Cross double‐difference inversion for simultaneous velocity model update and microseismic event location

Microseismic monitoring is an approach for mapping hydraulic fracturing. Detecting the accurate locations of microseismic events relies on an accurate velocity model. The one‐dimensional layered velocity model is generally obtained by model calibration from inverting perforation data. However, perforation shots may only illuminate the layers between the perforation shots and the recording receivers with limited raypath coverage in a downhole monitoring problem. Some of the microseismic events may occur outside of the depth range of these layers. To derive an accurate velocity model covering all of the microseismic events and locating events at the same time, we apply the cross double‐difference method for the simultaneous inversion of a velocity model and event locations using both perforation shots and microseismic data. The cross double‐difference method could provide accurate locations in both the relative and absolute sense, utilizing cross traveltime differences between P and S phases over different events. At the downhole monitoring scale, the number of cross traveltime differences is sufficiently large to constrain events locations and velocity model as well. In this study, we assume that the layer thickness is known, and velocities of P‐ and S‐wave are inverted. Different simultaneous inversion methods based on the Geiger's, double‐difference, and cross double‐difference algorithms have been compared with the same input data. Synthetic and field data experiments suggest that combining both perforation shots and microseismic data for the simultaneous cross double‐difference inversion of the velocity model and event locations is available for overcoming the trade‐offs in solutions and producing reliable results.     

Seismic traveltime inversion of 3D velocity model with triangulated interfaces

Seismic traveltime tomographic inversion has played an important role in detecting the internal structure of the solid earth. We use a set of blocks to approximate geologically complex media that cannot be well described by layered models or cells. The geological body is described as an aggregate of arbitrarily shaped blocks, which are separated by triangulated interfaces. We can describe the media as homogenous or heterogeneous in each block. We define the velocities at the given rectangle grid points for each block, and the heterogeneous velocities in each block can be calculated by a linear interpolation algorithm. The parameters of the velocity grid positions are independent of the model parameterization, which is advantageous in the joint inversion of the velocities and the node depths of an interface. We implement a segmentally iterative ray tracer to calculate traveltimes in the 3D heterogeneous block models. The damped least squares method is employed in seismic traveltime inversion, which includes the partial derivatives of traveltime with respect to the depths of nodes in the triangulated interfaces and velocities defined in rectangular grids. The numerical tests indicate that the node depths of a triangulated interface and homogeneous velocity distributions can be well inverted in a stratified model.     

Feasibility of waveform inversion of Rayleigh waves for shallow shear-wave velocity using a genetic algorithm

Conventional surface wave inversion for shallow shear (S)-wave velocity relies on the generation of dispersion curves of Rayleigh waves. This constrains the method to only laterally homogeneous (or very smooth laterally heterogeneous) earth models. Waveform inversion directly fits waveforms on seismograms, hence, does not have such a limitation. Waveforms of Rayleigh waves are highly related to S-wave velocities. By inverting the waveforms of Rayleigh waves on a near-surface seismogram, shallow S-wave velocities can be estimated for earth models with strong lateral heterogeneity. We employ genetic algorithm (GA) to perform waveform inversion of Rayleigh waves for S-wave velocities. The forward problem is solved by finite-difference modeling in the time domain. The model space is updated by generating offspring models using GA. Final solutions can be found through an iterative waveform-fitting scheme. Inversions based on synthetic records show that the S-wave velocities can be recovered successfully with errors no more than 10% for several typical near-surface earth models. For layered earth models, the proposed method can generate one-dimensional S-wave velocity profiles without the knowledge of initial models. For earth models containing lateral heterogeneity in which case conventional dispersion-curve-based inversion methods are challenging, it is feasible to produce high-resolution S-wave velocity sections by GA waveform inversion with appropriate priori information. The synthetic tests indicate that the GA waveform inversion of Rayleigh waves has the great potential for shallow S-wave velocity imaging with the existence of strong lateral heterogeneity.     

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。     

Generation of a pseudo-2D shear-wave velocity section by inversion of a series of 1D dispersion curves

Multichannel Analysis of Surface Waves utilizes a multichannel recording system to estimate near-surface shear (S)-wave velocities from high-frequency Rayleigh waves. A pseudo-2D S-wave velocity (v_S) section is constructed by aligning 1D models at the midpoint of each receiver spread and using a spatial interpolation scheme. The horizontal resolution of the section is therefore most influenced by the receiver spread length and the source interval. The receiver spread length sets the theoretical lower limit and any v_S structure with its lateral dimension smaller than this length will not be properly resolved in the final v_S section. A source interval smaller than the spread length will not improve the horizontal resolution because spatial smearing has already been introduced by the receiver spread.In this paper, we first analyze the horizontal resolution of a pair of synthetic traces. Resolution analysis shows that (1) a pair of traces with a smaller receiver spacing achieves higher horizontal resolution of inverted S-wave velocities but results in a larger relative error; (2) the relative error of the phase velocity at a high frequency is smaller than at a low frequency; and (3) a relative error of the inverted S-wave velocity is affected by the signal-to-noise ratio of data. These results provide us with a guideline to balance the trade-off between receiver spacing (horizontal resolution) and accuracy of the inverted S-wave velocity. We then present a scheme to generate a pseudo-2D S-wave velocity section with high horizontal resolution using multichannel records by inverting high-frequency surface-wave dispersion curves calculated through cross-correlation combined with a phase-shift scanning method. This method chooses only a pair of consecutive traces within a shot gather to calculate a dispersion curve. We finally invert surface-wave dispersion curves of synthetic and real-world data. Inversion results of both synthetic and real-world data demonstrate that inverting high-frequency surface-wave dispersion curves – by a pair of traces through cross-correlation with phase-shift scanning method and with the damped least-square method and the singular-value decomposition technique – can feasibly achieve a reliable pseudo-2D S-wave velocity section with relatively high horizontal resolution.     

Inverting full waveforms into 1D seismic velocity model of the upper crust by neighborhood algorithm - Corinth Gulf,Greece

We investigated inversion of full waveforms into formal 1D velocity models. ‘Formal’ means that the models are primarily intended to simulate complete seismograms close to real records, rather than to reflect the true crustal structure from the geological point of view. The method is demonstrated for a magnitude M_w 5.3 earthquake (centroid depth of 4.5 km), recorded at 8 three-component stations in the Corinth Gulf region, Greece, spanning the epicentral distance range from 15 to 102 km, and frequency range from 0.05 to 0.2 Hz. The forward problem was solved by the discrete wavenumber method, while the inversion was performed with the neighborhood algorithm. As such, not only the best-fit models, but also suites of the models almost equally well satisfying data were obtained. The best resolution was found in the topmost ～10 km. Extensive testing of the model parametrization enabled identification of the most robust features of the solution. The P- and S-wave velocities are characterized by a strong increase with depth in the topmost ～4–5 km. This part of the model can be approximated by a layer with constant velocity gradient. Compared to a previously existing model of the region, the satisfactory waveform match was extended from the maximum frequency of 0.1 Hz up to 0.2 Hz. This extension will improve calculation of the seismic source parameters in the region, e.g. determination of source time functions and slip distributions of potential future M_w > 6 events.     

层状TI介质中微地震定位和各向异性速度结构同时反演

微地震监测被广泛应用于非常规油气资源的水力压裂作业、油藏描绘和水驱前缘监测工程中.微地震定位采用的初始速度模型一般是基于地震测井记录和射孔数据建立,该速度模型的不准确性易引起定位误差.为降低这种定位误差,本文发展了一种微地震定位和各向异性速度结构同时反演的方法.研究对象为1-D的层状TI介质,其中对称轴方向任意.利用改进的分区多步最短路径算法计算qP、qSV和qSH波的到达时间和射线路径,结合共轭梯度法求解带约束的阻尼最小二乘问题.数值模拟结果表明,该算法能同时进行各向异性速度结构模型（每层的Thomsen参数和界面深度）和微震震源参数（空间坐标和发震时刻）的反演,并且对随机噪声不敏感,有利于实际工程应用.

     

遗传算法和LM算法联合反演瑞雷波相速度

上世纪中叶以来,微震探查法等基于面波相速度频散测定以及其反演的地下构造勘探方法,在地壳研究、工程地质勘探等方面得到了广泛的应用.本研究分析了遗传算法（GA）应用在面波频散反演当中出现的问题,采用遗传算法和Levenberg-Marquardt 算法（LM法）的联合运用法——以遗传算法反演出来的大局的搜索结果为初始点,再进行LM法搜索,由此克服两者的缺点,实现高精度的反演.     

The inversion of 3-D crustal structure and hypocenter location in the Beijing-Tianjin-Tangshan-Zhangjiakou area by genetic algorithm

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Seismic moment tensor inversion using 3D velocity model and its application to the 2013 Lushan earthquake sequence

Source inversion of small-magnitude events such as aftershocks or mine collapses requires use of relatively high frequency seismic waveforms which are strongly affected by small-scale heterogeneities in the crust. In this study, we developed a new inversion method called gCAP3D for determining general moment tensor of a seismic source using Green's functions of 3D models. It inherits the advantageous features of the “Cut-and-Paste” (CAP) method to break a full seismogram into the Pnl and surface-wave segments and to allow time shift between observed and predicted waveforms. It uses grid search for 5 source parameters (relative strengths of the isotropic and compensated-linear-vector-dipole components and the strike, dip, and rake of the double-couple component) that minimize the waveform misfit. The scalar moment is estimated using the ratio of L₂ norms of the data and synthetics. Focal depth can also be determined by repeating the inversion at different depths. We applied gCAP3D to the 2013 M_s 7.0 Lushan earthquake and its aftershocks using a 3D crustal-upper mantle velocity model derived from ambient noise tomography in the region. We first relocated the events using the double-difference method. We then used the finite-differences method and reciprocity principle to calculate Green's functions of the 3D model for 20 permanent broadband seismic stations within 200 km from the source region. We obtained moment tensors of the mainshock and 74 aftershocks ranging from M_w 5.2 to 3.4. The results show that the Lushan earthquake is a reverse faulting at a depth of 13–15 km on a plane dipping 40–47° to N46° W. Most of the aftershocks occurred off the main rupture plane and have similar focal mechanisms to the mainshock's, except in the proximity of the mainshock where the aftershocks' focal mechanisms display some variations.     

基于局部一维模型与走时标定的区域 三维速度模型构建技术研究

构建区域介质三维速度模型并以之获得准确的区域震相走时, 是提高区域地震定位精度的重要手段之一. 为充分利用已有的一维模型、 GT事件、 地质资料等实现三维模型构建, 尝试基于目标区域内已有的部分局部一维模型, 通过克里金空间插值建立初始三维模型, 然后利用GT事件走时数据并参考其它地震地质资料对其不断进行修正, 使得其走时偏差图与GT事件走时偏差图一致, 进而获得能够提高区域地震定位精度的三维模型. 使用不同模型进行的地震定位实验表明, 以此方法建立的三维模型的定位偏差较初始模型减少约20%, 较好地起到了减小区域震相走时残差, 提高区域地震定位精度的作用.     

基于局部一维模型与走时标定的区域三维速度模型构建技术研究

构建区域介质三维速度模型并以之获得准确的区域震相走时,是提高区域地震定位精度的重要手段之一.为充分利用已有的一维模型、GT事件、地质资料等实现三维模型构建,尝试基于目标区域内已有的部分局部一维模型,通过克里金空间插值建立初始三维模型,然后利用GT事件走时数据并参考其它地震地质资料对其不断进行修正,使得其走时偏差图与GT事件走时偏差图一致,进而获得能够提高区域地震定位精度的三维模型.使用不同模型进行的地震定位实验表明,以此方法建立的三维模型的定位偏差较初始模型减少约20％,较好地起到了减小区域震相走时残差,提高区域地震定位精度的作用.     

Stepwise joint inversion of surface wave dispersion,Rayleigh wave ZH ratio,and receiver function data for 1D crustal shear wave velocity structure

Accurate determination of seismic velocity of the crust is important for understanding regional tectonics and crustal evolution of the Earth. We propose a stepwise joint linearized inversion method using surface wave dispersion, Rayleigh wave ZH ratio (i.e., ellipticity), and receiver function data to better resolve 1D crustal shear wave velocity (v _S) structure. Surface wave dispersion and Rayleigh wave ZH ratio data are more sensitive to absolute variations of shear wave speed at depths, but their sensitivity kernels to shear wave speeds are different and complimentary. However, receiver function data are more sensitive to sharp velocity contrast (e.g., due to the existence of crustal interfaces) and v _P/v _S ratios. The stepwise inversion method takes advantages of the complementary sensitivities of each dataset to better constrain the v _S model in the crust. We firstly invert surface wave dispersion and ZH ratio data to obtain a 1D smooth absolute v _S model and then incorporate receiver function data in the joint inversion to obtain a finer v _S model with better constraints on interface structures. Through synthetic tests, Monte Carlo error analyses, and application to real data, we demonstrate that the proposed joint inversion method can resolve robust crustal v _S structures and with little initial model dependency.     

P-wave minimum 1D velocity model for central and northern Pakistan

Journal of Seismology - We present a P-wave minimum 1D velocity model for central and northern Pakistan along with station delays. The velocity model and appropriate station delays are obtained...     

重力与地震资料的模拟退火约束联合反演

联合反演是综合地球物理研究的重要定量解释手段.本文在总结和分析重力与地震资料联合反演的研究现状基础上,利用改进的全局寻优的快速模拟退火算法,实现了重力和地震资料的约束同步联合反演.针对性地设计了密度和速度界面不完全一致的模型,理论模型的试验说明了方法的效果和适用性.结合最近完成的广东徐闻地区实际资料的处理和解释,表明该方法可准确确定复杂构造物性界面的密度和速度结构,在该地区的油气勘探中发挥了作用.在先验信息约束下,该联合反演方法要明显优于单独的重力反演.     

基于数据规则化和稀疏反演的三维表面多次波压制方法

表面多次波是海洋地震勘探中的主要问题.目前,二维数据驱动的表面多次波压制技术(SRME)已经比较成熟,并且已经成为工业界压制海洋表面多次波的主流方法.但是由于二维SRME算法没有考虑横测线方向上多次波的贡献,导致在处理实际三维海洋资料时存在比较大的误差.将二维SRME算法扩展到三维空间后可以得到三维SRME算法,但是由于目前实际采集的三维海洋资料的观测系统存在拖缆漂移,而且横测线方向采样过于稀疏,直接应用三维SRME算法无法准确预测表面多次波.本文提出的通过数据规则化配合稀疏反演的三维表面多次波压制方法能够解决这种实际资料和三维SRME算法之间的矛盾.本文通过研究数据规则化与反规则化技术,使得数据分布满足三维SRME的要求;通过研究稀疏反演技术,有效解决了横测线方向采样稀疏对于多次波预测的影响,三维实际海洋资料的应用结果验证了方法的有效性和可行性.     

三维井地磁测联合约束反演

井中磁测在铁矿等磁性金属矿床勘查中具有举足轻重的作用.针对磁性金属矿床深部资源勘查中存在的有效信号弱、矿体形态复杂等技术难题,本文利用井中三分量磁测资料和地面磁测资料直接反演地下空间磁化率的分布情况,充分发挥纵、横向分辨率高的优势,通过磁化率的变化来确定矿（化）体的范围.分析了磁化率和磁场H_ax、H_ay、Z_a、ΔT各参量之间的关系,导出了磁化率反演方程;将钻孔编录、磁化率测井等结果作为约束条件构建了目标函数.以组合倾斜板状体模型为例,验证了方法的有效性,并在青海野马泉铁多金属矿区开展应用试验,试验结果与已有地质资料基本一致.该方法有效抑制了因反演数据源单一、缺乏约束条件而造成反演结果的多解性,实现了磁测资料的精细反演解释,为查明地下矿体空间位置、形态及规模,提高找矿效果,提供了一种新的解决方案.

     

Quasi-2D hybrid joint inversion of seismic and geoelectric data

Many joint inversion schemes use 1D forward modelling in the integrated interpretation of various geophysical data. In extending the joint inversion approach to the investigation of 2D structures, the discretization of the model parameters and the appropriate choice of the forward‐modelling procedure play a very important role. In this paper, a hybrid seismic–geoelectric joint inversion method is proposed for the investigation of 2D near‐surface geological structures. The electric and seismic models are coupled together through the use of common boundaries between the adjacent layers. Assuming a 2D model composed of homogeneous layers with curved boundaries, a fast ray‐tracing algorithm is used for the calculation of refraction seismic traveltime data. In the geoelectric forward modelling, a locally 1D approximation is used. The boundary surfaces are written in the form of series expansion; the inversion algorithms are formulated for the expansion coefficients and the petrophysical parameters as unknowns. Two versions of the inversion method are proposed: in versions A and B, interval‐wise constant functions and Chebyshev polynomials are, respectively, used as basis functions of the series expansion. The versions are tested by means of synthetic and in situ measured data. The tests show that both methods are stable and accurate.     

联合多源数据反演郯庐断裂带南段地壳三维速度结构

郯庐断裂带南段位于不同块体交汇区, 高分辨率的地壳速度结构有助于理解该地区的构造特征及成因.本文基于多源数据, 利用2015年安徽实验中气枪的体波和高频面波, 2008—2018年区域地震体波信号以及背景噪声面波频散等资料, 将不同来源、不同周期的面波频散数据和体波走时进行联合反演, 获取了郯庐断裂带南段的高精度地壳速度结构.研究结果表明: (1)加入面波信息进行联合反演后, 获取的P波和S波速度模型的分辨能力较单一体波数据反演在中下地壳均有显著提升.(2)郯庐断裂带是控制区域异常的主要因素, 两侧具有明显的速度差异.地震主要发生在断层附近, 集中分布于高低速交界区.(3)秦岭—大别造山带下方5~10 km深度存在明显的高速异常体, 对应于超高压变质岩, 是大陆深俯冲经历超高压变质作用后折返上升到中上地壳形成的.(4)长江中下游成矿带的矿集区呈现高的P波和S波速度值, 可能是陆内俯冲、岩石圈拆沉、幔源岩浆底侵和一系列成矿作用共同造就的.

     

Application of 3D empirical travel times to routine event location

The unmodeled effects of lateral heterogeneity are a primary cause of event mislocation in routine methods. Approaches that account for the effect of lateral heterogeneity on travel times are commonly used in specialized studies, but some methods have recently been developed that are suitable for routine location. A variety of changes to the routine procedures have been suggested by other authors. These proposed changes are shown to be compatible to with the use of 3D travel time predictions. 3D empirical travel times are discussed in a routine context. This one step approach, based on direct use of a database of the most reliable previous observations, is shown to be suitable as an additional final step in routine procedures to give a supplementary high accuracy location. The empirical travel time approach is tested on a reference dataset of 155 ground truth events and shown to reduce epicentral mislocation by 45%. The approach is found to be particularly effective at reducing large mislocations. Improvement is demonstrated for every region represented in the dataset but particularly large improvements are shown for events in Europe, USA and Japan.