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.     

A NEW APPROACH FOR DERIVING PSEUDOVELOCITY LOGS FROM RESISTIVITY LOGS1

This paper describes a method of generating pseudovelocity logs using measurements of electrical resistivity. A theoretical relation between electrical resistivity and transit time, which is applicable to a wide range of lithologies, has been developed. The application of this relation using a method which defines lithoresistivity zones as lithological intervals related to the same formation and showing small resistivity variations, has been tested in the Recôncavo sedimentary basin in Bahia, Brazil. A comparison of derived pseudovelocity logs with actual sonic logs for five wells whows the validity of the present approach.     

Hydrostatic pressure tests for the permeability - formation factor relation on crystalline rocks from the KTB drilling project

Transport properties (permeability and electrical conductivity) have been measured at different hydrostatic pressure runs on 7 crystalline rocks (gneisses and amphibolites) sampled from the KTB drilling project. The decrease of permeability by pressure are compared with the pressure-dependent data of the electrical conductivity (formation factor) resulting from complex impedance measurements. According to the equivalent-channel model (ECM), there exists a linear relationship between these parameters by representing both properties on logarithmic scales. The results show that it is possible to extrapolate high-pressure permeability from low-pressure (< 60 MPa) permeability data by using the pressure-dependent electrical conductivity (up to 300 MPa).     

多分辨分析理论在井-震匹配中的应用

简单介绍了多分辨率逼近理论,详尽分析了地震与声测井资料在尺度上的差异,进而提出了一种解决井-震尺度差异的新方法--多分辨率逼近方法。通过理论模型及实际资料算例验证了该方法的有效性,并且与常用的抗混频滤波方法进行了比较。结果表明,多分辨率逼近方法更能保持信号的局部化性质,使地震与声波测井资料能更好地匹配。     

Classical and Bayesian Seismic Yield Estimation: The 1998 Indian and Pakistani Tests

— The nuclear tests in May, 1998, in India and Pakistan have stimulated a renewed interest in yield estimation, based on limited data from uncalibrated test sites. We study here the problem of estimating yields using classical and Bayesian methods developed by Shumway (1992), utilizing calibration data from the Semipalatinsk test site and measured magnitudes for the 1998 Indian and Pakistani tests given by Murphy (1998). Calibration is done using multivariate classical or Bayesian linear regression, depending on the availability of measured magnitude-yield data and prior information. Confidence intervals for the classical approach are derived applying an extension of Fieller's method suggested by Brown (1982). In the case where prior information is available, the posterior predictive magnitude densities are inverted to give posterior intervals for yield. Intervals obtained using the joint distribution of magnitudes are comparable to the single-magnitude estimates produced by Murphy (1998) and reinforce the conclusion that the announced yields of the Indian and Pakistani tests were too high.     

阿尔奇公式的适用性分析及其拓展

阿尔奇年代的储层孔隙结构简单,岩石孔隙可以被实验电解质完全充填,随着油气田勘探开发的逐步深入,对储层孔隙结构复杂程度的认识更加深入.发现岩石孔隙不仅有有效孔隙,也有无效孔隙.不仅有效孔隙导电,无效孔隙也导电,某些岩石骨架同样也导电.如何去除无效孔隙和其他各类岩石附加导电现象的影响,正确评价有效孔隙的贡献往往令人困惑.笔者发现：通过岩石电阻率计算地层因数只是在没有岩石附加导电环境下的特殊应用,在更为普适的条件下,地层因数实质是借助岩石电阻变化率反映孔隙连通性的重要参数.与物理学位移、速度的关系类似,电阻率和电阻变化率之间同样有着密切关系.这一观点的提出为在复杂孔隙结构条件下评价储层孔隙有效性提供了手段.     

一种评价致密砂岩储层孔隙结构的新方法及其应用(英文)

致密砂岩储层的孔隙结构对其渗透性和电性影响显著,是此类复杂储层岩石物理研究的关键。针对仅从连通喉道半径评价渗透率的多解性以及储层孔隙结构与电性关系研究欠缺等不足,综合影响物性的主要因素,提出了一种同时考虑孔隙度、最大连通喉道半径及分选性三种因素的新型孔隙结构参数δ的计算公式。利用岩心及实测数据对比分析表明,δ值能够较连通喉道半径等传统方法更精确地刻画致密砂岩储层渗透性,同时它与储层电性具有密切关系,可用于估算地层因素F和胶结指数m。据此提出将孔隙结构对电阻率的影响进行归一化校正以及基于核磁共振测井预测储层完全含水电阻率R0的评价方法,从而突出储层流体性质变化引起的电性变化,并提供了一种新的致密砂岩储层流体识别思路,研究结果得到了实验资料和实际测井试油资料的验证。     

Cauchy prior distribution-based AVO elastic parameter estimation via weakly nonlinear waveform inversion

Cauchy priori distribution-based Bayesian AVO reflectivity inversion may lead to sparse estimates that are sensitive to large reflectivities. For the inversion, the computation of the covariance matrix and regularized terms requires prior estimation of model parameters, which makes the iterative inversion weakly nonlinear. At the same time, the relations among the model parameters are assumed linear. Furthermore, the reflectivities, the results of the inversion, or the elastic parameters with cumulative error recovered by integrating reflectivities are not well suited for detecting hydrocarbons and fuids. In contrast, in Bayesian linear AVO inversion, the elastic parameters can be directly extracted from prestack seismic data without linear assumptions for the model parameters. Considering the advantages of the abovementioned methods, the Bayesian AVO reflectivity inversion process is modified and Cauchy distribution is explored as a prior probability distribution and the time-variant covariance is also considered. Finally, we propose a new method for the weakly nonlinear AVO waveform inversion. Furthermore, the linear assumptions are abandoned and elastic parameters, such as P-wave velocity, S-wave velocity, and density, can be directly recovered from seismic data especially for interfaces with large reflectivities. Numerical analysis demonstrates that all the elastic parameters can be estimated from prestack seismic data even when the signal-to-noise ratio of the seismic data is low.     

Joint elastic‐electrical properties of reservoir sandstones and their relationships with petrophysical parameters

We measured in the laboratory ultrasonic compressional and shear‐wave velocity and attenuation (0.7–1.0 MHz) and low‐frequency (2 Hz) electrical resistivity on 63 sandstone samples with a wide range of petrophysical properties to study the influence of reservoir porosity, permeability and clay content on the joint elastic‐electrical properties of reservoir sandstones. P‐ and S‐wave velocities were found to be linearly correlated with apparent electrical formation factor on a semi‐logarithmic scale for both clean and clay‐rich sandstones; P‐ and S‐wave attenuations showed a bell‐shaped correlation (partial for S‐waves) with apparent electrical formation factor. The joint elastic‐electrical properties provide a way to discriminate between sandstones with similar porosities but with different clay contents. The laboratory results can be used to estimate sandstone reservoir permeability from seismic velocity and apparent formation factor obtained from co‐located seismic and controlled source electromagnetic surveys.     

Simple scaling properties of Canadian annual average streamflow

The spatial scaling properties of Canadian annual average streamflow (abbreviated as AASF) are assessed using both the product moments (PMs) and the probability weighted moments (PWMs) of AASF across the entire country and in its sub-climatic regions. By the PMs, the log relationship between the kth moments of AASF and the drainage area can be almost represented by a perfect straight line across the entire country and in its sub-climatic regions, whose regression parameters are a linear function of the moment order. By the PWMs, the logarithm of the kth PWM is a linear function of the logarithm of drainage area for the entire country and its sub-climatic regions, where its slope (or scale exponent) in a region is constant and is independent of the order. These results indicate that Canadian AASF exhibits simple scaling and drainage area alone may describe most of the variability in the moments of AASF. The third approach, based on the log linearity between quantiles and drainage area, is applied to Region 2, also demonstrate simple scaling of AASF in that region, as concluded from using PMs and PWMs methods, which indicates that all three methods are consistent. The simple scaling results provide a basis for using the index flood method to conduct regional frequency analysis of AASF in Canada.     

误差反传播神经网络法地震反演

针对测井资料约束下的地震反演具体问题，在假定反演目标和地震资料之间存在某种非线性映射的情况下，用神经网络逼近反演问题中的正演和反演过程，综合构成一个大网络系统，并根据地震反演的具体问题，给出该系统的能量函数．系统采用误差反传播法进行学习，从而实现用神经网络自适应地外推测井资料，有机地将神经网络与地震反演结合起来．对实际资料的测井速度外推结果表明，此法具有好的应用前景．     

Correlation of vertical electrical sounding and electrical borehole log data for groundwater exploration

We have correlated the longitudinal unit conductance CL obtained from interpreted vertical electrical sounding data with the formation resistivity R_t and the formation resistivity factor F, obtained by carrying out electrical borehole logging. Interpreted geophysical data of eleven soundings and two electrical borehole log records are used for the analysis. The geophysical data used were acquired in a sedimentary basin. The study area is called Lower Maner Basin located in the province of Andhra Pradesh, India. Vertical electrical soundings were carried out using a Schlumberger configuration with half current electrode separation varying from 600–1000 m. For logging the two boreholes, a Widco logger‐model 3200 PLS was used. True formation resistivity R_t was calculated from a resistivity log. Formation resistivity factor F was also calculated at various depths using R_t values. An appreciable inverse relation exists between the correlated parameters. The borehole resistivity R_t and the formation resistivity factor F decrease with the increase in the longitudinal unit conductance CL. We have shown the use of such a relation in computing borehole resistivity R_t and formation resistivity factor F at sites that posses only vertical electrical sounding data, with a fair degree of accuracy. Validation of the correlation is satisfactory. Scope for updating the correlation is discussed. Significance and applications of the relation for exploration of groundwater, namely to update the vertical electrical sounding data interpretation by translating the vertical electrical sounding data into electrical borehole log parameters, to facilitate correlations studies and to estimate the porosity (φ), permeability (K) and water saturation S_w of water bearing zones are discussed.     

Full-Bayesian inversion of the Edwards Aquifer

The Bayesian inverse approach proposed by Woodbury and Ulrych (2000) is extended to estimate the transmissivity fields of highly heterogeneous aquifers for steady state ground water flow. Boundary conditions are Dirichlet and Neumann type, and sink and source terms are included. A first-order approximation of Taylor's series for the exponential terms introduced by sinks and sources or the Neumann condition in the governing equation is adopted. Such a treatment leads to a linear finite element formulation between hydraulic head and the logarithm of the transmissivity-denoted as ln(T)-perturbations. An updating procedure similar to that of Woodbury and Ulrych (2000) can be performed. This new algorithm is examined against a generic example. It is found that the linearized solution approximates the true solution with an R2 coefficient = 0.96 for an ln(T) variance of 9 for the test case. The addition of hydraulic head data is shown to improve the ln(T) estimates, in comparison to simply interpolating the sparse ln(T) data alone. The new Bayesian code is also employed to calibrate a high-resolution finite difference MODFLOW model of the Edwards Aquifer in southwest Texas. The posterior ln(T) field from this application yields better head fit when compared to the prior ln(T) field determined from upscaling and cokriging. We believe that traditional MODFLOW grids could be imported into the new Bayes code fairly seamlessly and thereby enhance existing calibration of many aquifers.     

Estimating thermal conductivity from core and well log data

The aim of the presented work was to introduce a method of estimating thermal conductivity using well log data. Many petrophysical properties of rocks can be determined both by laboratory measurements and well-logs. It is thus possible to apply geophysical data to empirical models based on relationships between laboratory measured parameters and derive continuous thermal conductivity values in well profiles. Laboratory measurements were conducted on 62 core samples of Meso-Paleozoic rocks from the Carpathian Foredeep. Mathematical models were derived using multiple regression and neural network methods. Geophysical data from a set of seven well logs: density, sonic, neutron, gamma ray, spectral gamma ray, caliper and resistivity were applied to the obtained models. Continuous thermal conductivity values were derived in three well profiles. Analysis of the obtained results shows good consistence between laboratory data and values predicted from well log data.     

Committee neural networks for porosity and permeability prediction from well logs

Neural computing has moved beyond simple demonstration to more significant applications. Encouraged by recent developments in artificial neural network (ANN) modelling techniques, we have developed committee machine (CM) networks for converting well logs to porosity and permeability, and have applied the networks to real well data from the North Sea. Simple three‐layer back‐propagation ANNs constitute the blocks of a modular system where the porosity ANN uses sonic, density and resistivity logs for input. The permeability ANN is slightly more complex, with four inputs (density, gamma ray, neutron porosity and sonic). The optimum size of the hidden layer, the number of training data required, and alternative training techniques have been investigated using synthetic logs. For both networks an optimal number of neurons in the hidden layer is in the range 8–10. With a lower number of hidden units the network fails to represent the problem, and for higher complexity overfitting becomes a problem when data are noisy. A sufficient number of training samples for the porosity ANN is around 150, while the permeability ANN requires twice as many in order to keep network errors well below the errors in core data. For the porosity ANN the overtraining strategy is the suitable technique for bias reduction and an unconstrained optimal linear combination (OLC) is the best method of combining the CM output. For permeability, on the other hand, the combination of overtraining and OLC does not work. Error reduction by validation, simple averaging combined with range‐splitting provides the required accuracy. The accuracy of the resulting CM is restricted only by the accuracy of the real data. The ANN approach is shown to be superior to multiple linear regression techniques even with minor non‐linearity in the background model.     

POROSITY AND PORE STRUCTURE FROM ACOUSTIC WELL LOGGING DATA1

Wyllie's time-average equation and subsequent refinements have been used for over 20 years to estimate the porosity of reservoir rocks from compressional (P)-wave velocity (or its reciprocal, transit time) recorded on a sonic log. This model, while simple, needs to be more convincingly explained in theory and improved in practice, particularly by making use of shear (S)-wave velocity. One of the most important, although often ignored, factors affecting elastic velocities in a rock is pore structure, which is also a controlling factor for transport properties of a rock. Now that S-wave information can be obtained from the sonic log, it may be used with P-waves to provide a better understanding of pore structure. A new acoustic velocities-to-porosity transform based on an elastic velocity model developed by Kuster and Toksöz is proposed. Employing an approximation to an equivalent pore aspect ratio spectrum, pore structure for reservoir rocks is taken into account, in addition to total pore volume. Equidimensional pores are approximated by spheres and rounded spheroids, while grain boundary pores and flat pores are approximated by low aspect ratio cracks. An equivalent pore aspect ratio spectrum is characterized by a power function which is determined by compressional-and shear-wave velocities, as well as by matrix and inclusion properties. As a result of this more sophisticated elastic model of porous rocks and a stricter theory of elastic wave propagation, the new method leads to a more satisfactory interpretation and fuller use of seismic and sonic log data. Calculations using the new transform on data for sedimentary rocks, obtained from published literature and laboratory measurements, are presented and compared at atmospheric pressure with those estimated from the time-average equation. Results demonstrate that, to compensate for additional complexity, the new method provides more detailed information on pore volume and pore structure of reservoir rocks. Examples are presented using a realistic self-consistent averaging scheme to consider interactions between pores, and the possibility of extending the method to complex lithologies and shaly rocks is discussed.     

波阻抗映射法外推

首先介绍了自适应滤波的方法和波阻抗映射法外推的基本原理．在小反射系数的假设条件下推导了对数波阻抗和地震道之间近似为线性映射的关系,应用自适应滤波的方法可以实现这种映射．实际资料的试算结果表明,该方法能够提供分辨率明显高于常规方法的波阻抗或层速度剖面,并与测井资料较吻合．因此,它作为测井约束反演的补充手段,是一种可用于开发地震的新方法．最后讨论了映射法波阻抗反演的局限性．     

Adaptive reconstruction method of impedance model with absolute and relative constraints

Inversion for seismic impedance is an ill-posed and band-limited problem so that inversion results are non-unique and unstable and low and high frequency components of inversion results are missed. Combining regularization with constraints of sonic log data and geological structure information can help to alleviate these problems. To achieve this, we developed an inversion method by constructing a new objective function which includes edge-preserving regularization and soft constraint based on Markov random field (MRF). The method directly introduces absolute constraints with prior impedance and sonic log data in the objective function and indirectly achieves relative constraints with geologic structures of layer interfaces and faults by adjusting the regularization parameter which is the scaling parameter δ. Moreover, we improved the inversion result using anisotropic diffusion smoothing method. Optimization approach utilized in inversion is a fast simulated annealing (FSA). We test the method on both synthetic and field data examples. Tests on 2-D synthetic data indicate that aspects of the discontinuity in the inversion results are significantly improved by adding δ values in faults and layer interfaces. We obtained better results by combining the first-order neighborhood and the third-order neighborhood of MRF. The inversion results of the field data provide more detailed information of the layers. The results of nearby faults were improved by introducing the geological structure constraints.     

Two-dimensional resistivity imaging and modelling in areas of complex geology

A system is described for the automatic measurement of electrical resistivity pseudo-sections. This comprises a linear array of up to 32 electrodes connected through a multicore cable to a computer controlled switching module and a resistivity meter. The processing of the measured sections to produce two-dimensional true resistivity images of the subsurface is briefly described. Some account is given of the capabilities and limitations of the technique. This is illustrated by a series of computed constant separation traverses for models of simple subsurface structures. Examples of processed images derived from sections measured in areas of relatively complex geology follow, a comparison being made of the interpretations obtained using an automatic imaging method and a manual iterative approach. It is concluded that with the equipment and software so far developed, in areas of modest subsurface geological complexity where some control is available and where the structures are essentially two-dimensional, then good approximations to the true geoelectric sections can be obtained down to depths of between 100 and 200 m.     

A new velocity model for clay-sand mixtures1

None of the standard porosity-velocity models (e.g. the time-average equation, Raymer's equations) is satisfactory for interpreting well-logging data over a broad depth range. Clays in the section are the usual source of the difficulty through the bias and scatter that they introduce into the relationship between porosity and P-wave transit time. Because clays are composed of fine sheet-like particles, they normally form pores with much smaller aspect ratios than those associated with sand grains. This difference in pore geometry provides the key to obtaining more consistent resistivity and sonic log interpretations. A velocity model for Clay–sand mixtures has been developed in terms of the Kuster and Toksöz, effective medium and Gassmann theories. In this model, the total pore space is assumed to consist of two parts: (1) pores associated with sand grains and (2) pores associated with clays (including bound water). The essential feature of the model is the assumption that the geometry of pores associated with sand grains is significantly different from that associated with clays. Because of this, porosity in shales affects elastic compliance differently from porosity in sand-Stones. The predictive power of the model is demonstrated by the agreement between its predictions and laboratory measurements and by its ability to predict sonic logs from other logs over large depth intervals where formations vary from unconsolidated to consolidated sandstones and shales.