一种改进的基于网格搜索的微地震震源定位方法

震源定位是微地震监测技术要解决的主要问题.目前,井下微地震监测多采用走时拟合法计算震源位置.常规方法受到环境噪声、初至拾取误差、速度模型误差等因素的影响,定位结果存在一定误差.为了提高定位精度,本文提出了一种改进的基于网格搜索的微地震震源定位方法.本文方法根据P波的偏振特征参数计算概率密度函数求取震源方位角,并采用改进的目标函数和搜索算法计算震源的径向距离和深度.模型数据和实际资料的处理结果表明,本文方法具有较强的抗噪性,计算得到的震源方位角更加接近真实值;与常规目标函数相比,本文方法采用的目标函数具有更好的收敛性,其定位结果受初至拾取误差和速度模型误差的影响更小;本文提出的搜索算法能够消除由于错误拾取造成的观测到时中的异常值对定位结果的影响.     

基于LTI和网格界面剖分的三维地震射线追踪算法

将二维线性走时插值射线追踪算法(LTI)推广应用至三维模型,并结合网格界面剖分方式,提出了一种三维射线追踪算法．该算法既可获得高精度的全局最小走时和射线路径,又具有快速稳定的特点．三维模型计算结果表明,在模型参数包括网格密度完全相同情况下,本文算法较传统的三维最短路径算法在计算效率、走时和射线的计算精度上均有明显改进．     

宽角反射地震波走时模拟的双重网格法

在研究地壳结构的人工源宽角反射地震资料解释中,常规宽角反射波走时和射线路径计算大都假定地壳模型为层状块状均匀介质.为了逼近实际地壳结构模型,要求模型尺度较大,为了提高地震资料解释的可靠性,须减小模型离散单元的尺寸,但同时计算量大大增加,使资料解释的效率较低.为此,本文尝试同时提高宽角反射地震资料解释效率和可靠性的方法,即使用双重网格计算宽角反射地震波走时和射线路径的最小走时树方法.双重网格法在均匀介质内部仅计算大网格节点,在速度变化点、震源点和检波点区域,同时计算小网格节点;在界面边界点使用比介质内部节点更大的子波传播区域.模型计算结果表明,对于大尺度的层状块状均匀介质模型,在保证精度的条件下,本文所提出的双重网格射线追踪方法的计算效率比单网格方法显著提高.     

Errors due to the anisotropic-common-ray approximation of the coupling ray theory

The common-ray approximation eliminates problems with ray tracing through S-wave singularities and also considerably simplifies the numerical algorithm of the coupling ray theory for S waves, but may introduce errors in travel times due to the perturbation from the common reference ray. These travel-time errors can deteriorate the coupling-ray-theory solution at high frequencies. It is thus of principal importance for numerical applications to estimate the errors due to the common-ray approximation applied. The anisotropic-common-ray approximation of the coupling ray theory is more accurate than the isotropic-common-ray approximation. We derive the equations for estimating the travel-time errors due to the anisotropic-common-ray (and also isotropic-common-ray) approximation of the coupling ray theory. The errors of the common-ray approximations are calculated along the anisotropic common rays in smooth velocity models without interfaces. The derivation is based on the general equations for the second-order perturbations of travel time.     

Accuracy of elastic finite differences in smooth media

The accuracy of finite-difference schemes of the 2nd and 4th order in 2-D and 3-D regular rectangular grids is studied. The method of designing the schemes and estimating their accuracy is proposed. The paper is devoted to the point schemes, expressed in terms of the discretized (point) values of the wave field and material parameters. Only the common schemes applicable in smooth parts of seismic models, outside structural interfaces, are taken into account. Finite differences at structural interfaces are studied elsewhere.The inaccuracy of finite-difference schemes is governed, above all, by the error in the phase velocity, caused by discretization. This error is estimated for several finite-difference schemes. It is explicitly dependent on the direction of propagation and on wave polarization. The maximum phase-velocity error over all directions of propagation enables the accuracy of the individual schemes to be appreciated in order to select the best one. The proposed approach is general and applicable to other finite-difference schemes, for example, of the 6th and higher orders.     

Three-dimensional Travel-time Calculation Based on Fermat's Principle

— We present a new travel-time calculation method based on Fermat's principle. In the method, travel times are recursively calculated on horizontal planes of increasing depth. For typical configurations of exploration geophysics, the distance between the planes is on the order of 100 m. The travel times on the first plane are calculated by connecting straight ray segments from the source point to the grid points on the plane and integrating the slowness along each segment. The times on the other planes are calculated by finding the minimum of the combination of the times on the plane above plus the additional time along segments connecting grid points on the two planes. The travel-time calculation method is designed for calculating either the first arrival times, or the time of the shortest travel path arrival. The method is extended to handle vertically transverse isotropic (VTI) media by an approach which increases the computing time only slightly. The algorithm is tested against synthetic examples for isotropic and VTI wave propagation.     

Errors Due to the Common Ray Approximations of the Coupling Ray Theory

The common ray approximation considerably simplifies the numerical algorithm of the coupling ray theory for S waves, but may introduce errors in travel times due to the perturbation from the common reference ray. These travel-time errors can deteriorate the coupling-ray-theory solution at high frequencies. It is thus of principal importance for numerical applications to estimate the errors due to the common ray approximation.We derive the equations for estimating the travel-time errors due to the isotropic and anisotropic common ray approximations of the coupling ray theory. These equations represent the main result of the paper. The derivation is based on the general equations for the second-order perturbations of travel time. The accuracy of the anisotropic common ray approximation can be studied along the isotropic common rays, without tracing the anisotropic common rays.The derived equations are numerically tested in three 1-D models of differing degree of anisotropy. The first-order and second-order perturbation expansions of travel time from the isotropic common rays to anisotropic-ray-theory rays are compared with the anisotropic-ray-theory travel times. The errors due to the isotropic common ray approximation and due to the anisotropic common ray approximation are estimated. In the numerical example, the errors of the anisotropic common ray approximation are considerably smaller than the errors of the isotropic common ray approximation.The effect of the isotropic common ray approximation on the coupling-ray-theory synthetic seismograms is demonstrated graphically. For comparison, the effects of the quasi-isotropic projection of the Green tensor, of the quasi-isotropic approximation of the Christoffel matrix, and of the quasi-isotropic perturbation of travel times on the coupling-ray-theory synthetic seismograms are also shown. The projection of the travel-time errors on the relative errors of the time-harmonic Green tensor is briefly presented.     

Finite-difference solution of the transport equation: First results

The ray-theoretical transport equation for inhomogeneous isotropic media (2D-SH case) is solved by the method of finite differences on a rectangular grid, both for an incident plane wave (explicit scheme) and a line source (implicit scheme). Results for homogeneous models and for heterogeneous models with structural discontinuities are discussed. First-arrival travel times calculated by various techniques serve as input for the solution of the transport equation and the computation of amplitudes of first arrivals. To obtain correct amplitudes the travel times must be highly accurate and the discontinuities must be smoothed out; the reason is that the spatial second derivatives of the travel time field enter the transport equation. In the simple cases studied, finite differences provide a fast and efficient tool for the computation of first-arrival amplitudes.     

Application of 3-D Crustal and Upper Mantle Velocity Model of North America for Location of Regional Seismic Events

—?Seismic event locations based on regional 1-D velocity-depth sections can have bias errors caused by travel-time variations within different tectonic provinces and due to ray-paths crossing boundaries between tectonic provinces with different crustal and upper mantle velocity structures. Seismic event locations based on 3-D velocity models have the potential to overcome these limitations. This paper summarizes preliminary results for calibration of IMS for North America using 3-D velocity model. A 3-D modeling software was used to compute Source-Station Specific Corrections (SSSCs(3-D)) for Pn travel times utilizing 3-D crustal and upper mantle velocity model for the region. This research was performed within the framework of the United States/Russian Federation Joint Program of Seismic Calibration of the International Monitoring System (IMS) in Northern Eurasia and North America.¶An initial 3-D velocity model for North America was derived by combining and interpolating 1-D velocity-depth sections for different tectonic units. In areas where no information on 1-D velocity-depth sections was available, tectonic regionalization was used to extrapolate or interpolate. A Moho depth map was integrated. This approach combines the information obtained from refraction profiles with information derived from local and regional network data. The initial 3-D velocity model was tested against maps of Pn travel-time residuals for eight calibration explosions; corrections to the 3-D model were made to fit the observed residuals. Our goal was to find a 3-D crustal and upper mantle velocity model capable predicting Pn travel times with an accuracy of 1.0–1.5 seconds (r.m.s.).¶The 3-D velocity model for North America that gave the best fit to the observed travel times, was used to produce maps of SSSCs(3-D) for seismic stations. The computed SSSCs(3-D) vary approximately from +5 seconds to ?5 seconds for the western USA and the Pre-Cambrian platform, respectively. These SSSCs(3-D) along with estimated modeling and measurement errors were used to relocate, using regional data, an independent set of large chemical explosions (with known locations and origin times) detonated within various tectonic provinces of North America. Utilization of the 3-D velocity model through application of the computed SSSCs(3-D) resulted in a substantial improvement in seismic event location accuracy and in a significant decrease of error ellipse area for all events analyzed in comparison both with locations based on the IASPEI91 travel times and locations based on 1-D regional velocity models.     

Linearized rays,amplitude and inversion

In this paper, ray theoretical amplitudes and travel times are calculated in slightly perturbed velocity models using perturbation analysis. Also, test inversions using travel time and amplitude are computed. The pertubation method is tested using a 3-D velocity model for NORSAR having velocity variations up to 8.0 percent. The perturbed amplitudes are found to be in excellent agreement with the calculated ray amplitudes. Velocity inversions based on travel time and amplitude are next investigated. Perturbation analysis using linearized ray equations is efficiently used to compute amplitude derivatives with respect to model parameters. The trial linearized inversions use smaller velocity variations of 1.7 percent to avoid possible effects due to ray shift, even though the perturbation analysis is valid for larger variations. The trial 2-D inversion results show that linearized amplitude inversions are complementary and not redundant to travel time inversions, even in smoothly varying models.     

P-wave Tomography in Inhomogeneous Orthorhombic Media

— A P-wave tomographic method for 3-D complex media (3-D distribution of elastic parameters and curved interfaces) with orthorhombic symmetry is presented in this paper. The technique uses an iterative linear approach to the nonlinear travel-time inversion problem. The hypothesis of orthorhombic anisotropy and 3-D inhomogeneity increases the set of parameters describing the model dramatically compared to the isotropic case. Assuming a Factorized Anisotropic Inhomogeneous (FAI) medium and weak anisotropy, we solve the forward problem by a perturbation approach. We use a finite element approach in which the FAI medium is divided into a set of elements with polynomial elastic parameter distributions. Inside each element, analytical expressions for rays and travel times, valid to first-order, are given for P waves in orthorhombic inhomogeneous media. More complex media can be modeled by introducing interfaces separating FAI media with different elastic properties. Simple formulae are given for the Fréchet derivatives of the travel time with respect to the elastic parameters and the interface parameters. In the weak anisotropy hypothesis the P-wave travel times are sensitive only to a subset of the orthorhombic parameters: the six P-wave elastic parameters and the three Euler angles defining the orientation of the mirror planes of symmetry. The P-wave travel times are inverted by minimizing in terms of least-squares the misfit between the observed and calculated travel times. The solution is approached using a Singular Value Decomposition (SVD). The stability of the inversion is ensured by making use of suitable a priori information and/or by applying regularization. The technique is applied to two synthetic data sets, simulating simple Vertical Seismic Profile (VSP) experiments. The examples demonstrate the necessity of good 3-D ray coverage when considering complex anisotropic symmetry.     

无网格局部Petrov-Galerkin法大地电磁场二维正演模拟

有限差分法和有限单元法在大地电磁场数值模拟中已经得到了广泛的应用,但其数值结果的精度在很大程度上依赖于网格的离散程度.当模拟起伏地形、弯曲界面等复杂地电模型大地电磁场响应时,常常需要花费大量的时间以便得到较合理的离散网格.无网格局部Petrov-Galerkin法(MLPG)不同于有限差分法和有限元法,其形函数和权函数脱离了网格的束缚.本文详细推导了二维大地电磁场边值问题的弱式形式,并将其离散为局部积分域内的表达形式.通过模拟二维海洋地电模型大地电磁场响应,并与结构网格有限元结果进行对比,验证了本文算法和程序的正确性及精度.设计了一个含有弯曲界面的二维地电模型,讨论了不同离散网格对MLPG无网格法模拟结果的影响,并与结构有限元法结果进行了比较,结果表明MLPG无网格法模拟结果受离散网格影响较小.最后利用MLPG无网格法计算了两个海洋起伏地形模型的大地电磁响应,讨论了海底起伏地形对大地电磁响应的影响.     

Automatic Generation of Locally Refined Composite Grids for Efficient Solute Transport Modeling

Widely used numerical models of solute transport processes in subsurface aquifers are limited to nonlocally refined rectangular, or logically rectangular, structured grids. This presents an unsuitable option to efficient numerical simulations maintaining an acceptable level of accuracy. Optimal selection of locally refined cells for efficient solute transport models is challenging to the current generation of numerical models. We present a novel and relatively simple to implement algorithm addressing these shortcomings. This method operates in four steps involving travel times simulations, a grid coarsening stage followed by a selective local grid refinement based on a cell-wise indicator, and a final postprocessing step. The refinement index is the sum of weighted logarithmic distributions of scaled forward and backward travel times. We calculate representative flow and transport properties at the two scales of the composite grid with a flow-based upscaling technique. We present two test problems to demonstrate the performances of this new gridding algorithm. We obtain the most important speedups for composite grids generated with the highest indicator thresholds. When hydrodynamic dispersion effects increase, we obtain less important speedups. An important outcome of this work is that grid design depends on nature and strength of the underlying flow and solute transport processes. Therefore, we suggest developing solute transport workflows integrating this grid generation algorithm as an integral component to build comprehensive and efficient groundwater models.     

Application of Snell's law in reflection raytracing using the multistage fast marching method

Accurate calculations of travel times and raypaths of reflection waves are important for reflection travel time tomography. The multistage shortest path method(MSPM) and multistage fast marching method(MFMM) have been widely used in reflection wave raytracing, and both of them are characterized by high efficiency and accuracy. However, the MSPM does not strictly follow Snell's law at the interface because it treats the interface point as a sub-source, resulting in a decrease in accuracy. The MFMM achieves high accuracy by solving the Eikonal equation in local triangular mesh. However, the implementation process is complex. Here we propose a new method which uses linear interpolation to compute the incident travel time of interface points and then using Snell's law to compute the reflection travel time of grid points just above the interface. Our new method is much simpler than the MFMM; furthermore, numerical simulations show that the accuracy of the MFMM and our new method are basically the same, thus the reflection tomography algorithms which use our new method are easier to implement without decreasing accuracy. Besides, our new method can be extended easily to other grid-based raytracing methods.     

三维介质中速度结构和界面的联合成像

根据波逆行原理推导了三维介质中地震波射线走时对界面偏导数的完整基本关系式,并对基本关系式进行简化,得到其在二维和一维介质中的关系式. 给出了任意多个复杂界面情况下,反演时所需的走时对界面偏导数系数矩阵. 为了检验三维介质中速度和界面联合成像理论的有效性,进行了数值模拟计算,很好地对三维速度结构和界面进行了重建.     

Estimation of Thomsen＇s anisotropic parameters from walkaway VSP and applications

Estimation of Thomsen＇s anisotropic parameters is very important for accuratetime-to-depth conversion and depth migration data processing. Compared with othermethods, it is much easier and more reliable to estimate anisotropic parameters that arerequired for surface seismic depth imaging from vertical seismic profile （VSP） data, becausethe first arrivals of VSP data can be picked with much higher accuracy. In this study, wedeveloped a method for estimating Thomsen＇s P-wave anisotropic parameters in VTImedia using the first arrivals from walkaway VSP data. Model first-arrival travel times arecalculated on the basis of the near-offset normal moveout correction velocity in VTI mediaand ray tracing using Thomsen＇s P-wave velocity approximation. Then, the anisotropicparameters 0 and e are determined by minimizing the difference between the calculatedand observed travel times for the near and far offsets. Numerical forward modeling, usingthe proposed method indicates that errors between the estimated and measured anisotropicparameters are small. Using field data from an eight-azimuth walkaway VSP in TarimBasin, we estimated the parameters 0 and e and built an anisotropic depth-velocity modelfor prestack depth migration processing of surface 3D seismic data. The results showimprovement in imaging the carbonate reservoirs and minimizing the depth errors of thegeological targets.     

Constraining the anisotropy structure of the crust by joint inversion of seismic reflection travel times and wave polarizations

In the context of wide-angle seismic profiling, the determination of the physical properties of the Earth crust, such as the elastic layer depth and seismic velocity, is often performed by inversion of P- and/or S-phases propagation data supplying the geometry of the medium (reflector depths) or any other structural parameter (P- or S-wave velocity, density...). Moreover, the inversion for velocity structure and interfaces is commonly performed using only seismic reflection travel times and/or crustal phase amplitudes in isotropic media. But it is very important to utilize more available information to constrain the non-uniqueness of the solution. In this paper, we present a simultaneous inversion method of seismic reflection travel times and polarizations data of transient elastic waves in stratified media to reconstruct not only layer depth and vertical P-wave velocity but also the anisotropy feature of the crust based on the estimation of the Thomsen’s parameters. We carry out a checking with synthetic data, comparing the inversion results obtained by anisotropic travel-time inversion to the results derived by joint inversion of seismic reflection travel times and polarizations data. The comparison proves that the first procedure leads to biased anisotropic models, while the second one fits nearly the real model. This makes the joint inversion method feasible. Finally, we investigate the geometry, P-wave velocity structure and anisotropy of the crust beneath Southeastern China by applying the proposed inversion method to previously acquired wide-angle seismic data. In this case, the anisotropy signature provides clear evidence that the Jiangshan-Shaoxing fault is the natural boundary between the Yangtze and Cathaysia blocks.     

Finite difference calculation of traveltime on non-orthogonal grid

Finite difference methods have been widely employed in solving the eikonal equation so as to calculate traveltime of seismic phase. Most previous studies used regular orthogonal grid. However, much denser grid is required to sample the interfaces that are undulating in depth direction, such as the Moho and the 660 km discontinuity.Here we propose a new finite difference algorithm to solve the eikonal equation on non-orthogonal grid(irregular grid).To demonstrate its efficiency and accuracy, a test was conducted with a two-layer model. The test result suggests that the similar accuracy of a regular grid with ten times grids could achieve with our new algorithm, but the time cost is only about 0.1 times. A spherical earth model with an undulant660 km discontinuity was constructed to demonstrate the potential application of our new method. In that case, the traveltime curve fluctuation corresponds to topography. Our new algorithm is efficient in solving the first arrival times of waves associated with undulant interfaces.     

Computation of Synthetic Seismograms in 2-D and 3-D Media Using the Gaussian beam Method

The Gaussian beam method is applied to vertical seismic profiling in 2-D and 3-D models. A simple approach to the computation of Gaussian beam seismograms in the vicinity of structural interfaces is proposed. The effects of (a) the radiation pattern of a point source, (b) non-causal attenuation, (c) transverse inhomogeneities in synthetic seismograms are studied on numerical examples.     

Construction of ray synthetic seismograms using interpolation of travel times and ray amplitudes

The seismic wave field, in its high-frequency asymptotic approximation, can be interpolated from a low- to a high-resolution spatial grid of receivers and, possibly, point sources by interpolating the eikonal (travel time) and the amplitude. These quantities can be considered as functions of position only. The travel time and the amplitude are assumed to vary in space only slowly, otherwise the validity conditions of the theory behind would be violated. Relatively coarse spatial sampling is then usually sufficient to obtain their reasonable interpolation. The interpolation is performed in 2-D models of different complexity. The interpolation geometry is either 1-D, 2-D, or 3-D according to the source-receiver distribution. Several interpolation methods are applied: the Fourier interpolation based on the sampling theorem, the linear interpolation, and the interpolation by means of the paraxial approximation. These techniques, based on completely different concepts, are tested by comparing their results with a reference ray-theory solution computed for gathers and grids with fine sampling. The paraxial method holds up as the most efficient and accurate in evaluating travel times from all investigated techniques. However, it is not suitable for approximation of amplitudes, for which the linear interpolation has proved to be universal and accurate enough to provide results acceptable for many seismological applications.