An improved grey wolf optimizer algorithm for the inversion of geoelectrical data

The grey wolf optimizer (GWO) is a novel bionics algorithm inspired by the social rank and prey-seeking behaviors of grey wolves. The GWO algorithm is easy to implement because of its basic concept, simple formula, and small number of parameters. This paper develops a GWO algorithm with a nonlinear convergence factor and an adaptive location updating strategy and applies this improved grey wolf optimizer (improved grey wolf optimizer, IGWO) algorithm to geophysical inversion problems using magnetotelluric (MT), DC resistivity and induced polarization (IP) methods. Numerical tests in MATLAB 2010b for the forward modeling data and the observed data show that the IGWO algorithm can find the global minimum and rarely sinks to the local minima. For further study, inverted results using the IGWO are contrasted with particle swarm optimization (PSO) and the simulated annealing (SA) algorithm. The outcomes of the comparison reveal that the IGWO and PSO similarly perform better in counterpoising exploration and exploitation with a given number of iterations than the SA.     

Grey wolf optimizer: a new strategy to invert geophysical data sets

There is no meta‐heuristic approach best suited for solving all optimization problems making this field of study highly active. This results in enhancing current approaches and proposing new meta‐heuristic algorithms. Out of all meta‐heuristic algorithms, swarm intelligence is preferred as it can preserve information about the search space over the course of iterations and usually has fewer tuning parameters. Grey Wolves, considered as apex predators, motivated us to simulate Grey Wolves in the optimization of geophysical data sets. The grey wolf optimizer is a swarm‐based meta‐heuristic algorithm, inspired by mimicking the social leadership hierarchy and hunting behaviour of Grey Wolves. The leadership hierarchy is simulated by alpha, beta, delta and omega types of wolves. The three main phases of hunting, that is searching, encircling and attacking prey, is implemented to perform the optimization. To evaluate the efficacy of the grey wolf optimizer, we performed inversion on the total gradient of magnetic, gravity and self‐potential anomalies. The results have been compared with the particle swarm optimization technique. Global minimum for all the examples from grey wolf optimizer was obtained with seven wolves in a pack and 2000 iterations. Inversion was initially performed on thin dykes for noise‐free and noise‐corrupted (up to 20% random noise) synthetic data sets. The inversion on a single thin dyke was performed with a different search space. The results demonstrate that, compared with particle swarm optimization, the grey wolf optimizer is less sensitive to search space variations. Inversion of noise‐corrupted data shows that grey wolf optimizer has a better capability in handling noisy data as compared to particle swarm optimization. Practical applicability of the grey wolf optimizer has been demonstrated by adopting four profiles (i.e. surface magnetic, airborne magnetic, gravity and self‐potential) from the published literature. The grey wolf optimizer results show better data fit than the particle swarm optimizer results and match well with borehole data.     

Inversion of near-field waveform data for earthquake source rupture process (I): Method and numerical test

In seismological study, most of the earthquake source rupture processes are inverted via matching the waveforms. The hypocenter location and fault parameters (such as strike direction, dip angle, etc.) are assumed firstly, and the fault is divided into a …     

Non‐linear prestack seismic inversion with global optimization using an edge‐preserving smoothing filter

Estimating elastic parameters from prestack seismic data remains a subject of interest for the exploration and development of hydrocarbon reservoirs. In geophysical inverse problems, data and models are in general non‐linearly related. Linearized inversion methods often have the disadvantage of strong dependence on the initial model. When the initial model is far from the global minimum, inversion iteration is likely to converge to the local minimum. This problem can be avoided by using global optimization methods. In this paper, we implemented and tested a prestack seismic inversion scheme based on a quantum‐behaved particle swarm optimization (QPSO) algorithm aided by an edge‐preserving smoothing ( EPS) operator. We applied the algorithm to estimate elastic parameters from prestack seismic data. Its performance on both synthetic data and real seismic data indicates that QPSO optimization with the EPS operator yields an accurate solution.     

Using orthogonal Legendre polynomials to parameterize global geophysical optimizations: Applications to seismic-petrophysical inversion and 1D elastic full-waveform inversion

We use Legendre polynomials to reparameterize geophysical inversions solved through a particle swarm optimization. The subsurface model is expanded into series of Legendre polynomials that are used as basis functions. In this framework, the unknown parameters become the series of expansion coefficients associated with each polynomial. The aim of this peculiar parameterization is threefold: efficiently decreasing the number of unknowns, inherently imposing a 1D spatial correlation to the recovered subsurface model and searching for maximally decoupled parameters. The proposed approach is applied to two highly non-linear geophysical optimization problems: seismic-petrophysical inversion and 1D elastic full-waveform inversion. In this work, with the aim to maintain the discussion at a simple level, we limit the attention to synthetic seismic data. This strategy allows us to draw general conclusions about the suitability of this peculiar parameterization for solving geophysical problems. The results demonstrate that the proposed approach ensures fast convergence rates together with accurate and stable final model predictions. In particular, the proposed parameterization reveals to be effective in reducing the ill conditioning of the optimization problem and in circumventing the so-called curse-of-dimensionality issue. We also demonstrate that the implemented algorithm greatly outperforms the outcomes of the more standard approach to global inversion in which each subsurface parameter is considered as an independent unknown.     

实数编码遗传算法在大地电磁测深二维反演中的应用

作为全局非线性优化的新方法之一的遗传算法,近年来已从生物工程流行到大地电磁测深资料解释中.然而,大地电磁反演问题具有不适定性,解的非唯一性.通过结合求解不适定问题的Tikhonov正则化方法,本文采用实数编码遗传算法求解大地电磁二维反演问题.此算法在构建目标函数时引入正则化的思想,利用遗传算法求解最优化问题.常规的基于局部线性化的最优化反演方法易使解陷入局部极小值,而且严重的依赖初始模型的选择.与传统线性化的迭代反演方法相比,实数编码遗传算法能够克服传统方法的不足且能获得更好的反演结果.通过对大地电磁测深理论模型进行计算,结果表明:该算法具有收敛速度快、解的精度高和避免出现早熟等优点,可用于大地电磁资料解释.     

GEODETIC AND TELESEISMIC CONSTRAINTS ON SLIP DISTRIBUTION OF 2015 MW6.4 PISHAN EARTHQUAKE

On July 3^rd, 2015, a M_W6.4 earthquake occurred on Pishan County, Xinjiang, located in the front of western Kunlun thrust belt, which is the largest earthquake(M_W6.0~7.0)in the past 40 years in this region. In this study, we collected both the near-filed geodetic coseismic deformation observations including 4 GPS sites and one high-resolution ALOS-2 InSAR imagery, and far-field teleseismic P waveforms from 25 stations provided by IRIS/USGS, to invert the fault parameters(strike and dip)and coseismic rupture model of 2015 M_W6.4 Pishan earthquake. Using the finite fault theory, a non-linear simulated annealing algorithm was employed to resolve our joint inversion problem. The strike (120°~130°) and dip angle(35°~40°)of optimal models are different from that of some previous studies, and the dip change is strongly constrained by combined data than that of strike. In fixing the geometric parameters of optimal fault model, we also considered data weight(5)(geodetic data/teleseismic P waveforms)and constrained weight from moment and smooth factor(2.5). Clearly, our results indicate that the slip distribution mainly concentrates in the depth range from 9 to 16km and a length range of 20km along the strike direction, which is similar to the spatial distribution of the relocated aftershocks. The maximum slip is~95cm. The seismic moment release is 5.45×10¹⁸N·m, corresponding to M_W6.42. Compared with the single data set, geodetic data or teleseismic waveform, our joint inversion model could simultaneously constrain the seismic moment and slip distribution well, thus avoiding effectively a lower-resolution rupture distribution determined by teleseismic-only inversion and a bias released moment estimated by the geodetic-only inversion. Importantly, we should consider both the near-field geodetic data and far-field teleseismic data in retrieving the rupture model for accurately describing the seismogenic structure of active fault in western Kunlun region.     

基于最佳摄动量法的桩基承载力反演

通过高应变动力试桩法来获得桩土参数是目前比较流行的试桩方法,其原理主要是通过以桩顶的实测信息来反演桩土参数,其中比较成熟的CAPW APC法主要用试凑法来反演桩土模型参数,其反演结果呈现一定的随机性且正确性过于依赖操作者经验。本文尝试以CAPW APC法所采用比较成熟的桩土模型为基础,引入基于最佳摄动量法的局部优化方法来反演桩土参数。在弹性波波动方程隐式差分的基础上,对反演参数采用摄动展开并推导出参数反演的递推公式,最后给出合适的反演算法。考虑到初始参数对局部优化方法的影响,根据场地的实际情况选取合适的初始模型,计算显示可以获得比较理想的结果,说明本法是对桩基动测方法的一种有效的新尝试。     

2009年3月19日汤加地震破裂过程快速反演/

2009年3月19日汤加MS7.9地震发生后,我们迅速利用地震破裂过程快速反演技术反演了全球地震台网(GSN)的宽频带波形资料,获得了这次地震的破裂过程．随后,收集了更多的资料重新进行了反演,反演结果的主要特征与快速反演结果基本一致．这次地震的震级为MW7.8,破裂持续时间约为70s,断层面上主要有3个滑动量较大的区域．      

L1范数约束被动源数据稀疏反演一次波估计

对于被动源地震数据,运用常规的互相关算法得到的虚拟炮记录中,不仅含有一次波反射信息,还包括了表面相关多次波.然而,通过传统的被动源数据稀疏反演一次波估计(EPSI)方法,可以求得只含有一次波,不含表面相关多次波的虚拟炮记录.本文改进了传统的被动源数据稀疏反演一次波估计问题的求解方法,将被动源稀疏反演一次波估计求解问题转化为双凸L1范数约束的最优化求解问题,避免了在传统的稀疏反演一次波估计过程中用时窗防止反演陷入局部最优化的情况.在L1范数约束最优化的求解过程中,又结合了2DCurvelet变换和小波变换,在2DCurvelet-wavelet域中,数据变得更加稀疏,从而使求得的结果更加准确,成像质量得到了改善.通过简单模型和复杂模型,验证了本文提出方法的有效性.     

Near-realtime source analysis of the 20 March 2012 Ometepec-Pinotepa Nacional,Mexico earthquake

We apply a single-step, finite-fault analysis procedure to derive a coseismic slip model for the large M_W 7.4 Ometepec-Pinotepa Nacional, Mexico earthquake of 20 March 2012, using teleseismic P waveforms recorded by the Global Seismographic Network. The inversion is conducted in near-realtime using source parameters available from the USGS/NEIC and the Global Centroid Moment Tensor (gCMT) project. The fault orientation and slip angle are obtained from the gCMT mechanism assuming that the fault coincides with the shallow-dipping nodal plane. The fault dimensions and maximum rise time are based on the magnitude reported for the event. Teleseismic data from the USGS/NEIC Continuous Waveform Buffer database are used in the inversion with record start times set to the P-wave arrivals used to compute the earthquake hypocenter. The inversion is stabilized by requiring a smooth transition of slip across the fault while minimizing the seismic moment. These constraints are applied using a smoothing weight that is estimated from the inverse problem, allowing the recovery of the least-complicated rupture history in a single step. Inversion of the deconvolved, ground-displacement waveforms reveals a simple, circular rupture similar in extent to the source identified by the USGS/NEIC using body-and surface-wave data, indicating that the teleseismic P waves can provide a first-order source model for the event in near-realtime. Additional inversions conducted using velocity records identify a more-detailed rupture model characterized by an elliptical 2500 km² source region extending updip and downdip from the hypocenter. This elliptical source preserves the orientation and overall dimensions of a dual-source slip model obtained recently by other investigators using local strong motions and global seismic waveforms. The results indicate that velocity waveforms could provide additional details of the earthquake rupture in near-realtime, finite-fault inversions using teleseismic P waves.     

A hybrid inversion method of damped least squares with simulated annealing used for Rayleigh wave dispersion curve inversion

Surface wave methods are becoming increasingly popular in many geotechnical applications and in earthquake seismology due to their noninvasive characteristics.Inverse surface wave dispersion curves are a crucial step in most surface wave methods.Many inversion methods have been applied to surface wave dispersion curve inversion,including linearized inversion and nonlinearized inversion methods.In this study,a hybrid inversion method of Damped Least Squares(DLS) with Very Fast Simulated Annealing(VFSA) is developed for multi-mode Rayleigh wave dispersion curve inversion.Both synthetic and in situ fi eld data were used to verify the validity of the proposed method.The results show that the proposed method is superior to the conventional VFSA method in aiming at global minimum,especially when parameter searching space is adjacent to real values of the parameters.The advantage of the new method is that it retains both the merits of VFSA for global search and DLS for local search.At high temperatures,the global search dominates the runs,while at a low temperatures,the local search dominates the runs.Thus,at low temperatures,the proposed method can almost directly approach the actual model.     

3-D multi-parameter type traveltime tomography in a spherical coordinate frame: comparison of double and triple class simultaneous inversions

It is now common practice to perform simultaneous traveltime inversion for the velocity field and the reflector geometry in reflection/refraction tomography, or the velocity field and the hypocenter locations in regional earthquake tomography, but seldom are all three classes of model parameters updated simultaneously. This is mainly due to the trade-off between the different types of model parameters and the lack of different seismic phases to constrain the model parameters. Using a spherical-coordinate ray tracing algorithm for first and later(primary reflected) arrival tracing algorithm in combination with a popular linearized inversion solver, it is possible to simultaneously recover the three classes of model parameters in regional or global tomographic studies. In this paper we incorporate the multistage irregular shortest-path ray tracing algorithm(in a spherical coordinate system) with a subspace inversion solver to formulate a simultaneous inversion algorithm for triple model parameters updating using direct and later arrival time information.Comparison tests for two sets of data(noise free and added noise) indicate that the new triple-class parameter inversion algorithm is capable of obtaining nearly the same results as the double-class parameter inversion scheme. Furthermore,the proposed multi-parameter type inversion method is not sensitive to a modest level of picking error in the traveltime data, and also performs well with a relatively large uncertainty in earthquake hypocentral locations. This shows it to be a feasible and promising approach in regional or global tomographic applications.     

2008年10月6日当雄Ms6.6级地震破裂过程

2008年10月6日16时30分(北京时间),西藏自治区拉萨市当雄县发生M_s6.6级地震.震中位于亚东-谷露近南北向裂谷带北段,是该活动构造带近年来发生的一次较大地震.我们利用中国地震台网中心(CENC)和美国地震学联合研究所(IRIS)提供的宽频带地震记录资料,基于点源和有限断层模型,通过波形拟合反演了该地震的震源过程.结果表明,本次地震的发震断层面走向为183.3°,倾角为49.5°,滑动角约为－115°,最大滑动量达130 cm,地震震源的深度为9.6 km,地震的标量地震矩为2.85×10¹⁸ N·m,破裂持续时间约10 s.根据地震破裂的几何学和运动学特征,推测该地震主要发生在亚东-谷露南北向裂谷活动构造带内的一个高角度西倾断层上,是一个以拉张为主且有一定的右旋分量的破裂事件,这与青藏高原现今GPS测量所揭示的该地区地壳运动特征基本一致,暗示了青藏高原南部从西向东地表运动从北北东向到南东东向的运动学转变所导致的地壳在近东西方向上的拉张变形特征.     

Fast and robust inversion of earthquake source rupture process and its application to earthquake emergency response

Fast inversion of source rupture process for significant earthquake is introduced and applied to earthquake emergency response. We retrieve and use the apparent source time functions (ASTFs) to stabilize the rupture process inversion, aiming to get the rupture process results correctly and quickly. The applications to 22 significant earthquakes occurred between January 2009 and July 2011 show an average inversion time consumed of about four hours, suggesting a high efficiency of this method, which much improves the inversion speed of the rupture process and is helpful in earthquake disaster mitigation and relief.     

地震波形多尺度反演的一点讨论

基于在反演过程中对初始模型依赖性强、易陷入局部极值等问题,本文引入小波分析,提出多尺度地震波形反演方法,从而将参数反演问题转化到小波域中重要系数优化问题。利用多尺度之间的内在联系及小波域中重要系数的稀疏性,有将改进了局部极值、计算量等问题。并对几种多尺度反演策略进行了比较讨论。基于波动方程正演及褶积模型的两种反演方法的数值实便结果显示了本方法良好的效果。     

The May 23 and 24, 1994 Taiwan earthquakes: comparison of source process between the two events

Inversion for the seismic fault rupture history is an important way to study the nature of the earthquake source. In this paper, we have selected two Taiwan earthquakes that occurred closely in time and located in the same region, inversed the distribution of the slip amplitudes, rakes, risetimes and the rupture times on the fault planes by using GDSN broad-band and long-period records and the adaptive hybrid global search algorithm, and compared the two events. The slip rate of every subfault calculated provides information about the distribution of tectonic stress and fault strength. To the former event (MS=6.0), the maximum slip amplitude 2.4 m and the minimum risetime 1.2 s are both located at the hypocentre. The latter earthquake (MS=6.6) consisted of two subevents and the second source has 4 s delay. The maximum slip amplitude 0.9 m located near hypocentre is corresponding to the minimum risetime 1.4 s, and the corresponding maximum slip rate 0.7 m.s-1 is similar to the peak value of other large slip rate areas. We consider that the latter event has more complicated temporal-spatial distribution than the former.     

基于共轭梯度算法的重力梯度数据三维聚焦反演研究

重力梯度数据相对于传统重力数据,能够更细致、准确地描述地球浅部构造和研究矿产资源分布等信息.本文采用共轭梯度算法,在加权密度域求解重力梯度数据三维聚焦反演最优化问题,以恢复地下三维密度分布,目标函数包括数据不拟合函数和最小支撑稳定函数.首先,在推导目标函数对加权密度的一阶导数时,为了得到更合理的计算公式,我们考虑变加权函数中含有密度变量;此外,本文通过密度上下限约束,改善了传统聚焦反演中聚焦因子选取困难的问题.新算法获得的反演结果,对聚焦因子的选择约束较少,相比传统聚焦算法,能够更容易的获得理想结果.将方法应用于理论模型验证其有效性和正确性,并应用本文方法处理文顿盐丘地区的航空全张量重力梯度数据,得到了与已知地质信息匹配的密度分布,表明本文方法具有处理实际数据的能力.     

改进混合蛙跳算法的CSAMT信号激电信息提取研究

从CSAMT信号中提取激电信息有利于提高频率域电磁法反演与解释的精度.目前的研究多以线性反演方法为主,存在依赖初始模型、易陷入局部极值的问题.针对CSAMT信号IP提取问题的非线性和非凸特征,本文提出了一种基于柯西分布和惯性权重的二阶段最小构造混合蛙跳反演方法来提取IP信息.该方法首先利用柯西算子取代随机算子来提高算法的全局搜索能力,并通过引入混沌震荡惯性权重来均衡进化过程中的个体经验和群体经验,保证算法后期的稳定收敛;然后通过引入第二阶段反演过程来强化极化率对观测数据的影响,同时将正则化参数引入混合蛙跳算法的适应度函数来改善反演的多解性问题;最后利用CPU并行计算加速了算法的模因组搜索过程.反演结果表明,上述方法能够较好地重构地电结构和提取激电信息,在加噪环境下具有较强的鲁棒性.相比其他非线性算法(标准混合蛙跳算法SFLA,差分进化算法DE和粒子群优化算法PSO)的反演结果,本文算法具有更强的全局搜索能力和更高的计算效率,适合对微弱的激电信息进行提取.