We propose a new technology to building a stable nonlinear predictive operator based on a combination of a neural network, a genetic algorithm, and the controlled gradient method. The main idea of the proposed technology lies in application of the combination of stochastic and deterministic approaches during construction of the operator in the learning stage. This operator can be used to predict different variables in spatial or/and time coordinates when their deterministic nature is unknown or it is impossible to apply direct inversion. It is assumed that there exists a possibility to predict some variables via other measured variables due to the existing unknown nonlinear dependence. For example, it is necessary to predict possible oil and gas production rates on a map (sweet spot) using different geological and geophysical maps (porosity, density, seismic attributes, gravity, magnetic, etc.) and based on initial oil and gas production rates for several wells in the area of interest. At the first stage, a learning set is used to build an operator, and, at the second stage, the operator is applied to predict the target parameters.
A neural network is a nonlinear operator widely used for predictive analysis in the petroleum industry (Ali, 1994; Roth and Tarantola, 1994; Schultz et al., 1994; Chen and Sidney, 1997; Russell et al., 1997; Boadu, 1998; Liu and Liu 1998; Mogensen and Link, 2001; Hampson et al., 2001; Veeken et al., 2009; Priezzhev et al., 2014). The neural network predictive operator has several significant advantages:
•1. The operator provides for controlled nonlinearity and power of freedom via a number of hidden nodes and type of activation function.
•2. The operator can be used in very complex cases in which the relationship between dependent (predicted) variables and independent variables is unknown or turns out to be too complex for using a deterministic approach.
An unconventional production data analysis technology that uses on gravity and magnetic data was applied to the Eagle Ford formation. The prediction technology uses a neural network with multivariate input and multivariate output and is based on an evolutionary algorithm for neural network teaching. Simultaneously, multivariate neural network output allows for predicting several parameters, such as oil, gas, and water production rates. This prediction is based on multivariate Gaussian distribution theory and an objective function, in this case, Mahalanobis distance versus square distance for one-parameter prediction. In addition, we applied gravity and magnetic depth decomposition technology based on potential field inverse theory.
Recent advances in seismic data acquisition and processing enable accurate seismic inversion below salt. We take advantage of this and apply a target-oriented pore-pressure-prediction method to recently acquired and processed dual-coil seismic data in the Green Canyon and the Walker Ridge areas of the Sigsbee Escarpment in the Gulf of Mexico. This simple pore-pressure method utilizes a direct transform of the acoustic impedance, with two adjustable parameters. The geology of the target zone is considered for choosing a calibration well for obtaining the transform parameters. A new, fit-for-purpose seismic inversion scheme is used for inversion of seismic impedance below salt. The amplitude fidelity of post-migrated and normalized data is verified through well-to-seismic ties. One of the wells is utilized as a calibration well and the other two as blind wells for comparing prediction results with the measured pore pressure and mudweight data. The predicted pore pressure at the blind wells both from well impedance and seismic impedance match with measured pore pressure and mud weights reasonably well. The subsalt velocity predicted from the inverted acoustic impedance is also in good agreement with the well-log velocity.
We propose to use 3D orthogonal decomposition of the seismic cube flattened along the target layer to detect fractures and subtle faults or other latent features under strong noise conditions. The technology is based on principal component analysis (PCA) using computation of eigenvalues and eigenvectors of the 3D autocorrelation function of the original seismic cube. Each orthogonal component is also a cube, and their sum is very close to that of the original cube. Orthogonality means the correlation coefficient between any two components will be about zero. Since the noise and acquisition footprints have no correlation with fractures or faults, reflections or other latent features, they stand out as separate orthogonal components. Wellbore information is usually required to select an orthogonal component useful for fracture detection. Fault and fracture auto tracking technology such as Ant-Tracking (Pedersen at al., 2002) can be applied to the selected orthogonal cube to improve the fracture image.
Seismic inversion requires two main operations relative to changes in the frequency spectrum. The first operation is deconvolution, used to increase the high frequency component of the observed seismic data and the second operation is integration of a reflectivity function to decrease the high frequencies and increase low frequencies of the seismic signal. The first operation is very unstable and non-unique for noisy seismic data. The second operation is very sable in high frequencies but has problems in low frequencies due to undefined low frequency data in seismic traces. By performing both of these operations simultaneously the operation will be stable in high frequency area and can be effectively stabilized in low frequency area based on an a priori acoustic impedance power spectrum and use Tikhonov and Arsenin‟s (1979) regularization technique. This approach can be applied to poststack and pre-stack seismic data.