**1. Introduction**

Seismic data have proved to be important quantitative tools that can bring valuable information about rock properties, especially when being integrated with statistical tools. For example, multiattribute transforms were used to predict log properties from seismic data [1]. Another common approach is to invert seismic data into elastic properties and then into petrophysical properties by statistical relationships obtained from logging data [2]. Porosity, lithology, and fluid properties were also estimated with the resampling of rock physics constraints [3–5]. Russel used multivariate statistics and neural networks to predict reservoir parameters from seismic attributes [6]. In addition, Bachrach inverted porosity and water saturation by stochastic rock physics modeling [7].

Other methodologies consider reservoir parameter inversion based on Bayesian classification theory [8,9]. Moreover, a geostatistical inversion method was used to predict reservoir properties in a higher certainty than that of deterministic methods [10]. In addition, some studies derived elastic properties from prestack seismic inversion to define facies [11,12]. Another straightforward methodology is to combine petroelastic modeling and stochastic inversion to predict hydrocarbon zones based on Bayesian theory [13]. A rock physics model was postulated to derive the elastic rock properties from mineral parameters and structure information [14]. Recently, rock properties were estimated from angle stack seismic data by a Bayesian inversion based on the Gibbs sampling algorithm [15].

Machine learning (ML) tools have been widely used in reservoir characterization [16]. For instance, formation porosity and permeability were estimated from logging and core data by using an artificial neural network (ANN) [17–19]. Other studies also used neural networks to predict essential rock properties such as permeability [20–22] and shear wave

velocity [23–26]. Neural networks can be combined with seismic attributes to predict rock physics properties from seismic data [27–30]. In addition, facies distributions were estimated by both supervised and unsupervised ML algorithms such as ANN [31,32], convolutional neural network (CNN) [33–35], support vector machine (SVM) [36–41], bagged tree (BT) [42,43], relevance vector machine (RVM) [44], seed region growing (SRG) [45], self-organizing map (SOM) [46,47], principal component analysis (PCA) [48–50], and generative topographic mapping (GTM) [51]. Some challenges are common in ML facies models such as over-fitting and over-parametrization. Moreover, such models should consider the limitations of seismic data to eliminate error as much as possible. One of the problems that contributes to the uncertainty of seismic-derived methods is seismic anisotropy.

This study aimed at forecasting zero-offset P-impedance (*ZP*) and S-impedance (*ZS*) by using statistical modeling and MLFN after applying a partial-log-constrained inversion to the near, mid, and far angle stacks. The outputs of this objective were zero-offset impedances that were more accurate than those obtained from isotropic simultaneous inversion. Another objective was to compare the abilities of both statistical modeling and neural networks to turn the randomness of the data into identified patterns. The next step was to apply the best *ZP* and *ZS* volumes to Thomsen's anisotropy equations to solve for the anisotropy parameters, Epsilon and Delta, assuming a vertical transverse isotropic (VTI) medium. Next, the zero-offset *ZP* and *ZS* were used as inputs to a facies model, which predicted the distribution of three classes: gas sand, wet sand, and shale. The idea of the facies model is to forecast the sand and gas probabilities by logistic regression [52] and then use them as inputs for a decision tree to predict the distribution of each facies class.

The three offset stacks were converted into angle stacks, which were the inputs of the partial-stack inversion, and angle gathers, which were the inputs of the simultaneous isotropic inversion. The ranges of the near, mid, and far stacks were from 5° to 15°, 15° to 25°, and 25◦ to 40°. The partial-stack inversion resulted in the *ZP* and *ZS* volumes at the central angles, 10°, 20°, and 32.5°, from which the zero-offset properties were forecasted. The target zone consisted of two gas-bearing shaly sand reservoirs in the Malay basin: A and B. The training data of the Bayesian and MLFN models were gathered from the wells (×1) and (×2); however, the facies log was only obtained at the well (×1) due to the availability of the petrophysical cut-offs and oil-mud resistivity imaging data. Another challenge was that the *ZS* log was only available at the well (×1), so it was estimated from other log properties by the MLFN neural network at the well (×2).

The resulting *ZP* and *ZS* were compared to those obtained from isotropic inversion by using the impedance logs. The MLFN resulted in the most accurate zero-offset impedances. Therefore, the *ZP* and *ZS* volumes were applied to Thomsen's anisotropy equations to solve for the anisotropy parameters Epsilon and Delta. The *ZP* and *ZS* of MLFN and isotropic inversion were transformed into the near and far elastic impedances, which were the lithology predictors, and then into the Mu–Rho (MR) ratio, Lambda–Rho/Mu– Rho (LR/MR) ratio, and Poisson's ratio (PR), which are the fluid predictors. The lithofluid model was applied to the inverted elastic volumes to forecast the litho-fluid facies distribution. The facies log was used to validate the predicted facies obtained from the isotropic and anisotropic approaches.
