模拟退火方法在三维速度模型地震波走时反演中的应用

采用块状建模以及三角形拼接的界面描述方式,并通过立方体速度网格线性插值获得块体内部的速度分布。正演过程中采用逐段迭代射线追踪方法计算三维复杂地质模型中的射线走时,并采用模拟退火方法进行了三维模型中的地震波走时反演研究。模型测试结果表明,使用的射线追踪和走时反演算法有效。     

三维地质模型中地震波共轭梯度非线性走时反演

地震体波走时层析成像是探测地球内部速度结构的重要方法之一。基于三维块状建模以及三角形拼接的界面描述方式,结合快速高效的逐段迭代射线追踪方法,获得三维复杂地质模型中的地震射线路径与走时信息,采用共轭梯度非线性反演算法,进行地震波走时反演。实验结果表明共轭梯度反演算法在三维层状模型中具有较高的有效性。     

Multi‐block finite‐difference method for 3D elastodynamic simulations in anisotropic subhorizontally layered media

Prediction of elastic full wavefields is required for reverse time migration, full waveform inversion, borehole seismology, seismic modelling, etc. We propose a novel algorithm to solve the Navier wave equation, which is based on multi‐block methodology for high‐order finite‐difference schemes on curvilinear grids. In the current implementation, the blocks are subhorizontal layers. Smooth anisotropic heterogeneous media in each layer can have strong discontinuities at the interfaces. A curvilinear adaptive hexahedral grid in blocks is generated by mapping the original 3D physical domain onto a parametric cube with horizontal layers and interfaces. These interfaces correspond to the main curvilinear physical contrast interfaces of a subhorizontally layered formation. The top boundary of the parametric cube handles the land surface with smooth topography. Free‐surface and solid–solid transmission boundary conditions at interfaces are approximated with the second‐order accuracy. Smooth media in the layers are approximated up to sixth‐order spatial schemes. All expected properties of the developed algorithm are demonstrated in numerical tests using corresponding parallel message passing interface code.     

郯庐断裂带鲁苏皖段及邻区地壳速度结构

郯庐断裂带是我国东部规模最大的深断裂带.为了揭示该断裂带的深部结构,本文利用江苏、安徽、山东、上海和浙江地震台网记录的近震到时资料,对8700个地震事件重新精确定位,进而开展了多震相地震走时成像法反演地壳速度结构.通过分析郯庐断裂带鲁苏皖段及邻区三维地壳速度结构图像,发现(1)研究区内不同构造块体具有差异明显的地壳速度...     

DETERMINATION OF LATERAL INHOMOGENEITIES IN REFLECTION SEISMICS BY INVERSION OF TRAVELTIME RESIDUALS*

Lateral inhomogeneities generate fluctuations in the traveltime of seismic waves. By evaluation of these traveltime fluctuations from different source and receiver positions, lateral inhomogeneities can be located using a pseudo inverse matrix method (Aki, Christoffersson and Husebye 1977). The formulation of the problem is possible for transmitted waves as well as for reflected and refracted waves. In reflection seismics this method is of importance, if no reflections from the inhomogeneities themselves, but only reflections from lower boundaries can be observed. The basic assumptions for the mathematical formulation are (1) the average velocities and depths of the reflecting horizons are known already from standard processing methods, and (2) the traveltime residuals are due to lateral velocity changes between different reflectors or between reflectors and the surface. The area of the earth to be considered is divided into layers and the layers into rectangular blocks. The parallel displacement of a ray after passing a disturbed block is neglected, only the traveltime residual is taken into account. In this paper the method and its application to data obtained with two-dimensional models are described.     

Piecewise‐continuous velocity inversion

We suggest a new method to determine the piecewise‐continuous vertical distribution of instantaneous velocities within sediment layers, using different order time‐domain effective velocities on their top and bottom points. We demonstrate our method using a synthetic model that consists of different compacted sediment layers characterized by monotonously increasing velocity, combined with hard rock layers, such as salt or basalt, characterized by constant fast velocities, and low velocity layers, such as gas pockets. We first show that, by using only the root‐mean‐square velocities and the corresponding vertical travel times (computed from the original instantaneous velocity in depth) as input for a Dix‐type inversion, many different vertical distributions of the instantaneous velocities can be obtained (inverted). Some geological constraints, such as limiting the values of the inverted vertical velocity gradients, should be applied in order to obtain more geologically plausible velocity profiles. In order to limit the non‐uniqueness of the inverted velocities, additional information should be added. We have derived three different inversion solutions that yield the correct instantaneous velocity, avoiding any a priori geological constraints. The additional data at the interface points contain either the average velocities (or depths) or the fourth‐order average velocities, or both. Practically, average velocities can be obtained from nearby wells, whereas the fourth‐order average velocity can be estimated from the quartic moveout term during velocity analysis. Along with the three different types of input, we consider two types of vertical velocity models within each interval: distribution with a constant velocity gradient and an exponential asymptotically bounded velocity model, which is in particular important for modelling thick layers. It has been shown that, in the case of thin intervals, both models lead to similar results. The method allows us to establish the instantaneous velocities at the top and bottom interfaces, where the velocity profile inside the intervals is given by either the linear or the exponential asymptotically bounded velocity models. Since the velocity parameters of each interval are independently inverted, discontinuities of the instantaneous velocity at the interfaces occur naturally. The improved accuracy of the inverted instantaneous velocities is particularly important for accurate time‐to‐depth conversion.     

Generalized Dix equation and analytic treatment of normal-moveout velocity for anisotropic media*

Despite the complexity of wave propagation in anisotropic media, reflection moveout on conventional common-midpoint (CMP) spreads is usually well described by the normal-moveout (NMO) velocity defined in the zero-offset limit. In their recent work, Grechka and Tsvankin showed that the azimuthal variation of NMO velocity around a fixed CMP location generally has an elliptical form (i.e. plotting the NMO velocity in each azimuthal direction produces an ellipse) and is determined by the spatial derivatives of the slowness vector evaluated at the CMP location. This formalism is used here to develop exact solutions for the NMO velocity in anisotropic media of arbitrary symmetry. For the model of a single homogeneous layer above a dipping reflector, we obtain an explicit NMO expression valid for all pure modes and any orientation of the CMP line with respect to the reflector strike. The contribution of anisotropy to NMO velocity is contained in the slowness components of the zero-offset ray (along with the derivatives of the vertical slowness with respect to the horizontal slownesses) — quantities that can be found in a straightforward way from the Christoffel equation. If the medium above a dipping reflector is horizontally stratified, the effective NMO velocity is determined through a Dix-type average of the matrices responsible for the ‘interval’ NMO ellipses in the individual layers. This generalized Dix equation provides an analytic basis for moveout inversion in vertically inhomogeneous, arbitrarily anisotropic media. For models with a throughgoing vertical symmetry plane (i.e. if the dip plane of the reflector coincides with a symmetry plane of the overburden), the semi-axes of the NMO ellipse are found by the more conventional rms averaging of the interval NMO velocities in the dip and strike directions. Modelling of normal moveout in general heterogeneous anisotropic media requires dynamic ray tracing of only one (zero-offset) ray. Remarkably, the expressions for geometrical spreading along the zero-offset ray contain all the components necessary to build the NMO ellipse. This method is orders of magnitude faster than multi-azimuth, multi-offset ray tracing and, therefore, can be used efficiently in traveltime inversion and in devising fast dip-moveout (DMO) processing algorithms for anisotropic media. This technique becomes especially efficient if the model consists of homogeneous layers or blocks separated by smooth interfaces. The high accuracy of our NMO expressions is illustrated by comparison with ray-traced reflection traveltimes in piecewise-homogeneous, azimuthally anisotropic models. We also apply the generalized Dix equation to field data collected over a fractured reservoir and show that P-wave moveout can be used to find the depth-dependent fracture orientation and to evaluate the magnitude of azimuthal anisotropy.     

三维非均匀地质模型中的逐段迭代射线追踪

地震射线追踪是地震定位、层析成像、偏移等领域的重要正演环节.随着这些领域研究的深入,针对传统的网格结构和层状结构在描述复杂地质模型遇到的很大困难,我们采用大小不等、形状各异的地质块组成的集合体来描述三维复杂地质模型,并用三角形面片来描述地质块之间的物性间断面,理论上可以描述任意复杂的地质模型.为适应任意非均匀速度分布的地质模型,基于费马原理,本文发展了与之相适应的逐段迭代射线追踪方法.该方法属于弯曲法范畴,对路径点采用一阶显式增量修正,相对于传统的迭代法,高效省时.数值试验表明,联合逐段迭代法和伪弯曲法的射线追踪扰动修正方案在三维复杂非均匀块状模型中有适用性和高效性.     

2D inversion of refraction traveltime curves using homogeneous functions

A method using simple inversion of refraction traveltimes for the determination of 2D velocity and interface structure is presented. The method is applicable to data obtained from engineering seismics and from deep seismic investigations. The advantage of simple inversion, as opposed to ray‐tracing methods, is that it enables direct calculation of a 2D velocity distribution, including information about interfaces, thus eliminating the calculation of seismic rays at every step of the iteration process. The inversion method is based on a local approximation of the real velocity cross‐section by homogeneous functions of two coordinates. Homogeneous functions are very useful for the approximation of real geological media. Homogeneous velocity functions can include straight‐line seismic boundaries. The contour lines of homogeneous functions are arbitrary curves that are similar to one another. The traveltime curves recorded at the surface of media with homogeneous velocity functions are also similar to one another. This is true for both refraction and reflection traveltime curves. For two reverse traveltime curves, non‐linear transformations exist which continuously convert the direct traveltime curve to the reverse one and vice versa. This fact has enabled us to develop an automatic procedure for the identification of waves refracted at different seismic boundaries using reverse traveltime curves. Homogeneous functions of two coordinates can describe media where the velocity depends significantly on two coordinates. However, the rays and the traveltime fields corresponding to these velocity functions can be transformed to those for media where the velocity depends on one coordinate. The 2D inverse kinematic problem, i.e. the computation of an approximate homogeneous velocity function using the data from two reverse traveltime curves of the refracted first arrival, is thus resolved. Since the solution algorithm is stable, in the case of complex shooting geometry, the common‐velocity cross‐section can be constructed by applying a local approximation. This method enables the reconstruction of practically any arbitrary velocity function of two coordinates. The computer program, known as godograf , which is based on this theory, is a universal program for the interpretation of any system of refraction traveltime curves for any refraction method for both shallow and deep seismic studies of crust and mantle. Examples using synthetic data demonstrate the accuracy of the algorithm and its sensitivity to realistic noise levels. Inversions of the refraction traveltimes from the Salair ore deposit, the Moscow region and the Kamchatka volcano seismic profiles illustrate the methodology, practical considerations and capability of seismic imaging with the inversion method.     

利用联合反演技术进行反射地震的波速成象

本文介绍了根据反射地震数据进行波速成象的一种方法,其基础为多种反演技术的综合。由于要求的波速图象C（x,z）具有间断性,除利用走时数据T（x,t）外,在地层比较水平的情况下,还利用了均方根速度V（x,t）和统计子波W（t）的数据来成象。计算机层析成象过程分为三步:首先重做速度分析,取得与初次反射走时一致的均方根速度数据;然后用反射走时与均方根速度联合反演对应分析道的层速度和界面深度;最后由联合反演结果和反射面走时求波速图象函数的数字化版。文中还给出了波速成象方法在我国西北某沉积盆地上的应用及验证结果。     

各向异性TI介质qP反射波走时层析成像

地震走时层析成像是反演地层各向异性参数分布的有效方法,但是关于地震各向异性介质走时层析成像的研究并不多,其技术远远没有达到成熟的阶段.在野外数据采集时,地表反射波观测方式相对井间和垂直地震剖面观测方式的成本更低,利用qP反射波走时反演各向异性参数具有更加广泛的实用价值.本文实现的TI介质地震走时层析成像方法结合了TI介质反射波射线追踪算法、走时扰动方程和非线性共轭梯度算法,它可以对任意强度的TI介质模型进行反演,文中尝试利用qP反射波走时重建TI介质模型的参数图像.利用qP反射波对层状介质模型和块状异常体模型进行走时反演,由于qP波相速度对弹性模量参数和Thomsen参数的偏微分不同,所以可以分别反演弹性模量参数和Thomsen参数.数值模拟结果表明:利用qP反射波可以反演出TI介质模型的弹性模量参数与Thomsen参数,不同模型的走时迭代反演达到了较好的收敛效果,与各向同性介质走时反演结果相比较,各向异性介质走时反演结果具有较好的识别能力.     

Non‐uniqueness with refraction inversion – a syncline model study

Non‐uniqueness occurs with the 1D parametrization of refraction traveltime graphs in the vertical dimension and with the 2D lateral resolution of individual layers in the horizontal dimension. The most common source of non‐uniqueness is the inversion algorithm used to generate the starting model. This study applies 1D, 1.5D and 2D inversion algorithms to traveltime data for a syncline (2D) model, in order to generate starting models for wave path eikonal traveltime tomography. The 1D tau‐p algorithm produced a tomogram with an anticline rather than a syncline and an artefact with a high seismic velocity. The 2D generalized reciprocal method generated tomograms that accurately reproduced the syncline, together with narrow regions at the thalweg with seismic velocities that are less than and greater than the true seismic velocities as well as the true values. It is concluded that 2D inversion algorithms, which explicitly identify forward and reverse traveltime data, are required to generate useful starting models in the near‐surface where irregular refractors are common. The most likely tomogram can be selected as either the simplest model or with a priori information, such as head wave amplitudes. The determination of vertical velocity functions within individual layers is also subject to non‐uniqueness. Depths computed with vertical velocity gradients, which are the default with many tomography programs, are generally 50% greater than those computed with constant velocities for the same traveltime data. The average vertical velocity provides a more accurate measure of depth estimates, where it can be derived. Non‐uniqueness is a fundamental reality with the inversion of all near‐surface seismic refraction data. Unless specific measures are taken to explicitly address non‐uniqueness, then the production of a single refraction tomogram, which fits the traveltime data to sufficient accuracy, does not necessarily demonstrate that the result is either ‘correct’ or the most probable.     

基于Love波相速度反演南北地震带地壳上地幔结构

收集了南北地震带区域地震台网中292个地震台站2008年1月至2011年3月期间的地震波形数据,由频时分析方法提取了Love波相速度频散曲线,经过反演得到了研究区内的Love波相速度分布.根据Love波纯路径频散,采用线性反演方法对0.25°×0.25°的网格点进行了一维S波速度结构反演,利用线性插值获取了南北地震带地区的三维S波速度结构.结果显示了松潘—甘孜地体和川滇菱形块体地区的下地壳具有明显的S波低速层分布,该异常分布特征支持解释青藏高原隆升及其地壳物质运移的下地壳流模型.在100至120km深度上,川滇菱形块体西北部呈现较强的S波高速异常,这可能是印度岩石圈板块沿喜马拉雅东构造结下插至该区域所致,该区域下地壳的低速软弱物质与上地幔的高速强硬物质形成了鲜明对比,暗示了地壳和上地幔可能具有不同的构造运动和变形方式,这为该区域的壳幔动力学解耦提供了条件.     

3-D simultaneous inversion for velocity and reflector geometry using multiple classes of arrivals in a spherical coordinate frame

The two key requirements in conducting 3-D simultaneous traveltime tomography on real data at the regional and global scale with multiple classes of arrival time information are (1) it needs an efficient and accurate arrival tracking algorithm for multiply transmitted, reflected (or refracted) and converted waves in a 3-D variable velocity model with embedded velocity discontinuities (or subsurface interfaces), and (2) a subdimensional inversion solver is required which can easily search for different types of model parameters to balance the trade-off between the different types of model parameter updated in the simultaneous inversion process. For these purposes, we first extend a popular grid/cell-based wavefront expanding ray tracing algorithm (the multistage irregular shortest-path ray tracing method), which previously worked only in Cartesian coordinate at the local scale, to spherical coordinates appropriate to the regional or global scale. We then incorporated a fashionable inversion solver (the subspace method) to formulate a simultaneous inversion algorithm, in which the multiple classes of arrivals (including direct and reflected arrivals from different velocity discontinuities) can be used to simultaneously update both the velocity fields and the reflector geometries. Numerical tests indicate that the new inversion method is both applicable and flexible in terms of computational efficiency and solution accuracy, and is not sensitive to a modest level of noise in the traveltime data. It offers several potential benefits over existing schemes for real data seismic imaging.     

横向各向同性介质中地震波走时模拟

横向各向同性介质是地球内部广泛分布的一种各向异性介质.针对这种介质，我们对各向同性介质的最小走时树走时模拟方法进行了推广，推广后的方法可适用于非均匀、对称轴任意倾斜的横向各向同性介质模型.为保证计算效率，最小走时树的构建采用了一种子波传播区域随地震波传播动态变化的改进算法.对于弱各向异性介质，我们使用了一种新的地震波群速度近似表示方法，该方法基于用射线角近似表示相角的思想，对3种地震波（qP, qSV和qSH）均有较好的精度.应用本文地震波走时模拟方法对均匀介质、横向非均匀介质模型进行了计算，并将后者结果与弹性波方程有限元方法的模拟结果进行了对比，结果表明两者符合得很好.本文方法可用于横向各向同性介质的深度偏移及地震层析成像的深入研究.     

First‐arrival traveltime tomography with modified total‐variation regularization

First‐arrival traveltime tomography is a robust tool for near‐surface velocity estimation. A common approach to stabilizing the ill‐posed inverse problem is to apply Tikhonov regularization to the inversion. However, the Tikhonov regularization method recovers smooth local structures while blurring the sharp features in the model solution. We present a first‐arrival traveltime tomography method with modified total‐variation regularization to preserve sharp velocity contrasts and improve the accuracy of velocity inversion. To solve the minimization problem of the new traveltime tomography method, we decouple the original optimization problem into the two following subproblems: a standard traveltime tomography problem with the traditional Tikhonov regularization and a L₂ total‐variation problem. We apply the conjugate gradient method and split‐Bregman iterative method to solve these two subproblems, respectively. Our synthetic examples show that the new method produces higher resolution models than the conventional traveltime tomography with Tikhonov regularization, and creates less artefacts than the total variation regularization method for the models with sharp interfaces. For the field data, pre‐stack time migration sections show that the modified total‐variation traveltime tomography produces a near‐surface velocity model, which makes statics corrections more accurate.     

基于非规则网格声波正演的时间域全波形反演

全波形反演是地震资料处理中速度建模的有力工具,相比层析成像等速度建模方法它能够得到速度场的更高频成分.本文给出了基于声波方程格子法正演的时间域全波形反演方法,该方法用非规则、非结构化的三角网格来离散计算区域及模型参数,能实现网格粒度与反演分辨率在空间上的自动匹配,内存需求少,计算效率高;采用L-BFGS优化方法,以分频段变网格的方式实施多尺度反演.以二维Overthrust模型进行了速度反演数值测试,显示了该方法的高效性和潜力.     

Traveltime parameters in a tilted elliptical anisotropic medium‡

In this paper, we derive analytical expressions for one‐way and two‐way kinematical parameters in elliptical tilted transverse isotropy media. We show that the homogeneous elliptical tilted transverse isotropy models result in hyperbolic moveout with a reflection point sideslip x₀, which can be considered as an additional traveltime parameter for one‐way wave propagation. For homogeneous elliptical tilted transverse isotropy models we show that the inversion of one‐way traveltime parameters suffers from the ambiguity for large tilts. It is shown that the accuracy of the inversion is sensitive to the error in x₀. We also derive and invert the traveltime parameters for a vertically heterogeneous elliptical tilted transverse isotropy model with a tilt gradually changing with depth. The a priori knowledge of parameter δ is very important for inversion. The wrong choise of this parameter results in significant errors in inverted model parameters.     

三角网波行面扩展最小走时射线追踪全局算法

To address the problem of subdividing inflexible rectangular grid models and their poor definition of velocity interfaces, we propose a complex structure triangular net for a minimum traveltime ray tracing global algorithm. Our procedure is: (1) Subdivide a triangle grid based on the Delaunay triangular subdivision criterion and the relationships of the points, lines, and the surfaces in the subdividing area. (2) Define the topology relationships and related concepts of triangular unit ray tracing. (3) The source point and wave arrival points at any time compose the propagating plane wave and the minimum traveltime and secondary source positions are calculated during the plane wave propagation. We adopt the hyperbolic approximation global algorithm for secondary source retrieving. (4) By minimum traveltime ray tracing, collect the path from receiver to source points with the neighborhood point’s traveltime and the direction of the secondary source. Numerical simulation examples are given to test the algorithm. The results show that the triangular net ray tracing method demonstrates model subdivision flexibility, precise velocity discontinuity interfaces, and accurate computations.     

Interpretation of shallow refraction seismic data by reflection/refraction tomography

A new algorithm for tomographic inversion of traveltimes of reflected and refracted seismic waves is developed. The inversion gives interface configurations and velocity distributions in layers. The important features of the algorithm are: (a) the inclusion of shot time delays in the list of unknown parameters; (b) the regularization is applied in such a way that the most probable model is characterized by the similarity of neighbouring interfaces. As the problem under consideration is non-linear, several iterations are necessary in order to obtain the final model. In the case of a very inexact initial model, a 'layer-by-layer' inversion strategy is recommended as a first inversion step. The inversion program is supplied with a user interface, thanks to which one can: (a) pick interactively and identify seismic traveltimes; (b) build and edit depth/velocity models; and (c) display calculated traveltime curves and compare them with picked traveltimes as well as with the original seismic sections. The efficiency of the inversion software developed is illustrated by a numerical example and a field example in which shallow seismic data are considered. Application to wide-aperture reflection/refraction profiling (WARRP) data is also possible.