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.     

基于柯西分布约束和快速近端目标函数优化的三维重力反演方法

优化算法的选取在很大程度上影响着三维重力反演的计算效率,从而制约着三维重力反演的实用性.在复杂地质构造背景下,不同岩性单元之间可能会发生物性突变,产生尖锐边界.为此,本文提出了一种新的基于柯西分布约束和快速近端目标函数（Fast Proximal Objective Function,FPOF）优化的三维重力反演方法.FPOF优化方法的一个突出特点是在每一步迭代过程中逐一计算剖分网格内的未知密度参数,因此,有较低的计算复杂度和较高的计算效率.此外,目标函数中柯西范数（Cauchy norm）的引入会对反演结果施加稀疏性,有助于产生块状效果.理论模型测试表明,本文方法不仅能产生更加聚焦的反演效果,而且反演所需的时间也比传统的共轭梯度优化方法少.最后将本文方法应用于我国西部某地区实际重力数据,反演结果与已知的地质信息有较好的一致性.     

非线性反演方法的新进展

线性方法在许多具体反演问题中遇到困难的情况下，人们提出了非线性方法，同时，计算技术的发展为非线性方法的应用提供了基础。最近几年，人们对非线性方法又进行了改进和发展，例如：Vasco(1993)提出了集合推论的思想；Sambridge(1995)基于Voronoi单元的思想，提出了自然相邻对不规则数据参数化和插值的方法，相邻算法正是基于以上思想和理论，以及其他非线性方法的实践而提出的一种新的非线性反演方法。     

Application of a parameter-shifted grey wolf optimizer for earthquake dynamic rupture inversion

Global optimization is an essential approach to any inversion problem. Recently, the grey wolf optimizer (GWO) has been proposed to optimize the global minimum, which has been quickly used in a variety of inversion problems. In this study, we proposed a parameter-shifted grey wolf optimizer (psGWO) based on the conventional GWO algorithm to obtain the global minimum. Compared with GWO, the novel psGWO can effectively search targets toward objects without being trapped within the local minimum of the zero value. We confirmed the effectiveness of the new method in searching for uniform and random objectives by using mathematical functions released by the Congress on Evolutionary Computation. The psGWO algorithm was validated using up to 10,000 parameters to demonstrate its robustness in a large-scale optimization problem. We successfully applied psGWO in two-dimensional (2D) synthetic earthquake dynamic rupture inversion to obtain the frictional coefficients of the fault and critical slip-weakening distance using a homogeneous model. Furthermore, this algorithm was applied in inversions with heterogeneous distributions of dynamic rupture parameters. This implementation can be efficiently applied in 3D cases and even in actual earthquake inversion and would deepen the understanding of the physics of natural earthquakes in the future.     

Assessing uncertainty in refraction seismic traveltime inversion using a global inversion strategy

To analyse and invert refraction seismic travel time data, different approaches and techniques have been proposed. One common approach is to invert first‐break travel times employing local optimization approaches. However, these approaches result in a single velocity model, and it is difficult to assess the quality and to quantify uncertainties and non‐uniqueness of the found solution. To address these problems, we propose an inversion strategy relying on a global optimization approach known as particle swarm optimization. With this approach we generate an ensemble of acceptable velocity models, i.e., models explaining our data equally well. We test and evaluate our approach using synthetic seismic travel times and field data collected across a creeping hillslope in the Austrian Alps. Our synthetic study mimics a layered near‐surface environment, including a sharp velocity increase with depth and complex refractor topography. Analysing the generated ensemble of acceptable solutions using different statistical measures demonstrates that our inversion strategy is able to reconstruct the input velocity model, including reasonable, quantitative estimates of uncertainty. Our field data set is inverted, employing the same strategy, and we further compare our results with the velocity model obtained by a standard local optimization approach and the information from a nearby borehole. This comparison shows that both inversion strategies result in geologically reasonable models (in agreement with the borehole information). However, analysing the model variability of the ensemble generated using our global approach indicates that the result of the local optimization approach is part of this model ensemble. Our results show the benefit of employing a global inversion strategy to generate near‐surface velocity models from refraction seismic data sets, especially in cases where no detailed a priori information regarding subsurface structures and velocity variations is available.     

非线性二次规划贝叶斯叠前反演

叠前反演的目的是基于弹性波理论从地震数据中获得地层参数的可靠估计,进而用于描述地层的流体和岩性特征.然而叠前反演问题都是高维的和非适定的,并且容易受各种噪声和采集过程中不确定因素的影响,因此,为了获得稳定可靠的解必需对反演过程加以合理的约束.本文提出了一种基于非线性二次规划的叠前三参数反演方法.首先基于贝叶斯参数估计理论,假设似然函数服从高斯分布,并使待反演的参数服从于改进的Cauchy分布,从而提高了反演结果的分辨率;其次用协方差矩阵来描述参数间的相关程度,进一步提高了反演结果的稳定性;最后将问题转化为一个非线性二次规划的求解问题,并在多种约束下得到问题的解.仿真实验和实际应用皆已表明,本文提出的反演方法运算速度快捷,既使在信噪比很低的情况下也可获得较好的反演结果,为储层的进一步识别提供更多的物性参数.     

大地电磁、重力、磁法和地震初至波走时的交叉梯度二维联合反演研究

为了准确的探测和描绘地下复杂的地质结构,同时克服地球物理单一方法反演的多解性和单一参数反演模型的不一致性等问题,近年来基于交叉梯度联合反演的综合地球物理解释已经得到了广泛的关注和应用.本文首先研究了两种地球物理方法的交叉梯度联合反演算法,在此基础上,推导并实现了多种地球物理方法(大地电磁,重力,磁法,地震初至波走时)的多交叉梯度约束的二维联合反演算法;其次,我们设计了结构不一致模型和复杂模型,针对多物性联合反演算法的准确性和有效性进行了模拟试算,并对复杂模型的单独反演结果和联合反演结果进行了交叉梯度值和物性交会图的对比;最后,本文将成熟的卫星资料多光谱综合分析技术应用到联合反演中,将多物性参数反演模型结果图通过RGB(红-绿-蓝)模式进行合成,得到融合的RGB合成图.结果表明:通过对结构不一致模型和复杂模型的联合反演结果和单独反演结果的对比分析,可以得出联合反演得到的结果更接近真实模型,并从得到的交叉梯度值进一步证明了联合反演模型相似度高,也从物性交会图中得到联合反演的物性相关性更好的结论,反向证明了算法的正确性.最终从得到的RGB合成图像,我们可以更直观的分析反演结果,更有利于准确划分地下模型结构.     

Depth and morphology of reflectors from the non-linear inversion of arrival-time and waveform semblance data. Part I: method and applications to synthetic data

We propose a two-dimensional, non-linear method for the inversion of reflected/converted traveltimes and waveform semblance designed to obtain the location and morphology of seismic reflectors in a lateral heterogeneous medium and in any source-to-receiver acquisition lay-out. This method uses a scheme of non-linear optimization for the determination of the interface parameters where the calculation of the traveltimes is carried out using a finite-difference solver of the Eikonal equation, assuming an a priori known background velocity model. For the search for the optimal interface model, we used a multiscale approach and the genetic algorithm global optimization technique. During the initial stages of inversion, we used the arrival times of the reflection phase to retrieve the interface model that is defined by a small number of parameters. In the successive steps, the inversion is based on the optimization of the semblance value determined along the calculated traveltime curves. Errors in the final model parameters and the criteria for the choice of the best-fit model are also estimated from the shape of the semblance function in the model parameter space. The method is tested and validated on a synthetic dataset that simulates the acquisition of reflection data in a complex volcanic structure. This study shows that the proposed inversion approach is a valid tool for geophysical investigations in complex geological environments, in order to obtain the morphology and positions of embedded discontinuities.     

部分区域约束下的交叉梯度多重地球物理数据联合反演

交叉梯度联合反演方法通过对多种地球物理模型实现结构耦合,在岩石物性关系不确定的情况下,既能提高反演结果的可靠性,又能减少反演的多解性,还能减少不同方法解释结果之间的矛盾.当不同的模型观测数据覆盖范围不一致时,交叉梯度联合反演通常需要取出重叠区域数据进行联合反演,并且建模时还要扩展一些模型范围.本文首先提出并实现了部分区域约束下的交叉梯度多重地球物理数据联合反演算法;接着进行了算法的模型试算;最后,我们将该反演算法用于本溪—集安深部地质调查重磁电综合地质地球物理解释中.结果表明:该算法不但能在重叠区域内很好地恢复结构相似的模型,而且在非重叠区域与重叠区域的边界处仍然可以得到平滑变化的模型;在本溪—集安10号剖面所获得的结构上相似的电阻率、密度及磁化率模型较好地反映了该区的深部地质结构,对于确定深部地质体的性质提供了有力的证据.     

基于非结构网格的电阻率三维带地形反演

地表起伏地形在野外矿产资源勘察中不可避免,其对直流电阻率法勘探影响巨大.近年来,电阻率三维正演取得诸多进展,特别是应用非结构网格我们能够进行任意复杂地形和几何模型的电阻率三维数值模拟,但面向实际应用的起伏地形下电阻率三维反演依然困难.本文基于非结构化四面体网格,并考虑到应用GPS/GNSS时,区域地球物理调查中可非规则布设测网的实际特点,实现了任意地形(平坦或起伏)条件下、任意布设的偶极-偶极视电阻率数据的不完全Gauss-Newton三维反演.合成数据的反演结果表明了方法的有效性,可应用于复杂野外环境下的三维电法勘探.     

南北地震带南段地壳厚度重震联合最优化反演

重力反演方法是研究地壳结构和物性界面起伏的有效地球物理手段之一.本文收集了南北地震带南段67个已有的固定台站接收函数反演的Moho面深度结果,并使用基于EGM2008重力异常模型计算的布格重力异常,验证了本文提出的重震联合密度界面反演方法的有效性.利用接收函数对台站下方Moho面深度估计作为先验约束,定义了一类评价函数,通过对重力反演算法中尺度因子,平移因子和稳定性因子的最优选择,最小化重力反演结果与接收函数模型之间的差异.结果表明,本文提出的方法,可以有效地同化不同地球物理方法获得的反演模型,且通过重震联合反演可以改进由于对空间分布不均匀的接收函数结果插值可能而引起的误差.本文还通过引入Crust1.0的Moho面深度为初值,同时考虑地壳密度的横向不均匀分布,通过模型之间的联合反演有效改善了地球物理反演模型间的不一致性问题.本文反演得到的最优化Moho面深度模型与已知67个台站位置接收函数模型之间的标准差约1.9km,小于Crust1.0与接收函数结果模型之间标准差为3.73km的统计结果.本文研究结果对于同化重震反演结果、精化地壳密度界面模型,都具有十分重要的参考意义.     

New advances in regularized inversion of gravity and electromagnetic data

The interpretation of potential and electromagnetic fields observed over 3D geological structures remains one of the most challenging problems of exploration geophysics. In this paper I present an overview of novel methods of inversion and imaging of gravity and electromagnetic data, which are based on new advances in the regularization theory related to the application of special stabilizing functionals, which allow the reconstruction of both smooth images of the underground geological structures and models with sharp geological boundaries. I demonstrate that sharp-boundary geophysical inversion can improve the efficiency and resolution of the inverse problem solution. The methods are illustrated with synthetic and practical examples of the 3D inversion of potential and electromagnetic field data.     

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.     

Pareto Joint Inversion of 2D Magnetotelluric and Gravity Data — Towards Practical Applications

In this paper, a Pareto inversion based global optimization approach, to obtain results of joint inversion of two types of geophysical data sets, is formulated. 2D magnetotelluric and gravity data were used for tests, but presented solution is flexible enough to be used for combination of any kind of two or more target functions, as long as misfits can be calculated and forward problems solved. To minimize dimensionality of the solution, space and introduce straightforward regularization Sharp Boundary Interface (SBI) method was applied. As a main optimization engine, Particle Swarm Optimization (PSO) was used. Synthetic examples based on a real geological model were used to test proposed approach and show its usefulness in practical applications.     

Multiscale linearized inversion of surface-wave dispersion curves

In recent years, surface-wave analysis method has been developed rapidly in many fields. Multichannel analysis of surface waves can provide near-surface one-dimensional shear-wave velocity profiles. Because linearized inversion of surface-wave dispersion curves relies heavily on the choice of the initial model, setting an inappropriate initial model can lead to poor inversion results, or even failure of inversion. However, it is difficult to establish a reasonable initial model without a priori information, which is unavailable in most cases. To cope with this problem, a multiscale linearized inversion method is proposed for surface-wave dispersion curves inversion. In contrast with the traditional single-scale linearized inversion, the key idea of the proposed multiscale surface-wave inversion method is the introduction of a merging and splitting process of layers. After every scale inversion, the merging and splitting operations automatically optimize the inversion model, making it gradually approach to a reasonable subsurface stratification. Multiscale surface-wave inversion method reduces the difficulty of establishing the initial model and has high computational efficiency. In addition, it has strong ability to identify high-velocity or low-velocity interlayers and thin layers, especially suited for the geological conditions with obvious stratification. In synthetic tests, the proposed method was compared with the single-scale surface-wave inversion and particle swarm optimization algorithm to demonstrate the effectiveness and practicability of multiscale surface-wave inversion method. We also applied the multiscale surface-wave inversion method to field seismic data acquired in Guizhou, China and Texas, USA. Borehole and crosshole test data were compared with the inversion results of field data to prove the reliability of the proposed method.     

基于混合差分进化算法的地球物理线性反演

地球物理反问题线性化处理之后, 各种反演算法归结为对病态线性方程组的求解. 为了快速准确地计算出地球物理参数, 本文提出了一种全新的基于LSQR算法的混合差分进化算法(Hybrid Differential Evolution Algorithm, HDE). 该算法利用LSQR算法给出DE算法的初始种群, 提高DE算法的计算速度和稳定性. 在不同噪声水平下, 对四种正则化方法Tikhonov、TSVD、LSQR和HDE的反演结果进行详细比较. 理论模型和实际数据反演的结果都表明: 改进的HDE算法应用于地球物理反问题的求解是成功的: 反演结果与原设定模型具有较高的相关性, 在稳定性和准确性上较常规的反演算法都具有一定的优势; 而且不需要给定正则化参数, 具有更强的实用性.     

A Bayesian trans-dimensional approach for the fusion of multiple geophysical datasets

We propose a Bayesian fusion approach to integrate multiple geophysical datasets with different coverage and sensitivity. The fusion strategy is based on the capability of various geophysical methods to provide enough resolution to identify either subsurface material parameters or subsurface structure, or both. We focus on electrical resistivity as the target material parameter and electrical resistivity tomography (ERT), electromagnetic induction (EMI), and ground penetrating radar (GPR) as the set of geophysical methods. However, extending the approach to different sets of geophysical parameters and methods is straightforward. Different geophysical datasets are entered into a trans-dimensional Markov chain Monte Carlo (McMC) search-based joint inversion algorithm. The trans-dimensional property of the McMC algorithm allows dynamic parameterisation of the model space, which in turn helps to avoid bias of the post-inversion results towards a particular model. Given that we are attempting to develop an approach that has practical potential, we discretize the subsurface into an array of one-dimensional earth-models. Accordingly, the ERT data that are collected by using two-dimensional acquisition geometry are re-casted to a set of equivalent vertical electric soundings. Different data are inverted either individually or jointly to estimate one-dimensional subsurface models at discrete locations. We use Shannon's information measure to quantify the information obtained from the inversion of different combinations of geophysical datasets. Information from multiple methods is brought together via introducing joint likelihood function and/or constraining the prior information. A Bayesian maximum entropy approach is used for spatial fusion of spatially dispersed estimated one-dimensional models and mapping of the target parameter. We illustrate the approach with a synthetic dataset and then apply it to a field dataset. We show that the proposed fusion strategy is successful not only in enhancing the subsurface information but also as a survey design tool to identify the appropriate combination of the geophysical tools and show whether application of an individual method for further investigation of a specific site is beneficial.     

Discrete cosine transform for parameter space reduction in Bayesian electrical resistivity tomography

Electrical resistivity tomography is a non-linear and ill-posed geophysical inverse problem that is usually solved through gradient-descent methods. This strategy is computationally fast and easy to implement but impedes accurate uncertainty appraisals. We present a probabilistic approach to two-dimensional electrical resistivity tomography in which a Markov chain Monte Carlo algorithm is used to numerically evaluate the posterior probability density function that fully quantifies the uncertainty affecting the recovered solution. The main drawback of Markov chain Monte Carlo approaches is related to the considerable number of sampled models needed to achieve accurate posterior assessments in high-dimensional parameter spaces. Therefore, to reduce the computational burden of the inversion process, we employ the differential evolution Markov chain, a hybrid method between non-linear optimization and Markov chain Monte Carlo sampling, which exploits multiple and interactive chains to speed up the probabilistic sampling. Moreover, the discrete cosine transform reparameterization is employed to reduce the dimensionality of the parameter space removing the high-frequency components of the resistivity model which are not sensitive to data. In this framework, the unknown parameters become the series of coefficients associated with the retained discrete cosine transform basis functions. First, synthetic data inversions are used to validate the proposed method and to demonstrate the benefits provided by the discrete cosine transform compression. To this end, we compare the outcomes of the implemented approach with those provided by a differential evolution Markov chain algorithm running in the full, un-reduced model space. Then, we apply the method to invert field data acquired along a river embankment. The results yielded by the implemented approach are also benchmarked against a standard local inversion algorithm. The proposed Bayesian inversion provides posterior mean models in agreement with the predictions achieved by the gradient-based inversion, but it also provides model uncertainties, which can be used for penetration depth and resolution limit identification.     

多尺度快速匹配追踪多域联合地震反演方法

多尺度快速匹配追踪多域联合地震反演是一种通过地震数据多尺度分解的迭代反演方法.与此同时,在快速匹配追踪算法中引入低频模型约束,有效提高了收敛精度,使反演结果具有丰富的高低频信息.首先通过对大尺度地震资料进行反演得到低频背景.在此基础上,采用中尺度与小尺度地震数据进行逐级迭代用以获得高频数据,因而有效缓解了常规反演方法对于初始模型精度的依赖.最后利用理论模型与实际地震数据进行测试,通过与常规时间域反演方法的反演结果进行对比可以看出,本文方法在地层连续变化处依然可以对变化地层进行精确刻画,且在纵向分辨率提升的同时保持了较好的横向连续性.     

Facies-constrained prestack seismic probabilistic inversion driven by rock physics

Seismic Rock physics plays a bridge role between the rock moduli and physical properties of the hydrocarbon reservoirs. Prestack seismic inversion is an important method for the quantitative characterization of elasticity, physical properties, lithology and fluid properties of subsurface reservoirs. In this paper, a high order approximation of rock physics model for clastic rocks is established and one seismic AVO reflection equation characterized by the high order approximation(Jacobian and Hessian matrix) of rock moduli is derived. Besides, the contribution of porosity, shale content and fluid saturation to AVO reflectivity is analyzed. The feasibility of the proposed AVO equation is discussed in the direct estimation of rock physical properties. On the basis of this, one probabilistic AVO inversion based on differential evolution-Markov chain Monte Carlo stochastic model is proposed on the premise that the model parameters obey Gaussian mixture probability prior model. The stochastic model has both the global optimization characteristics of the differential evolution algorithm and the uncertainty analysis ability of Markov chain Monte Carlo model. Through the cross parallel of multiple Markov chains, multiple stochastic solutions of the model parameters can be obtained simultaneously, and the posterior probability density distribution of the model parameters can be simulated effectively. The posterior mean is treated as the optimal solution of the model to be inverted.Besides, the variance and confidence interval are utilized to evaluate the uncertainties of the estimated results, so as to realize the simultaneous estimation of reservoir elasticity, physical properties, discrete lithofacies and dry rock skeleton. The validity of the proposed approach is verified by theoretical tests and one real application case in eastern China.