A Best-Estimate Approach for Determining Self-potential Parameters Related to Simple Geometric Shaped Structures

A new approach is proposed in order to interpret field self-potential (SP) anomalies related to simple geometric-shaped models such as sphere, horizontal cylinder, and vertical cylinder. This approach is mainly based on solving a set of algebraic linear equations, and directed towards the best estimate of the three model parameters, e.g., electric dipole moment, depth, and polarization angle. Its utility and validity are demonstrated through studying and analyzing synthetic self-potential anomalies obtained by using simulated data generated from a known model and a statistical distribution with different random errors components. Being theoretically tested and proven, this approach has been consequently applied on two real field self-potential anomalies taken from Colorado and Turkey. A comparable and acceptable agreement is obtained between the results derived by the new proposed method and those deduced by other interpretation methods. Moreover, the depth obtained by such an approach is found to be very close to that obtained by drilling information.     

基于遗传神经网络的大地电磁反演

为进一步提高大地电磁非线性反演的稳定性、运算效率及准确度,将遗传神经网络算法引入大地电磁反演.首先针对大地电磁二维地电模型建立BP（Back Propagation）神经网络基本框架进行学习训练,网络输入为已知地电模型的视电阻率参数,输出为该地电模型参数;再利用遗传算法对神经网络学习训练过程进行优化,计算出多种地电模型网络连接权值和阈值的最优解;最后将最优连接权值和阈值对未知模型进行反演测试,网络输入为未知地电模型的视电阻率参数,输出为该地电模型参数.模型实验表明：遗传神经网络算法充分结合了遗传算法的全局寻优性和神经网络的局部寻优性,相比单一神经网络算法,在网络学习训练中提高了解的收敛成功率和计算速度,在反演测试中能更准确地逼近真实模型.将遗传神经网络算法与最小二乘正则化反演进行对比,理论模型和实测数据都验证了遗传神经网络算法在大地电磁反演中的可行性和有效性.     

Application of various methods for 2D inverse modeling of residual gravity anomalies

This paper presents a neural network approach to determine 2D inverse modeling of a buried structure from gravity anomaly profile. The results of the applied neural network method are compared with the results of two other methods, least-squares minimization and the simple method. Sphere, horizontal cylinder and vertical cylinder and their gravity effects are considered as the synthetic models and the synthetic data, respectively. The synthetic data are also corrupted with noise to evaluate the capability of the methods. Then the Dehloran bitumen map in Iran is chosen as a real data application. Anomaly value of the cross-section, which is taken from the gravity anomaly map of Dehloran bitumen, is very close to those obtained from these methods.     

剩余时差校正及泊松比反演

利用突出泊松比变化的Shuey简化方程推导出逐点计算泊松比的反演公式.在泊松比反演之前，对地震数据进行剩余时差校正，可以使振幅随炮检距（或入射角）的变化趋势更明显，可以提高反演的精度.通过对理论模型及实际资料的处理，说明这种反演方法是可行的，由反演结果可以预测低泊松比异常，寻找天然气.     

剩余时差校正及泊松比反演

利用突出泊松比变化的Shuey简化方程推导出逐点计算泊松比的反演公式.在泊松比反演之前,对地震数据进行剩余时差校正,可以使振幅随炮检距(或入射角)的变化趋势更明显,可以提高反演的精度.通过对理论模型及实际资料的处理,说明这种反演方法是可行的,由反演结果可以预测低泊松比异常,寻找天然气.     

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.     

A general approach for porosity estimation using artificial neural network method: a case study from Kansas gas field

This study aims to design a back-propagation artificial neural network (BP-ANN) to estimate the reliable porosity values from the well log data taken from Kansas gas field in the USA. In order to estimate the porosity, a neural network approach is applied, which uses as input sonic, density and resistivity log data, which are known to affect the porosity. This network easily sets up a relationship between the input data and the output parameters without having prior knowledge of petrophysical properties, such as porefluid type or matrix material type. The results obtained from the empirical relationship are compared with those from the neural network and a good correlation is observed. Thus, the ANN technique could be used to predict the porosity from other well log data.     

有限长圆柱体磁异常场全空间正演方法

在经典位场理论中,许多简单形体位场异常难以通过积分得到全空间的解析式.圆柱体是一类很重要的理论模型体,常用于模拟圆柱状地质体或非地质体(如管线),但目前还不能用解析公式正演有限长圆柱体在三维空间里的磁异常,而多是采用近似简化为有限长磁偶极子或线模型代替.对于有限长圆柱体,特别是半径相对于上顶埋深较大时,这种近似的误差不可忽略.本文利用共轭复数变量替换法,推导出有限长圆柱体在全空间的引力位一阶、二阶导数,利用Poisson关系得到磁异常正演公式,进而利用有限长圆柱体磁异常正演公式求解管状体的磁异常,得到不同磁化方向、不同大小的管线产生的磁场的特征,并将其推广到截面为椭圆的情况.最后通过模拟计算定量给出了将圆柱体近似为线模型的条件.     

3D inversion of DC data using artificial neural networks

In this paper, we investigate the applicability of artificial neural networks in inverting three-dimensional DC resistivity imaging data. The model used to produce synthetic data for training the artificial neural network (ANN) system was a homogeneous medium of resistivity 100 Ωm with an embedded anomalous body of resistivity 1000 Ωm. The different sizes for anomalous body were selected and their location was changed to different positions within the homogeneous model mesh elements. The 3D data set was generated using a finite element forward modeling code through standard 3D modeling software. We investigated different learning paradigms in the training process of the neural network. Resilient propagation was more efficient than any other paradigm. We studied the effect of the data type used on neural network inversion and found that the use of location and the apparent resistivity of data points as the input and corresponding true resistivity as the output of networks produces satisfactory results. We also investigated the effect of the training data pool volume on the inversion properties. We created several synthetic data sets to study the interpolation and extrapolation properties of the ANN. The range of 100–1000 Ωm was divided into six resistivity values as the background resistivity and different resistivity values were also used for the anomalous body. Results from numerous neural network tests indicate that the neural network possesses sufficient interpolation and extrapolation abilities with the selected volume of training data. The trained network was also applied on a real field dataset, collected by a pole-pole array using a square grid (8 ×8) with a 2-m electrode spacing. The inversion results demonstrate that the trained network was able to invert three-dimensional electrical resistivity imaging data. The interpreted results of neural network also agree with the known information about the investigation area.     

A New Best-Estimate Methodology for Determining Magnetic Parameters Related to Field Anomalies Produced by Buried Thin Dikes and Horizontal Cylinder-like Structures

A new best estimate methodology is proposed and oriented towards the determination of parameters related to a magnetic field anomaly produced by a simple geometric-shaped model or body such as a thin dike and horizontal cylinder. This approach is mainly based on solving a system of algebraic linear equations for estimating the three model parameters, e.g., the depth to the top (center) of the body (z), the index parameter or the effective magnetization angle (θ) and the amplitude coefficient or the effective magnetization intensity (k). The utility and validity of this method is demonstrated by analyzing two synthetic magnetic anomalies, using simulated data generated from a known model with different random errors components and a known statistical distribution. This approach was also examined and applied to two real field magnetic anomalies from the United States and Brazil. The agreement between the results obtained by the proposed method and those obtained by other interpretation methods is good and comparable. Moreover, the depth obtained by such an approach is found to be in high accordance with that obtained from drilling information. The advantages of such a proposed method over other existing interpretative techniques are clarified, where it can be generalized to be automatically applicable for interpreting other geological structures described by mathematical formulations.     

基于BP神经网络的波阻抗反演及应用

人工神经网络是近期发展最快的人工智能领域研究成果之一.本文在介绍BP神经网络的有关原理的基础上,提出一种基于BP神经网络模型的波阻抗反演方法,该方法克服了常规基于模型的波阻抗反演方法严重依赖于初始模型的选择和易陷入局部最优等局限性.利用该方法对实际地震剖面进行了波阻抗参数反演处理,结果表明人工神经网络方法在波阻抗反演中的应用是可行的并且是有效的.     

Magnetotelluric inversion for azimuthally anisotropic resistivities employing artificial neural networks

An extension of an artificial neural network (ANN) approach to solve the magnetotelluric (MT) inverse problem for azimuthally anisotropic resistivities is presented and applied for a real dataset. Three different model classes, containing general 1-D and 2-D azimuthally anisotropic features, have been considered. For each model class, characteristics of three-layer feed forward ANNs trained through an error back propagation algorithm have been adjusted to approximate the inverse modeling function. It appears that, at least for synthetic models, reasonable results would be obtained by applying the amplitudes of the complex impedance tensor elements as inputs. Furthermore, the Levenberg-Marquart algorithm possesses optimal performance as a learning paradigm for this problem. The evaluation of applicability of the trained ANNs for unknown data sets excluded from the learning procedure reveals that the trained ANNs possess acceptable interpolation and extrapolation abilities to estimate model parameters accurately. This method was also successfully used for a field dataset wherein anisotropy had been previously recognized.     

电阻率二维神经网络反演

由于非线性特性地球物理反演一直以来都是一个比较困难的问题. 近十年来,非线性反演方法如人工神经网络、遗传算法在地球物理数据解释中得到越来越多的应用,但目前基本仍限于一维反演问题. 对于二维反问题,反演参数较多,神经网络反演运用较少. 本文利用BP神经网络优化方法,实现了电阻率二维非线性反演. 与传统线性化的迭代反演比较,神经网络反演能够克服传统方法的不足、获得更好的反演结果.     

Application of Normalized Full Gradient Method to Self Potential (SP) Data

Recently, Normalized Full Gradient (NFG) method has widespread applications to natural potential fields, especially in gravity and magnetic. In this study, usage of NFG in Self-Potential (SP) data evaluation is tested. Results are compared to other SP interpretation methods. The NFG method is applied to synthetic and field SP data. As a consequence of application of the method to the anomalies of spherical, cylindrical and vertical sheet models, whose theoretical structures are explicit, the structures were found very close to their actual locations. In order to see the capability of the method in detecting the number of sources, NFG method was applied to different spherical models at different depths and locations. The least-squares inverse solution was applied to the same models and NFG method was found more powerful in detecting model structure. Sensitivity of NFG method for application to noisy data is also tested. An anomaly is generated by adding a random noise to two close sphere SP anomalies. The method seems to work for the two close spheres at high S/N ratio. Then, NFG method was applied to two field examples. The first one is the cross section taken from the SP anomaly map of the Ergani-Süleymanköy (Turkey) copper mine. The depth of the mineral deposit at that site was found about 38 m from the ground level. This result is well matched to previous studies. NFG was also applied to SP data from Seferihisar Izmir (Western Turkey) geothermal field and the location of the point source was determined. The field data of this site have already been modeled by the thermoelectric source (coupling) solution method. When these two methods are compared, they seem to support each other. It is concluded that the NFG method works perfectly when the structure model is simple. It is observed that natural potential sources close to earth’s surface are identified by the method more accurately at greater harmonics, while deep sources are identified at lesser harmonics. It produces reasonable results for noisy multi-source models than the other parameter identification methods (inverse solution, power spectrum, etc.).     

正则化方法在无线电波层析中的应用

无线电波透视法是常用的工作面地质构造探测方法之一,目前普遍使用的SIRT方法层析分辨率不高。本文采用约束正则化方法,推导Tikhonov正则化和全变差正则化的最小化问题表达式,讨论影响层析结果的主要因素,对典型理论模型进行了层析成像实验。结果表明:正则化方法具有比SIRT方法更好的分辨率;射线条数越多、噪声水平越低,层析分辨率越高;Tikhonov正则化在正则参数增大时层析结果更光滑,减小时则更贴近异常,全变差正则化与其相反。最后对实际坑透数据进行层析,识别出的异常构造基本吻合已知疑似构造位置,从而说明正则化方法在无线电波透视应用中的可行性。      

重磁异常反演的拟BP神经网络方法及其应用

把神经网络与重磁异常反演理论相结合,提出了用于重磁反演的一种拟BP神经网络方法．基于3层神经网络结构,把隐含层神经元设定为三维空间物性（磁化强度或密度）单元．对实测与理论重磁异常经S型函数变换,采用自动修改物性单元物性值的拟BP算法,反演三维空间的物性分布．利用该网络对理论模型数据和内蒙古某花岗岩体上的航磁资料进行了反演计算,取得了满意的反演效果．     

Integrating facies-based Bayesian inversion and supervised machine learning for petro-facies characterization in the Snadd Formation of the Goliat Field,south-western Barents Sea

Seismic petro-facies characterization in low net-to-gross reservoirs with poor reservoir properties such as the Snadd Formation in the Goliat field requires a multidisciplinary approach. This is especially important when the elastic properties of the desired petro-facies significantly overlap. Pore fluid corrected endmember sand and shale depth trends have been used to generate stochastic forward models for different lithology and fluid combinations in order to assess the degree of separation of different petro-facies. Subsequently, a spectral decomposition and blending of selected frequency volumes reveal some seismic fluvial geomorphological features. We then jointly inverted for impedance and facies within a Bayesian framework using facies-dependent rock physics depth trends as input. The results from the inversion are then integrated into a supervised machine learning neural network for effective porosity discrimination. Probability density functions derived from stochastic forward modelling of endmember depth trends show a decreasing seismic fluid discrimination with depth. Spectral decomposition and blending of selected frequencies reveal a dominant NNE trend compared to the regional SE–NW pro-gradational trend, and a local E–W trend potentially related to fault activity at branches of the Troms-Finnmark Fault Complex. The facies-based inversion captures the main reservoir facies within the limits of the seismic bandwidth. Meanwhile the effective porosity predictions from the multilayer feed forward neural network are consistent with the inverted facies model, and can be used to qualitatively highlight the cleanest regions within the inverted facies model. A combination of facies-based inversion and neural network improves the seismic reservoir delineation of the Snadd Formation in the Goliat Field.     

Estimating magnetic dike parameters using a non‐linear constrained inversion technique: an example from the Särna area,west central Sweden

In this paper, we describe a non‐linear constrained inversion technique for 2D interpretation of high resolution magnetic field data along flight lines using a simple dike model. We first estimate the strike direction of a quasi 2D structure based on the eigenvector corresponding to the minimum eigenvalue of the pseudogravity gradient tensor derived from gridded, low‐pass filtered magnetic field anomalies, assuming that the magnetization direction is known. Then the measured magnetic field can be transformed into the strike coordinate system and all magnetic dike parameters – horizontal position, depth to the top, dip angle, width and susceptibility contrast – can be estimated by non‐linear least squares inversion of the high resolution magnetic field data along the flight lines. We use the Levenberg‐Marquardt algorithm together with the trust‐region‐reflective method enabling users to define inequality constraints on model parameters such that the estimated parameters are always in a trust region. Assuming that the maximum of the calculated g_zz (vertical gradient of the pseudogravity field) is approximately located above the causative body, data points enclosed by a window, along the profile, centred at the maximum of g_zz are used in the inversion scheme for estimating the dike parameters. The size of the window is increased until it exceeds a predefined limit. Then the solution corresponding to the minimum data fit error is chosen as the most reliable one. Using synthetic data we study the effect of random noise and interfering sources on the estimated models and we apply our method to a new aeromagnetic data set from the Särna area, west central Sweden including constraints from laboratory measurements on rock samples from the area.     

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.     

Fair Function Minimization for Direct Interpretation of Residual Gravity Anomaly Profiles Due to Spheres and Cylinders

A new interpretative approach is proposed to interpret residual gravity anomaly profiles in order to determine the depth, the amplitude coefficient and the geometric shape factor of simple spherical and cylindrical buried structures. This new approach is based on both Fair function minimization and on stochastic optimization modeling. The validity of this interpretative approach is demonstrated through studying and analyzing two synthetic gravity anomalies, using simulated data generated from a known model with different random noises components and a known statistical distribution. Being theoretically proven, this new approach has been applied on three real field gravity anomalies from Sweden, Senegal and the United States. The agreement between the results obtained by the proposed method and those obtained by other interpretation methods is good and comparable.