等效源法三维随机点位场数据处理和转换

为了实现曲面随机点位场数据的曲面延拓和转换,以磁异常位场数据为例,采用一组磁偶极子作为等效源,置于观测面下方的一个曲面上,把观测磁异常作为这组磁偶极子所产生磁异常的边界条件,通过求解线性方程组的方法反演磁偶极子磁矩的大小,再根据反演结果正演所要计算的磁异常数据,实现了曲面随机点磁异常位场数据的向上延拓、向下延拓、求导以及化极处理.在数据量较大时,为了提高反演计算的速度,把磁异常数据和磁偶极子分成若干小块,再利用各块磁异常数据分别反演该块数据下方磁偶极子的磁矩,并通过迭代计算来逐步取得更准确的反演结果.模型试验表明,磁异常位场数据向上延拓的均方根误差小于±2nT,向下延拓和化极也可以取得较高的精度,所提出的分块处理方法提高了延拓和转换的速度,实际资料处理给出了曲面随机点航磁异常数据向下延拓和化极的一个例子.     

Magnetic mapping for the detection and characterization of UXO: Use of multi-sensor fluxgate 3-axis magnetometers and methods of interpretation

Fluxgate vector magnetometers can be powerful instruments in magnetic mapping and in the detection of unexploded ordnance (UXO). Being lightweight and having low power requirements, they allow the development of multi-sensor use. The main problems in using fluxgate magnetometers arise from calibration errors and drift but these can be overcome using a quick and simple method of calibration in the field. This method also has the advantage of compensating permanent and induced magnetic fields generated by magnetized objects carried with the sensors. Measurement accuracy is similar to that obtained with scalar magnetometers. Multi-magnetometer profiling allows direct inversion of raw magnetic data along profiles in order to locate and characterize dipoles typically generated by UXO. The method used is a non-linear inverse procedure that estimates the three coordinates and magnetization vector of the dipole. Application of the technique to both a synthetic case and a field example illustrates the advantages of the method compared with the use of the analytic signal.     

A Robust Two-Step Inversion of Complex Magnetotelluric Apparent Resistivity Data

Though two-dimensional inversion is now a standard procedure, interpretation of magnetotelluric (MT) data under the assumption of isotropic and one-dimensional structures is a valuable procedure for a first step interpretation of exploratory and solid earth geophysics investigation data. Because its interpretation requires an efficient inverse modelling, we propose and evaluate an inversion procedure, which consists of two steps. Both steps employ jointly the modulus and the phase of the apparent resistivity function. The first one consists of the use of the asymptotic Bostick-Niblett approach. The second employs the result of the inversion obtained in the first step as a starting model to initialize the linearized inversion performed using a multiple re-weighted least-squares approach. We applied the analysis both to synthetic data and to field data from the Parana Basin in Brazil. The results show that the inversion procedure presents a faster convergence without loss of accuracy, increases the resolving power of the MT technique, and may improve its capability to delineate conductors up to a depth of one hundred kilometers. Therefore a reasonable interpretation of the data employing one-dimensional model can be achieved even in the presence of relatively noisy data, and under conditions that slightly violate the premise of lateral homogeneity.     

3D inversion of gravity data by separation of sources and the method of local corrections: Kolarovo gravity high case study

We present a novel methodology for 3D gravity/magnetic data inversion. It combines two algorithms for preliminary separation of sources and an original approach to 3D inverse problem solution. The first algorithm is designed to separate sources in depth and to remove the shallow ones. It is based on subsequent upward and downward data continuation. For separation in the lateral sense, we approximate the given observed data by the field of several 3D line segments. For potential field data inversion we apply a new method of local corrections. The method is efficient and does not require trial-and-error forward modeling. It allows retrieving unknown 3D geometry of anomalous objects in terms of restricted bodies of arbitrary shape and contact surfaces. For restricted objects, we apply new integral equations of gravity and magnetic inverse problems. All steps of our methodology are demonstrated on the Kolarovo gravity anomaly in the Danube Basin of Slovakia.     

磁化强度矢量反演新方法及其在卡拉塔格铜多金属矿床找矿中的应用

磁异常的反演是地球物理勘探的重要手段,三维磁化率反演是磁异常定量解释中的一种重要方法.由于剩磁的存在使得磁化方向与地磁场方向产生偏差,从而影响了磁异常反演与解释的精度.本文基于磁异常模量反演和磁化强度矢量反演方法得到了一种新的磁化强度矢量反演方法.与以往的磁化强度矢量反演方法相比,该方法以磁异常模量反演得到的磁化率模型为约束,采用Lp范数正则化方法求解,提高了磁化强度矢量反演的精度和效率.本文通过模拟试验的反演计算,验证了这种磁化强度矢量反演方法的有效性.最后,将本文方法应用于新疆东天山卡拉塔格地区航磁数据的解释,获得了地下空间不同磁性差异的磁性体的空间分布特征,为进一步分析研究区隐伏矿床提供了重要信息.     

Application of the normalized surface magnetic charge model to UXO discrimination in cases with overlapping signals

This paper presents an application of the normalized surface magnetic charge (NSMC) model to discriminate objects of interest, such as unexploded ordnance (UXO), from innocuous items in cases when UXO electromagnetic induction (EMI) responses are contaminated by signals from other objects. Over the entire EMI spectrum considered here (tens of Hertz up to several hundreds of kHz), the scattered magnetic field outside the object can be produced mathematically by equivalent magnetic charges. The amplitudes of these charges are determined from measurement data and normalized by the excitation field. The model takes into account the scatterer's heterogeneity and near- and far-field effects. For classification algorithms, the frequency spectrum of the total NSMC is proposed and investigated as a discriminant. The NSMC is combined with the differential evolution (DE) algorithm in a two-step inversion procedure. To illustrate the applicability of the DE–NSMC algorithm, blind test data are processed and analyzed for cases in which signals from nearby objects frequently overlap. The method was highly successful in distinguishing UXO from accompanying clutter.     

反演磁性地质界面的意义与方法

磁性地质界面的反演是地球物理勘探的重要课题之一,对于提高磁测资料的地质解释效果有重要意义.通过磁测资料反演磁性地质界面主要分两步：第一步,从总异常中分离有磁性界面起伏引起的磁异常;第二步,由分离的磁异常反演磁性界面的深度.本文分别从这两个方面回顾了提取异常和反演界面的较有代表性的技术.     

DEFINITION AND APPLICATION OF THE FREQUENCY -EFFECT TRANSFORM FUNCTION TO THE INTERPRETATION OF IP SOUNDINGS*

This paper deals with a new method of quantitative interpretation of induced polarization soundings in the frequency-domain. From the general expression of the apparent frequency-effect for soundings carried out on a multi-layered earth the application of Hankel's inversion theorem allows to introduce a new function, called here the “frequency-effect transform”. The new interpretation method consists of two steps: 1) the inversion of field data to obtain the frequency-effect transform graph and 2) the analysis of this graph to derive the layering parameters. The first step is performed by means of a slightly revised version of a simple numerical procedure, previously suggested by the author for the inversion of d.c. resistivity sounding data. The second step is carried out by a complete curve-matching procedure, applied directly on the transform graph. This implies suitable master curves, whose preparation doesn't meet all the mathematical difficulties which are present when preparing master curves of the apparent frequency-effect function.     

用最小二乘两步迭代法求解磁性球体几何与磁性参数

通过对常规最小二乘法在求解磁性球体参数过程中产生发散解的原因分析表明:非线性方程组中待定参数过多,特别是角度参数,是影响最小二乘法收敛性的主要因素.为此,提出将磁异常三分量作为观测值,用矢量磁矩作为待定参数,以替代磁化强度磁倾角和磁偏角,从而消除了非线性观测方程中的角度参数影响.根据观测值与磁矩的线性关系以及磁性球体中心位置的非线性关系,采用最小二乘两步迭代法对磁性球体几何与磁性参数进行分步求解,使得在利用最小二乘法时仅含有3个未知参数,大大减少了参数的维数.理论模型推导过程中,顾及了地磁背景场影响和多磁性体情况,给出了相应的数据处理方法.通过实测数据验证表明:提出的方法是收敛的,能达到很高的磁性体几何及磁性参数精度.     

基于印模法的地面磁电阻率数据三维非线性共轭梯度反演

本文提出了能提高异常体分辨能力,同时得到绝对电导率的地面磁电阻率数据三维反演方法.磁电阻率响应用准直流的低频磁场代替;数值模拟由频率域电场满足的Helmholtz方程出发,采用三维交错网格有限差分法;长直导线源作为发射源,其中源的计算包含在背景场中;结合地面磁电阻率数据各分量的特点,选择y分量进行反演研究;反演采用三维非线性共轭梯度反演技术,为了提高异常体的深度分辨能力,进行迭代重构反演;用印模法对初始模型进行重构,采用的是辅模型在浅部,元模型在深部的组合方式.从合成数据和实际数据的反演结果可以得到以下的认识：（1）由频率域麦克斯韦方程组出发,低频磁场数据反演可以直接得到电导率,而不是相对电导率之比;（2）采用印模法组合初始模型,进行迭代重构反演,可以提高地面磁电阻率数据反演对异常体的分辨能力,确定埋深位置,同时不会丧失对于浅部异常体的分辨能力;（3）在结合印模法的地面磁电阻率数据三维反演中,深部异常体的分辨能力受地表不均匀导电体影响较小;（4）确定印模深度可以采用上一次重构反演结束时的模型变化量,通过相邻两次重构反演结束时的模型变化量之差来确定迭代重构是否终止.因为静磁场与重力场在数学上的相似性,本文的反演方法可以被运用到重力场等位场的地面数据的反演中.

     

Towards non-linear inversion for characterization of time-lapse phenomena through numerical modelling

We compare two geophysical survey measurements of the same type made at different times in order to characterize the change in the geological medium during the elapsed time. The aim of this study is to develop a strategy using a full non-linear inversion algorithm as the interpretation tool. In this way, not only the location and the form of the changes are recovered, but also the changes in the material parameters of the geological medium can be estimated. In order to solve this fully non-linear problem, the so-called ‘multiplicative regularized contrast source inversion’ (MR-CSI) method is employed. The unique property of this iterative method is that it does not solve the forward problem at each iterative step. This makes it possible to use the non-linear inversion algorithm for large-scale computation problems. The numerical results show that by taking into account the non-linear nature of the problem, interpretation of the time-lapse data can be significantly improved, compared with that obtained using linear inversion.     

A split operator approach to reactive transport with the forward particle tracking Eulerian Lagrangian localized adjoint method

A forward particle tracking Eulerian Lagrangian localized adjoint method (ELLAM) is applied to the multicomponent reactive transport problem using a split operator approach. Two split operator algorithms are compared, the Strang algorithm and the sequential non-iterative algorithm (SNIA). The reaction equations are integrated using a coupled predictor corrector algorithm with adaptive time stepping. Reaction time steps are adjusted at the inflow boundary to reflect the actual time of transport inside the solution domain.Results show that split operator ELLAM formulations are competitive with direct or fully coupled ELLAM solutions for reactive transport problems. The SNIA algorithm is more accurate than the Strang splitting algorithm when large time steps are used. The reaction algorithm employed dominates computational effort in runs with large time step sizes. To illustrate the use of the method in practical problems, the model is fitted to aerobic aniline degradation data from laboratory scale column experiments. Model inversion is achieved using non-linear regression with a shuffled complex evolution optimization algorithm and parameter uncertainty is assessed using a Bayesian uncertainty analysis procedure.     

Modelling of local velocity anomalies: a cookbook

The determination of small-scale velocity anomalies (from tens to a few hundreds of metres) is a major problem in seismic exploration. The impact of such anomalies on a structural interpretation can be dramatic and conventional techniques such as tomographic inversion or migration velocity analysis are powerless to resolve the ambiguity between structural and velocity origins of anomalies. We propose an alternative approach based on stochastic modelling of numerous anomalies until a set of models is found which can explain the real data. This technique attempts to include as much a priori geological information as possible. It aims at providing the interpreter with a set of velocity anomalies which could possibly be responsible for the structural response. The interpreter can then choose one or several preferred models and pursue a more sophisticated analysis. The class of retained models are all equivalent in terms of data and therefore represent the uncertainty in the model space. The procedure emulates the real processing sequence using a simplified scheme. Essentially, the technique consists of five steps: 1 Interpretation of a structural anomaly in terms of a velocity anomaly with its possible variations in terms of position, size and amplitude. 2 Drawing a model by choosing the parameters of the anomaly within the acceptable range. 3 Modelling the traveltimes in this model and producing the imaging of the reflected interface. 4 Comparing the synthetic data with the real data and keeping the model if it lies within the data uncertainty range. 5 Iterate from step 2. In order to avoid the high computational cost inherent in using statistical determinations, simplistic assumptions have been made: ? The anomaly is embedded in a homogeneous medium: we assume that the refraction and the time shift due to the anomaly have a first-order effect compared with ray bending in the intermediate layers. ? We model only the zero-offset rays and therefore we restrict ourselves to structural problems. ? We simulate time migration and so address only models of limited structural complexity. These approximations are justified in a synthetic model which includes strong lateral velocity variations, by comparing the result of a full processing sequence (prestack modelling, stack and depth migration) with the simplified processing. This model is then used in a blind test on the inversion scheme.     

An Improved Analytic Signal Technique for the Depth and Structural Index from 2D Magnetic Anomaly Data

This paper presents a new inversion method for the interpretation of 2D magnetic anomaly data, which uses the combination of the analytic signal and its total gradient to estimate the depth and the nature (structural index) of an isolated magnetic source. However, our proposed method is sensitive to noise. In order to lower the effect of noise, we apply upward continuation technique to smooth the anomaly. Tests on synthetic noise-free and noise corrupted magnetic data show that the new method can successfully estimate the depth and the nature of the causative source. The practical application of the technique is applied to measured magnetic anomaly data from Jurh area, northeast China, and the inversion results are in agreement with the inversion results from Euler deconvolution of the analytic signal.     

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.

     

Two-step interface and velocity inversion—— Study o e of the Tangshan seismic region

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Object-based model verification by a genetic algorithm approach: Application in archeological targets

A new target-oriented parameterization scheme, named the object-based model, is suggested to represent man-made or natural targets as regular shapes embedded in a two-dimensional resistivity background. The numerical values of the target parameters (size, depth, location and resistivity) are estimated in three steps consisting of conventional regularized inversion, exclusion of anomalous regions and delineation of target bodies. The method produces sharp edges and sharp variation in intrinsic resistivity between the targets and background.The number of target objects is decided by the visual inspection of the 2D resistivity section derived from the application of a conventional cell-based regularized inversion. The 2D background is also extracted from the same section. A genetic algorithm approach is used at the final stage to test a large number of distinct models. Each test model consists of the same number of objects buried in the 2D background. The size, depth, location and resistivity of the targets are estimated from a class of models generated by the application of biological rules. The derived images of buried bodies have sharp edges and can then be understood by engineers and archeologists. However, if the hypothesis about the ‘conceptual model’ is very different from the geometry of the subsurface, the proposed approach will not be able to produce satisfactory results.     

A refined method of recovering potential coefficients from surface gravity data

Summary A new method for computing the potential coefficients of the Earth's external gravity field is presented. The gravimetric boundary-value problem with a free boundary is reduced to the problem with a fixed known telluroid. The main idea of the derivation consists in a continuation of the quantities from the physical surface to the telluroid by means of Taylor's series expansion in such a way that the terms whose magnitudes are comparable with the accuracy of today's gravity measurements are retained. Thus not only linear, but also non-linear terms are taken into account. Explicitly, the terms up to the order of the third power of the Earth's flattening are retained. The non-linear boundary-value problem on the telluroid is solved by an iteration procedure with successive approximations. In each iteration step the solution of the non-linear problem is estimated by the solutions of two linear problems utilizing the fact that the non-linear boundary condition may be split into two parts; the linear spherical approximation of the gravity anomaly whose magnitude is significantly greater than the others and the non-linear ellipsoidal corrections. Finally, in order to solve the problem in terms of spherical harmonics, the transform method composed of the fast Fourier transform and Gauss Legendre quadrature is theoretically outlined. Immediate data processing of gravity data measured on the physical Earth's surface without any continuation of gravity measurements to a reference level surface belongs to the main advantage of the presented method. This implies that no preliminary data handling is needed and that the error data propagation is, consequently, maximally suppressed.     

地面矩形大定源电磁法频率域三维非线性共轭梯度反演

本文实现了地面矩形大定源三维频率域反演.矩形大定源三维模型响应计算采用交错网格有限差分技术.正演的微分方程为异常电场满足的非齐次Helmholtz方程,方程右手边源项中的大定源产生的背景格林函数由虚界面法结合虚框法计算.频率域三维反演采用非线性共轭梯度反演技术.反演的数据类型为垂直磁场的频率域响应H_z的实部和虚部分量.数值结果表明,（1）三维模型正演模拟数值结果与前人一致,为三维反演奠定基础;（2）针对两个三维导电模型,分别进行了三维反演数值试算.反演结果可以清晰恢复出异常体的电阻率和位置信息,表明地面矩形大定源三维频率域非线性共轭梯度反演具有可行性.本文研究的意义在于,在电磁响应时频转换技术的基础上,如果将野外实测的瞬变电磁数据变换为对应的频率响应,则结合本文提出的三维反演技术,可以为矩形大定源瞬变电磁数据的三维解释提供一个新的思路.