## 1 Introduction  
Porosity has a significant impact on the economic feasibility of a deposit, as is widely known. Porosity can be quantified using a variety of approaches, including seismic data [1] (by indirect methods), well logs [2, 3] (via direct measurements), and accurate laboratory analysis [4]. Seismic data are used to estimate elastic characteristics, which are then used to calculate petrophysical properties. However, it is critical to recognize the uncertainties that pervade both stages of this complex inversion process. If these uncertainties are not managed properly, they might lead to cumulative errors that propagate throughout the structure of the final output. The integrated technique, which harmonizes seismic data with well logs, combines rock physics and seismic inversions. This approach extracts elastic and petrophysical parameters directly from the initial data [5, 6, 7, 8, 9]. Beyond that, one essential component in the thorough characterization of siliciclastic reservoirs is the porosity attribute. It is essential for controlling fluid flow and storing fluid in these rock formations. Most of the published research has focused on using seismic and well-logmeasurements to estimate porosity, e.g., [PERSON] et al. [10] and [PERSON] et al. [11], presented a seismic petrophysical inversion technique (similar to [12]) to determine porosity from the seismic impedance. [PERSON] et al. [13] presented a Monte Carlo-based seismic petrophysical inversion technique that simultaneously estimates porosity and pore aspect ratio using the Xu-White model and the Zoeppritz equation. These investigations demonstrate that the quantitative representations of petrophysical results can be more accurate by incorporating the changing porosity using inversion techniques. In regions with few well-log readings, [PERSON] [14] calculated reservoir porosity using seismic data and deep learning to make precise predictions. The main objective of the work was to reduce initial uncertainty by continuously modifying the models' input data and increasing the prediction models' accuracy. When using inversion models, the initial uncertainty of the input data is typically neglected, leading to values that underestimate this uncertainty [15]. In the current work, two distinct inversion models--the BLI model and the AVO model--were utilized to enhance the porosity results obtained from the prediction models to reduce the effects of uncertainty in the resulting values. The BLI model was used because it combines the data inversion methodology with the Bayesian process, widely used for its ability to use a priori information to minimize the effects of uncertainty effectively [16; 17; 18; 19; 20; 21; 22], thus improving the accuracy and reliability of the model results. Statistical rock physics modeling integrates statistical analyses with rock physics models to extrapolate information beyond well-log observations [23; 24]. Ensuring initial input data distributions adhere to a Gaussian distribution is critical [25]. It is worth mentioning that meticulous pre-processing and analysis were conducted to control distributions and meet Gaussian distribution requirements. The model utilized, developed by [25], offers an analytical matrix comprising mean and covariance, representing Gaussian posterior distribution results within a Bayesian structural framework. This strategic selection notably enhances result quality by managing intrinsic dataset uncertainty alongside a priori information. The investigation begins with seismic and well data inversion, utilizing techniques such as Bayesian Linearized Inversion (BLI) and Amplitude Versus Offset (AVO). At the start of the investigation, to effectively manage computational resources, predictive models were initially applied to a subset of the seismic data (a time window of 500 milliseconds versus 100 traces). Additionally, information from the primary records of the seventeen wells was utilized.