During the last decade, there has been an increasing interest in the use of attributes derived from 3-D seismic data to define reservoir properties, such as the presence and amount of porosity and fluid content. Therefore, it is worthwhile to continue the advances in the study and application of expert systems in the petroleum industry so that it is possible to use the attributes in reservoir characterization more effectively. The establishment of the existence of an intelligent formulation between two sets of data (inputs/outputs) has been the main topic of such studies. One such topic of great interest was the characterization of 3D seismic data with relation to lithology, rock type, fluid content, porosity, shear wave velocity, and other reservoir properties. Petrophysical parameters, such as water saturation and porosity, are very important data for hydrocarbon reservoir characterization. Hitherto, several researchers endeavored to predict them from seismic data using statistical methods and intelligent systems (Russell et al., 2002; Russell et al., 2003; Chopra and Marfurt, 2006). Correct recognition of porosity model and estimation of petrophysical parameters in reservoirs is a key issue in any oil project. The correct estimation of porosity as a petrophysical parameter can inform decisions that have high financial risk, such as drilling. By determining reservoir characterizations and assessing petrophisical parameters with a adequate accuracy during the first steps of studies, researchers would be able to produce optimum exploitation with a minimum number of wells.This paper focuses on the link between seismic attributes and reservoir properties such as lithology, porosity, and pore-fluid saturation. Typically, seismic attributes have been the only information obtainable from seismic data. Using statistical rock-physics, the type of seismic attributes that are direct functions (analytically defined) of the elastic properties can be probabilistically transformed, sample-by-sample and independently one of each other, into reservoir properties. In this paper, we combine the methods of geostatistics and MULTIATTRIBUTE prediction for the integration of seismic and well-log data, and illustrate this new procedure with a case study. A number of new ideas are developed for the statistical determination of reservoir parameters using seismic attributes, combining the classical techniques of multivariate statistics and the more recent methods of neural network analysis. We first extract average porosity values at the zone of interest, and then compare these values to average seismic attributes over the same zone. The technique of cross-validation is subequently used to show which attributes are significant. We then apply the results of the training and cross-validation to data slices derived from both the seismic data cube and the inverted cube to produce an initial porosity map. Finally, we improve the fit between the well log values and the porosity map using co-kriging.The main purpose of this paper is to present a quantitative assessment of porosity as a petrophisical parameter in an offshore oil field in Iran using the newly proposed method of reservoirs parameter estimation. This paper shows that by using both seismic data and well logging data it is possible to obtain a more accurate model of porosity in a given reservoir. Specifically, the study determines the relationship between a set of seismic attributes and a reservoir parameter such as porosity at well locations, and then uses this relationship to compute reservoir parameters from sets of seismic attributes throughout a seismic volume. Therefore, a primary plan of porosity is available for the area of study. In the next step, by using geostatistics and, according to the initial plan, as a secondary variable in collocated cokriging, we can approach a more accurate plan to show the distribution of porosity. In effect, the proposed method combines geostatistics with MULTIATTRIBUTE TRANSFORMS. This technique uses multivariate statistics and neural networks to improve the secondary dataset used in the collocated cokriging technique.

In this study, an attempt is made to predict effective porosity in one of the oil fields in the Persian Gulf by designing a probablistic neural network (PNN) and simultanusely making use of seismic attributes and effective porosity logs in the reservoir window. This was done by deriving a MULTIATTRIBUTE transformation between an optimum subset of seismic attributes and the effective porosity logs.The geophysical data used in this study consist of 3D seismic pre-stack time migrated (PSTM) data with 12.5*12.5 m grid size and a 4 ms sampling rate. The length of the seismic traces are two seconds. Well logs of five vertical wells in the study area, including Sonic (DT), Density (RHOB), Effective Porosity (PHIE) and Seismic Well Velocity Surveys (Check Shots), were used. The reservoir layer is a Mishrif member of the Sarvak formation with Cretaceous age, which is common in oil reservoirs in the Persian Gulf. The top of the Mishrif is adjusted with the Middle Turonian Unconformity and covered with shaley Laffan formation. The Mishrif Reservoir in study area contains two reservoir zones. The lower zone with higher clay content is separate from the upper zone. The upper zone consists of clean limesone with better reservoir properties. Seismic traces close to the well locations were used to generate seismic attributes. Effective porosity logs at the reservoir area were the target logs in this study.The designed neural network consists of one input layer, one hidden layer with four processing units (neuron), and one output layer with one neuron. In order to prepare training samples for the neural network, PHIE logs were converted to time domain using a time-depth relationship calculated from the DT logs and check shot curves for each well location. Subsequently, these logs were filtered (using a Hanning filter with 4 ms length) and resampled with seismic sampling rate (4 ms). Finally, a set of seismic attributes, including sixteen sample-based seismic attributes, were generated using HRS software. Training samples in this study consisted of 57 samples (selected seismic attributes and their related effective porosity from PHIE logs in the time domain). For training the network, the samples were divided into three data sets: the training samples, cross validation samples and testing samples. The training data were used for adjusting the weights of the network; the cross validation data were used to prevent overtraining theneural network; and the testing data were used to ensure generalizabillity of the network output.A forward stepwise regression process was used to determine an optimum subset of attributes for use in the training of the neural networks. The optimum subset of attributes in this study consists of the Dominant Frequency, Amplitude Weighted Frequency, Integrated Absolute Amplitude and Filter 45-60 Hz.After the network was trained using training and cross validation data sets, it was used to predict the testing data. The results show a good correlation between real and predicted data, with 92% correlation. Finally, in order to attain a better generalization of the network, testing data sets were inserted to trained data and the network was trained again. This network was then used to predict effective porosity in well locations which increased the correlation coefficient to 95%. This study shows the ability of the PNN networks to predict effective porosity even with a paucity of training examplares.

In this paper we shall examine the quadratic Fourier transform which is introduced by the generalized quadratic function for one order parameter in the ordinary Fourier transform. This will be done by analyzing corresponding six subcases of the quadratic Fourier transform within a reproducing kernel Hilbert spaces framework.

This work aims to study F-TRANSFORMS based on general implicators and to investigate their basic properties. Interestingly, we show that some of the properties of F-TRANSFORMS fail to hold in the case of implicators, such as S-and QL-implicators. Further, we establish an equivalence between L-fuzzy transformation systems and F-TRANSFORMS.

This article introduces a systematic study for computational aspects of classical wavelet TRANSFORMS over finite fields using tools from computational harmonic analysis and also theoretical linear algebra. We present a concrete formulation for the Frobenius norm of the classical wavelet TRANSFORMS over finite fields. It is shown that each vector defined over a finite field can be represented as a finite coherent sum of classical wavelet coefficients.