Estimating Crustal Heterogeneity from Double-difference Tomography

Seismic velocity parameters in limited, but heterogeneous volumes can be inferred using a double-difference tomographic algorithm, but to obtain meaningful results accuracy must be maintained at every step of the computation. MONTEILLER et al. (2005) have devised a double-difference tomographic algorithm that takes full advantage of the accuracy of cross-spectral time-delays of large correlated event sets. This algorithm performs an accurate computation of theoretical travel-time delays in heterogeneous media and applies a suitable inversion scheme based on optimization theory. When applied to Kilauea Volcano, in Hawaii, the double-difference tomography approach shows significant and coherent changes to the velocity model in the well-resolved volumes beneath the Kilauea caldera and the upper east rift. In this paper, we first compare the results obtained using MONTEILLER et al.'s algorithm with those obtained using the classic travel-time tomographic approach. Then, we evaluated the effect of using data series of different accuracies, such as handpicked arrival-time differences (``picking differences'), on the results produced by double-difference tomographic algorithms. We show that picking differences have a non-Gaussian probability density function (pdf). Using a hyperbolic secant pdf instead of a Gaussian pdf allows improvement of the double-difference tomographic result when using picking difference data. We completed our study by investigating the use of spatially discontinuous time-delay data.     

Tomography and the Herglotz-Wiechert inverse formulation

In this paper, linearized tomography and the Herglotz-Wiechert inverse formulation are compared. Tomographic inversions for 2-D or 3-D velocity structure use line integrals along rays and can be written in terms of Radon transforms. For radially concentric structures, Radon transforms are shown to reduce to Abel transforms. Therefore, for straight ray paths, the Abel transform of travel-time is a tomographic algorithm specialized to a one-dimensional radially concentric medium. The Herglotz-Wiechert formulation uses seismic travel-time data to invert for one-dimensional earth structure and is derived using exact ray trajectories by applying an Abel transform. This is of historical interest since it would imply that a specialized tomographic-like algorithm has been used in seismology since the early part of the century (seeHerglotz, 1907;Wiechert, 1910). Numerical examples are performed comparing the Herglotz-Wiechert algorithm and linearized tomography along straight rays. Since the Herglotz-Wiechert algorithm is applicable under specific conditions, (the absence of low velocity zones) to non-straight ray paths, the association with tomography may prove to be useful in assessing the uniqueness of tomographic results generalized to curved ray geometries.     

复杂介质小波多尺度井间地震层析成像方法研究

复杂介质井间地震层析成像是一个很复杂的非线性反 演问题，常规的线性化反演方法无法得到好的解. 采用基于图形的弯曲射线追踪方法， 并将小波多尺度思想引入到井间层析成像，提出了小波多尺度井间地震层析成像方法，很好 地解决了非线性成像的难题，提高了图像的质量和分辨率. 物理模型实验结果表明， 该方法适合于复杂介质成像，并具有良好的实用性和效果.     

速度差对井间走时层析成像质量的影响及其改进方法

在井间地震初至走时层析成像中,随着相邻地质体速度差的增大,使得射线分布不均匀,以及网格剖分不合适,导致层析成像结果不理想.物理和数值模型的井间走时层析成像表明：当速度差超过300%时,层析结果畸变较大;在300%～150%之间时,层析结果较好;低于150%时,层析结果好.在此基础上,提出了井间多尺度初至走时层析成像方法,即对同一模型采用多种网格剖分来同时进行层析成像,以获得研究区域的速度图像.数学和物理模型的井间多尺度走时层析结果表明：该方法很好地兼顾了层析成像的分辨率和精度,极大地改善了井间地震层析成像的质量.即使速度差超过30%,其多尺度的层析结果仍然较好.因此,这种方法具有实际应用的潜力.     

变阻尼约束层析成像及其在VSP资料中的应用(英文)

初至波走时层析成像已经取得了广泛的应用,然而,由于观测系统的限制,射线在模型中分布不均匀,导致层析结果的分辨能力不足。变阻尼约束方法应用不均匀的先验信息来匹配不均匀的数据分布,可以减小速度模型校正量与射线覆盖程度的相关性。本文将变阻尼约束方法应用于初至波旅行时层析成像中,并将平滑约束方法加入正则化方程组中来避免单独使用变阻尼约束带来的不稳定性,利用阿尔法滤波器对反演中间迭代结果进行平滑和去噪,采用LSQR算法求解线性方程组来提高收敛速度和压制误差传递。本文应用上述层析成像算法对VSP观测系统进行速度反演,分别应用于检测板速度模型数据和实际VSP资料速度反演中,结果表咀变阻尼约束层析成像可以改善射线不均匀覆盖带来的影响,从而提高速度反演结果的质量;VSP资料检波点附近的速度反演结果可靠性高。     

基于Matlab平台GUI的地震走时层析成像快速实现

地震走时层析成像是地球物理反演中的成熟方法之一,已在许多领域得到广泛应用,并取得了良好的效果。本文围绕地震走时层析成像GUI的快速实现,首先简要介绍了地震走时成像方法的原理和方法,并基于Matlab软件平台,利用GUI开发环境编写了二维横向非均匀地震走时层析成像图形用户界面（GUI）,实现了方便快捷地反演地震测深资料的速度结构并以人机交互方式快捷灵活地将图像显示出来;结合实际观测资料处理结果表明,本文编制的GUI软件能够有效地实现地震走时层析成像结果的窗口化、图像化和快捷化。     

Automating adjoint wave-equation travel-time tomography using scientific workflow

Recent advances in commodity high-performance computing technology have dramatically reduced the computational cost for solving the seismic wave equation in complex earth structure models. As a consequence, wave-equation-based seismic tomography techniques are being actively developed and gradually adopted in routine subsurface seismic imaging practices. Wave-equation travel-time tomography is a seismic tomography technique that inverts cross-correlation travel-time misfits using full-wave Fréchet kernels computed by solving the wave equation. This technique can be implemented very efficiently using the adjoint method, in which the misfits are back-propagated from the receivers (i.e., seismometers) to produce the adjoint wave-field and the interaction between the adjoint wave-field and the forward wave-field from the seismic source gives the gradient of the objective function. Once the gradient is available, a gradient-based optimization algorithm can then be adopted to produce an optimal earth structure model that minimizes the objective function. This methodology is conceptually straightforward, but its implementation in practical situations is highly complex, error-prone and computationally demanding. In this study, we demonstrate the feasibility of automating wave-equation travel-time tomography based on the adjoint method using Kepler, an open-source software package for designing, managing and executing scientific workflows. The workflow technology allows us to abstract away much of the complexity involved in the implementation in a manner that is both robust and scalable. Our automated adjoint wave-equation travel-time tomography package has been successfully applied on a real active-source seismic dataset.     

Application of travel-time seismic tomography for archaeological studies of building foundations and basements

The applicability of the travel-time seismic tomography algorithm with the adaptive environment parameterization for the engineering and archaeological studies is investigated. The investigation object is the environment under the ruins of the St. Onuphrius Church at the Big Solovetsky Island. Experimental geometry for the tomography studies is designed and the data are acquired and processed. The goal is to study in detail the church basement and underlying geological environment structure that can not be recovered with other geophysical methods. The synthetic experiments are performed using the standard checkerboard tests with the cells of 2, 3, and 4 m in size in order to estimate the adequacy of the results obtained. The recovered three-dimensional velocity pattern is in a good agreement with the data on the church and archaeological information.     

Simultaneous Inversion for Velocity and Reflector Geometry Using Multi-phase Fresnel Volume Rays

Traditional ray tomography methods based on the high frequency assumption are sometimes unable to obtain a high resolution tomographic picture due to a deficient coverage of ray paths in real applications, especially for low velocity anomalous regions. In contrast, finite-frequency ray theory is more suitable for handling real seismic propagation problems because the travel time depends not only on the velocity distribution along a central ray (or traditional geometric ray), but also on the velocity values within a region (referred to as the first Fresnel Volume) which incorporates the central ray. In this study, we develop an algorithm to calculate multi-phase Fresnel Volume finite-frequency rays, and then present an inversion method to simultaneous invert for both velocity and reflector geometry by using these multi-phase Fresnel Volume finite-frequency rays. Using synthetic data examples, we compare the reconstructions of the velocity field and the reflector orientation using the Fresnel Volume ray tomographic methods and the traditional ray tomography approach. Results show that the former is advantageous over the latter, especially when the ray density is relatively low. An additional benefit of the Fresnel Volume finite-frequency ray tomographic method is that it can start with a low frequency to capture the coarse velocity structure, thereby mitigating the local minimum trapping problem, and then be tuned to a high frequency for delineating the fine velocity structure.     

衍射地震CT技术的数值研究

本文首先解决了声波方程的非Born近似的正演计算问题,从而获得理论上不带近似的正演数据;然后,推导了井间（CBP）、垂直地震剖面（VSP）和地面反射（SRP）三种不同的数据采集方式下的衍射CT的重建公式;利用这些重建算法和正演数据,系统地研究了影响到地球物理CT成象质量的三种因素,即:（1）数据采集方式,（2）异常程度和（3）成象区域的尺寸,对重建图象的影响;并比较了衍射地震CT和射线地震CT的成象质量。     

Seismic detectability of anomalous structure at the top of the Earth’s outer core with broadband array analysis of SmKS phases

I have examined precisely the differential travel times and waveforms of SmKS seismic phases propagating under the southern Indian Ocean obtained from African broadband seismic arrays. The SmKS phases analyzed in this study travel in the mantle with weak heterogeneity confirmed by a global tomographic study for the distance range of 115-135°. The SmKS differential times were obtained from a vespagram (a stack intensity on a time-slowness diagram), and comparison with the vespagram created from synthetic waveforms with PREM gives the travel-time residual for each event-array pair. Although the residuals of S3KS-S2KS times exhibit apparently a systematic dependence on epicentral distance, this is likely due to small-scale heterogeneity beneath the Oceania where is covered by the SmKS ray entering points at the CMB. Waveform modeling was applied to a record section with a small travel-time residual that suggests a small effect from the mantle heterogeneity on the data set, I found that a low-velocity zone in the outermost 50 km in the core rather than PREM can explain an additional arrival detected just after the S3KS phase. This result is still inconclusive because of the small number of data and non-uniqueness of the model and ambiguity due to mantle structure. However, accumulation of the precise measurement described in this study may help the reduction of uncertainty and trade-offs.     

频率域2.5-D井间波形层析成像及其实际应用

从频率域3-D声波波动方程出发,结合井间观测方式的特点,基于Tarantola广义反演理论,提出了一种频率域2.5-D井间波形层析成像方法.数值模型试验结果表明：该方法对薄层厚度的分辨能力能达到约主频波长的1/4,且分辨率显著高于走时层析成像,尤其垂直分辨率有实质改善.模拟资料的抗噪试验表明：在信噪比为0.8的情况下,随机噪声对波形层析成像的影响较小;而相干噪声对全波形层析成像的影响显著,特别是初至波附近的强振幅干扰影响更为严重.井间实际资料的试处理结果表明：波形层析成像能很好地刻画井间介质的分布情况与储层连通性,对于油藏开发阶段的方案实施具有指导意义.     

SOME SOURCES OF DISTORTION IN TOMOGRAPHIC VELOCITY IMAGES1

Two particular sources of distortion, which may be encountered when applying tomographic imaging techniques to crosshole seismic data, have been investigated. Errors in survey locations of the shots and receivers can produce significant distortions in the images obtained. A simple method for solving simultaneously for the velocity field and shot and receiver location errors is presented and applied to synthetic and real data. Reflection and refraction of rays at velocity interfaces may produce poor density and angular coverage of the rays within the region of interest. It is shown that the effect of the velocity field on the ray coverage can significantly affect the resolution in the velocity image, even if ray bending is taken into account. One consequence of this effect is that, in some cases, little improvement in image quality is achieved by using curvi-ray rather than straight-ray inversion techniques, despite the occurrence of pronounced ray bending.     

Further improvement of temporal resolution of seismic data by autoregressive (AR) spectral extrapolation

Seismic data have still no enough temporal resolution because of band-limited nature of available data even if it is deconvolved. However, lower and higher frequency information belonging to seismic data is missing and it is not directly recovered from seismic data. In this paper, a method originally applied by Honarvar et al. [Honarvar, F., Sheikhzadeh, H., Moles, M., Sinclair, A.N., 2004. Improving the time-resolution and signal–noise ratio of ultrasonic NDE signals. Ultrasonics 41, 755–763.] which is the combination of the most widely used Wiener deconvolution and AR spectral extrapolation in frequency domain is briefly reviewed and is applied to seismic data to improve temporal resolution further. The missing frequency information is optimally recovered by forward and backward extrapolation based on the selection of a high signal–noise ratio (SNR) of signal spectrum deconvolved in signal processing technique. The combination of the two methods is firstly tested on a variety of synthetic examples and then applied to a stacked real trace. The selection of necessary parameters in Wiener filtering and in extrapolation are discussed in detail. It is used an optimum frequency windows between 3 and 10 dB drops by comparing results from these drops, while frequency windows are used as standard between 2.8 and 3.2 dB drops in study of Honarvar et al. [Honarvar, F., Sheikhzadeh, H., Moles, M., Sinclair, A.N., 2004. Improving the time-resolution and signal–noise ratio of ultrasonic NDE signals. Ultrasonics 41, 755–763.]. The results obtained show that the application of the purposed signal processing technique considerably improves temporal resolution of seismic data when compared with the original seismic data. Furthermore, AR based spectral extrapolated data can be almost considered as reflectivity sequence of layered medium. Consequently, the combination of Wiener deconvolution and AR spectral extrapolation can reveal some details of seismic data that cannot be observed in raw signal or which lost during the previous processing.     

Optimization of Cell Parameterizations for Tomographic Inverse Problems

—?We develop algorithms for the construction of irregular cell (block) models for parameterization of tomographic inverse problems. The forward problem is defined on a regular basic grid of non-overlapping cells. The basic cells are used as building blocks for construction of non-overlapping irregular cells. The construction algorithms are not computationally intensive and not particularly complex, and, in general, allow for grid optimization where cell size is determined from scalar functions, e.g., measures of model sampling or a priori estimates of model resolution. The link between a particular cell j in the regular basic grid and its host cell k in the irregular grid is provided by a pointer array which implicitly defines the irregular cell model. The complex geometrical aspects of irregular cell models are not needed in the forward or in the inverse problem. The matrix system of tomographic equations is computed once on the regular basic cell model. After grid construction, the basic matrix equation is mapped using the pointer array on a new matrix equation in which the model vector relates directly to cells in the irregular model. Next, the mapped system can be solved on the irregular grid. This approach avoids forward computation on the complex geometry of irregular grids. Generally, grid optimization can aim at reducing the number of model parameters in volumes poorly sampled by the data while elsewhere retaining the power to resolve the smallest scales warranted by the data. Unnecessary overparameterization of the model space can be avoided and grid construction can aim at improving the conditioning of the inverse problem. We present simple theory and optimization algorithms in the context of seismic tomography and apply the methods to Rayleigh-wave group velocity inversion and global travel-time tomography.     

Internal multiple attenuation by Kirchhoff extrapolation

Surface‐related multiple elimination is the leading methodology for surface multiple removal. This data‐driven approach can be extended to interbed multiple prediction at the expense of a huge increase of the computational burden. This cost makes model‐driven methods still attractive, especially for the three dimensional case. In this paper we present a methodology that extends Kirchhoff wavefield extrapolation to interbed multiple prediction. In Kirchhoff wavefield extrapolation for surface multiple prediction a single round trip to an interpreted reflector is added to the recorded data. Here we show that interbed multiples generated between two interpreted reflectors can be predicted by applying the Kirchhoff wavefield extrapolation operator twice. In the first extrapolation step Kirchhoff wavefield extrapolation propagates the data backward in time to simulate a round trip to the shallower reflector. In the second extrapolation step Kirchhoff wavefield extrapolation propagates the data forward in time to simulate a round trip to the deeper reflector. In the Kirchhoff extrapolation kernel we use asymptotic Green's functions. The prediction of multiples via Kirchhoff wavefield extrapolation is possibly sped up by computing the required traveltimes via a shifted hyperbola approximation. The effectiveness of the method is demonstrated by results on both synthetic and field data sets.     

Two-dimensional data-space joint inversion of magnetotelluric,gravity, magnetic and seismic data with cross-gradient constraints

In recent years, joint inversion has been widely used for integrated geological interpretation. We extended a data-space joint inversion algorithm of magnetotelluric, gravity and magnetic data to include first-arrival seismic travel-time and normalized cross-gradient constraints. We describe the main features of the algorithm and apply it to synthetic data generated for hypothetical models. For the synthetic data, we find that the joint inversion with multiple parameters is superior to the joint inversion with two or even three parameters, which can reduce the multisolution of inversion results more effectively. Furthermore, data-space joint inversion involves fewer memory requirements and better calculation speeds than traditional model-space joint inversion. The normalized cross-gradient constraints can better couple model parameters of different magnitudes compared with traditional unnormalized cross-gradient constraints, resulting in higher levels of structural similarity among resistivity, density, magnetic susceptibility and velocity models.     

远震反演中新的地壳异常体改正方法

近年来，远震走时层析成像方法有了长足的发展，在地下结构反演的研究中获得了众多成果。针对射线在台站下方覆盖率较差而导致远震反演方法对地壳速度约束不足的问题，本文提出了一种新的地壳异常体改正方法——对同一台站的相对走时残差进行求和平均去均值，消除了地壳中复杂的速度异常体对上地幔速度结构反演的干扰，反演结果具有更优的相对走时残差分布，同时反演得到的速度模型具有更小的数据方差。     

TIME-TO-DEPTH MIGRATION USING WAVEFRONT CURVATURE*

A well-known technique for the migration of normal-incidence two-way travel-time maps is extended to common-source-point travel-time data. The travel time and the travel-time gradient are used to compute the parameters defining the tangent plane of the reflecting interface. It is also shown how the curvature matrix of the received wavefront can be used to compute the curvature of the reflecting interface. The method is initially derived for common-source-point data and then extended to common-midpoint data. In a three-dimensional medium the wavefront curvature matrix is computed by solving a 2 × 2 symmetric matrix Riccati equation. In a two-dimensional medium and in a medium with constant velocity gradient, the wavefront curvature matrix is computed by solving a scalar Riccati equation and two linear equations. The migration procedures are also simplified. When the velocity function is unknown, the migration procedures cannot be used. An inverse modeling algorithm which simultaneously performs the migration and estimates the velocity function must then be applied. Two different inversion schemes are discussed briefly.     

Gravity probability tomography: a new tool for buried mass distribution imaging

Following the probability tomography principles previously introduced to image the sources of electric and electromagnetic anomalies, we demonstrate that a similar approach can be used to analyse gravity data. First, we give a coherent derivation of the Bouguer anomaly concept as a Newtonian-type integral for an arbitrary mass distribution buried below a non-flat topography. A discretized solution of this integral is then derived as a sum of elementary contributions, which are cross-correlated with the gravity data function in the expression for the total power associated with the Bouguer anomaly. To image the mass distribution underground we introduce a mass contrast occurrence probability function using the cross-correlation product of the observed Bouguer anomaly and the synthetic field due to an elementary mass contrast source. The tomographic procedure consists of scanning the subsurface with the elementary source and calculating the occurrence probability function at the nodes of a regular grid. The complete set of grid values is used to highlight the zones of highest probability of mass contrast concentrations. Some synthetic and field examples demonstrate the reliability and resolution of the new gravity tomographic approach.