that investigates the possible use of the full elastic Born approximation in multipole borehole acoustics. As a first step we exclude the fluid-filled borehole with the motivation that one or two wavelengths away from the fluid-filled borehole, radiating borehole mode amplitudes (e.g., Stoneley wave, formation dipole wave, etc.) are small compared to body wave amplitudes (P-, SV- and SH-waves). Consequently, for scatterers one or two wavelengths away from the fluid-filled borehole, it suffices to only consider their interaction with body waves.In this paper we apply the contrast-source stress-velocity forward scattering (integral equation) formulation for solid configurations in its first order (Born-) approximation (De Hoop, 1995) assuming a multipole force source excitation in a zero-offset configuration. To scrutinize the validity of the Born approximation, we consider the simplest type of scatterer, i.e., one characterized by a (Heaviside) step function change in one or more of the contrast (perturbation) parameters and we derive analytic zero-offset formulas for the scattered wave particle velocity and displacement in both the space–frequency and space–time domain, respectively. We assume the scatterer to be located in the far-field. More complicated layered configurations can easily be derived by superposition of the given solution types. Explicit results are given for the dipole and quadrupole excitation, where the former is allowed to have an arbitrary orientation relative to the scatterer and where the latter one is located in a plane perpendicular to the scatterer. In the time domain it is shown, how the scattered wave field decomposes in a specular and diffuse wave field (two terms borrowed from ‘Optics’), where the former contribution vanishes in the absence of an imaging condition and where the latter is always present. For the dipole case, we subject our results to a sensitivity analysis with respect to the three independent perturbation parameters (i.e., density and two compliance parameters) and we compare these results to a full waveform benchmark code that has implemented the reflectivity method (Kennett, 1983), for a ‘horizontally’ stratified elastic medium. This allowed us to pinpoint the root cause of the observed (small) differences. As it turns out these deviations could be traced back to the inaccurateness of the first order Born scattering coefficients. An additional confirmation of this fact is provided through a comparison between the zero-offset scattering coefficients and the corresponding Zoeppritz reflection coefficients. Most notably, it was found that the PP first order scattering coefficient needs a higher than quadratic correction in two of the three independent perturbation parameters, i.e., the two compliance parameters, δΛ and δM. With respect to the density perturbation parameter (δρ) the PP scattering coefficient correction is quadratic with respect to this perturbation parameter, as is to be expected for a first order approximation. Moreover, also the SS first order scattering coefficient only needs a quadratic correction with respect to its associated perturbation parameters, i.e., δρ and δM.Finally, we give a brief outline on how to numerically implement the Born approximation (employing arbitrary offsets) in a configuration where a source–receiver pair is moving continuously relative to the ‘contrast’ (Geology), as is the case in borehole acoustic applications.     

三峡地区上地壳结构的远震虚震源反射地震成像

远震虚震源反射成像方法利用远震初至波在台网之下地表与地下界面间形成的反射波(PPdp震相)波形资料进行台网地区地震反射结构研究.此方法先用台网各台站的平均初至波形求取震源信号,再用该震源信号与各道地震记录作反褶积从而取得反射剖面.本文介绍了远震虚震源反射成像的基本原理和实现步骤,并以三峡地区的观测资料为例,得到三峡库首区上地壳的反射地震剖面.成像剖面中解释出的四川盆地和秭归盆地的底界面位置和形态与地表地质观测和大地构造背景吻合.为验证虚震源成像的能力,本文使用弹性波正演模拟合成地震数据,经过处理实际资料一样的步骤获得虚震源成像结果.正演模拟表明,叠加多个远震的反射地震剖面可以有效地改善成像的信噪比和连续性;虚震源成像需要选择特定的震源频率范围,以减轻高频噪音以及低频造成的成像问题.在研究上地壳结构时,建议在不适合主动源采集和缺乏低频信号的地区尝试远震虚震源方法.     

用接收函数方法研究汶川和芦山地震之间未破裂段的地壳结构

芦山与汶川地震之间存在约40 km的地震空区.震源区和地震空区的深部构造背景的研究对深入了解中强地震的深部孕育环境及地震空区的地震活动性具有重要科学意义.利用本小组布设的15个临时观测地震台以及21个芦山科考台站和21个四川省地震局固定台站记录的远震数据,用H-K叠加方法得到各个台站的地壳厚度和平均泊松比,并构建了接收函数共转换点(CCP)偏移叠加图像以及反演得到台站下方的S波速度模型.我们的结果揭示了震源区和地震空区地壳结构特征差异:(1)汶川震源区的地壳平均泊松比为~0.28;芦山震源区为~0.29;而地震空区处于泊松比变化剧烈的区域;(2)汶川地震与芦山地震的震源区以西下方的Moho面呈现深度上的突变(这与前人的研究成果基本一致),分别从~44 km突变到~59 km,~40 km突变到~50 km,而地震空区地壳平均厚度呈现渐变性变化;(3)地震空区Moho面下凹且具有低速的上地壳.综合一维S波速度结构和H-k以及CCP的初步结果,这可能显示汶川地震的发震断裂在深部方向上向西倾斜并形成切割整个地壳的大型断裂;芦山地震则可能是由于上、下地壳解耦引起的;而地震空区处于两种地震形成机制控制区域的过渡带中.     

利用共转换点叠加方法研究华北地区地壳结构

利用华北地震台阵L测线的35个台站记录的895个远震数据进行了接收函数的计算,并利用H-κ叠加方法得到华北克拉通西部陆块东侧和中部陆块内基岩台站下方的地壳结构.利用得到的基岩台站下方的地壳结构和通过波形模拟方法得到的渤海湾盆地的沉积层结构作为背景模型对测线进行共转换点(CCP)叠加成像.在渤海湾盆地,通过增大CCP叠加...     

基于伴随方法的线性台阵背景噪声面波和远震体波联合成像研究

伴随层析成像（Adjoint Tomography）通过求解全波方程来准确模拟地震波在复杂介质中的传播,并利用波形信息来反演地下结构,是新一代的高分辨率成像方法.其中3-D伴随层析成像需要庞大的计算资源,而2-D反演相对更具计算效率.面波和远震体波是研究地壳上地幔速度结构的重要方法,它们对S波速度及Moho面的敏感度不同,通过联合反演,可以得到更为准确的S波速度结构及Moho面.通过两种数据的高度互补性,本文提出基于伴随方法的线性台阵背景噪声面波和远震体波联合成像方法,同时约束台阵下方S波速度结构及Moho面形态.我们将该方法应用到符合华北克拉通岩石圈典型结构特征的理论模型上,测试结果表明联合反演方法优势明显,相比于面波伴随层析成像,能获得更高分辨率的S波速度结构,同时能精准约束Moho面形态.相比于体波伴随层析成像,联合反演能有效压制高频假象,降低波形反演过程中的非线性化程度.本研究有望提供一种更为高效精准的线性台阵成像方法,搭建联合伴随层析成像理论框架,提升岩石圈成像分辨率,并为后续其他类型波形数据的引入提供思路和方法.     

井间电磁场的一维、二维联合反演方法

提出了针对轴对称二维井间模型的一维、二维联合反演方法.该方法基于纵向成层背景地层的Green函数,以一维反演结果作为联合反演的迭代初始值,同时反演一维背景地层和二维异常剖面的电导率.采用递推技术计算Green函数的系数,可以很方便地同时得到Green函数对空间坐标的积分和对背景层电导率的微分,大大加快了计算雅可比矩阵〖WTHX〗M〖WTBZ〗的速度并使计算方便、准确.反演实例说明了该方法的有效性.反演实例还显示,背景层电导率较二维成像剖面的电导率收敛速度要快,测量数据的精度对二维剖面电导率成像质量的影响大于对背景层电导率分布的影响.     

远震层析成像中的地壳校正研究及应用

远震层析成像是研究一个地区上地幔三维速度结构的有力手段.但由于远震射线在地壳内的交叉较差,因此无法准确约束地壳内的三维速度结构.为了消除地壳内横向不均匀性对深部速度成像产生的影响,必须进行地壳校正.本文详细描述了地壳校正的基本原理和步骤,主要包括三维地壳模型的选取、地壳内走时差的计算以及校正后的相对走时差的计算.以勘察加地区为例,通过计算各台站的平均相对走时差和远震层析成像结果分析了地壳校正的实际效果,同时验证了该方法的实用性.     

快速有效的转换波共转换点叠加技术

转换波共转换点(Common Conversion Point简称CCP)叠加的关键在于CCP抽道集和非双曲线正常时差校正NMO(Normal MoveOut). 目前方法的精度限制了其在中-浅层或大炮检距情况下的应用. 我们对CCP叠加技术进行了系统研究,导出了新的CCP位置计算公式和非双曲线时距关系式,并给出了具体的CCP抽道集方法. 理论模型试验和实验资料处理表明本文方法精度高、简便易行,特别是对于中-浅层和大炮检距情况也能得到良好的叠加效果.     

Seismic codas on the Earth and the Moon: a comparison

The phenomenon of the seismic coda, which is composed of seismic energy delayed by scattering, is seen on both the Earth and the Moon. On the Moon the scattered coda is very large relative to body wave arrivals with a delay of the time of maximum energy, whereas on Earth scattered codas are relatively small and show no delay of the energy maximum. In both cases the form of the coda is controlled by three distance scales, the mean free path L, which is the average distance seismic energy travels before it is scattered, the attenuation distance $\text{x1}$, which is the average distance seismic energy travels before it is attenuated, and the source-receiver distance R. Two coda models are discussed based on these parameters; a strong scattering (diffusion) model, and a weak scattering (single scattering) model. A discussion of the diffusion scattering model indicates that if $\text{x1/L ? 1}$, diffusion scattering is an appropriate model, but if $\text{x1/L ? 1}$, single scattering is the appropriate model, within the appropriate range of R. A survey of the literature indicates that for the frequency range 0.5–10 Hz, diffusion scattering is important in lunar codas, but for the frequency range 1–25 Hz single scattering is important in terrestrial codas. Another important effect of attenuation is the elimination of scattering paths much longer than $\text{x1}$. On the Moon, this means that seismic energy in the coda can only propagate directly in the near-surface strong scattering zone between surface sources and the seismometer for source-seismometer separations of the order of $\text{(x1L)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$; otherwise, scattering is limited to regions near the source and the receiver. On Earth, this effect probably prevents multiple scattering.     

Global Event Location with Full and Sparse Data Sets Using Three-dimensional Models of Mantle P-wave Velocity

—?In order to improve on the accuracy of event locations at teleseismic distances it is necessary to adequately correct for lateral variations in structure along the ray paths, either through deterministic model-based corrections, empirical path/station corrections, or a combination of both approaches. In this paper we investigate the ability of current three-dimensional models of mantle P-wave velocity to accurately locate teleseismic events. We test four recently published models; two are parameterized in terms of relatively long-wavelength spherical harmonic functions up to degree 12, and two are parameterized in terms of blocks of constant velocity which have a dimension of a few hundreds of km. These models, together with detailed crustal corrections, are used to locate a set of 112 global test events, consisting of both earthquakes and explosions with P-wave travel-time data compiled by the Internation al Seismological Centre (ISC). The results indicate that the supposedly higher resolution block models do not improve the accuracy of teleseismic event locations over the longer wavelength spherical harmonic models. For some source locations the block models do not predict the range of observed travel-time residuals as well as the longer wavelength models. The accuracy of the locations largely varies randomly with geographic position although events in central Asia are particularly well located. We also tested the effect of reduced data sets on the locations. Multiple location iterations using 30 P-wave travel times indicate that teleseismic events may be located within an area of 1000?km² of the true location 66% of the time with only the model-based corrections, and increasing to 75% if calibration information is available. If as few as 8 phases are available then this is possible only 50% of the time. Further refinement in models and/or procedure, such as the addition of P _n phases, azimuth data, and consideration of P-wave anisotropy may provide further improvement in the teleseismic location of small events.