Determining acoustic impedance cube by inverting seismic data using feedforward and radial basis neural networks in an Iranian oilfield

Abstract

Accurate three-dimensional acoustic impedance modeling in offshore clastic reservoirs remains a significant challenge due to sparse well control and the highly nonlinear relationship between seismic attributes and subsurface elastic properties. This study introduces an integrated, physics-guided machine learning (ML) workflow that combines rock-physics-driven pseudo-well generation with neural networks to directly map seismic attributes to acoustic impedance under data-limited conditions. A soft-sand rock physics workflow was applied, in which grain moduli were determined using the Voigt-Reuss-Hill average. The dry rock frame was modeled at critical porosity by Hertz-Mindlin contact theory and then interpolated toward zero porosity using the Modified Hashin-Shtrikman lower bound. Gassmann fluid substitution was subsequently performed. Using this approach, 45 pseudo-wells were generated and conditioned through lithofacies classification and spatial statistics, mitigating the risk of overfitting associated with the three available real wells. Six seismic attributes-envelope, RMS amplitude, instantaneous phase, instantaneous frequency, quadrature trace, and sweetness-were selected as predictors. Two neural architectures, a multi-layer feedforward network (MLFN) and a radial basis function network (RBFN), were trained and benchmarked using a leave-one-well-out cross-validation scheme. The MLFN achieved higher predictive accuracy (CC = 0.87, NRMSE = 0.493) compared to the RBFN (CC = 0.79, NRMSE = 0.613), which may reflect its greater capacity to model broader hierarchical relationships between seismic attributes and acoustic impedance. The resulting impedance volume delineates laterally coherent high-impedance sandstone units and low-impedance porous intervals consistent with geological interpretation. These results suggest that integrating physics-guided pseudo-well augmentation with feed-forward neural networks offers a practical and computationally efficient approach for acoustic impedance inversion in data-limited offshore settings. Future work may explore validation across diverse geological settings to assess the robustness and transferability of the proposed methodology. This study provides a basis for hybrid and uncertainty-aware inversion frameworks that may help address complexities in heterogeneous reservoir systems, highlighting the importance of reproducible and widely applicable data-driven seismic inversion methods under sparse well control.

Keywords: Acoustic impedance; MLFN; Pseudo-well generation; RBFN; Rock physics modeling; Seismic inversion.

Fig. 1

A 3D seismic volume, spanning inlines 54–612 and crosslines 1600–1900, with a vertical extent up to 1000 ms TWT, covering 21.1 km² with locations of wells A, B, and C.

Fig. 2

A flowchart of the impedance modeling approach integrating seismic data, physics-informed pseudo-wells, and neural network-based prediction using MLFN and RBFN.

Fig. 3

Well-tie quality along a cross-section at crossline 1625 spanning inlines 54–612 with the location of Well A, covering the interval between horizons A & B.

Fig. 4

(a) Horizon-A and (b) Horizon-B displayed from the seismic cube after well-tie calibration. Both panels include a TWT-based color legend and show the precise locations of wells A, B, and C.

Fig. 5

Cross-correlation analysis for Well A across the interval between horizons A and B: (a) V_p and (b) Rho cross-plots, illustrating the correlation between measured (horizontal axis) and predicted (vertical axis) values. The horizontal axis is derived from the well logs data, while the vertical axis represents the results obtained from the RPM.

Fig. 6

Lithofacies distribution in three wells based on petrophysical classification: (a) Well A, (b) Well B, and (c) Well C. Proportions of shale, compacted sandstone, shaly sandstone, water-bearing clean sandstone, and oil-bearing clean sandstone are illustrated for each well.

Fig. 7

Rock-physics calibration and elastic trends for Well A between Horizon-A (841 m) and Horizon-B (944 m). (a) Calibration of the RPM using V_p and Rho logs, where blue curves represent the observed logs and orange curves the model-predicted logs. The close agreement, particularly for V_p and Rho, supports the reliability of acoustic impedance modeling. (b) Elastic trends derived from the calibrated model, with blue showing the observed logs and orange the derived trends, capturing the low-frequency, depth-dependent behavior and serving as key inputs to the statistical stage of pseudo-well generation. All logs and trends are shown in the depth domain; subsequent integration with the seismic data is performed through a well-tie-derived time–depth relationship.

Fig. 8

Background trends and residuals for Well A between Horizon-A (841 m) and Horizon-B (944 m). (a) Background trends of V_shale, porosity, and MSI, where the blue curves represent the observed logs and the orange curves the derived trends, capturing the low-frequency, depth-dependent behavior across the target interval. (b) Corresponding residual components of V_shale, porosity, and MSI (left to right), highlighting localized deviations from the background trends that represent higher-frequency variability and support the statistical modeling stage of pseudo-well generation for data augmentation. All trends and residuals are shown in the depth domain; their subsequent integration with the seismic data is achieved through well-tie-based time–depth conversion.

Fig. 9

Final step in the sequential workflow for pseudo-well generation in Well A between Horizon-A (841 m) and Horizon-B (944 m). (a–c) Vertical variogram modeling of MSI (left), Phi_T (middle), and V_shale (right) residuals. The blue curve represents the observed variogram derived from the residuals, while the orange curve shows the fitted Gaussian model. The models were built using a maximum lag of 40 samples, nugget of 0.12, sill of 1.0, and a Gaussian structure with a vertical range of 12 samples. The close fit confirms that the Gaussian variogram effectively captures the vertical correlation structure required for statistical simulation in pseudo-well generation.

Fig. 10

Multi-property quality control for Well-A between horizons A and B. From left to right, V_shale, Phi_T, V_P, V_S, and Rho are shown, where black curves indicate the observed logs and green curves correspond to the Gaussian realizations. The close agreement demonstrates that the variogram range and statistical parameters effectively capture both intra-layer variability and overall property distributions, supporting reliable inputs for pseudo-well generation.

Fig. 11

Density plot V_P vs. Phi_T for Well A, based on 15 pseudo-wells generated after high accuracy RPM and statistical simulation. Black dots show the observed log samples, while the color scale represents sample density, with warmer colors indicating higher concentrations. The close match between observed data and the dense regions of the pseudo-wells confirms that the simulations reliably reproduce the variability and correlation structure required for data augmentation and impedance modeling. All properties are shown in the depth domain; subsequent integration with the seismic data is achieved through well-tie-based time–depth conversion.

Fig. 12

Spatial distribution of Well A (red) and 15 pseudo-wells (blue) within the variogram-based effective radius (268.8 m) between horizons A and B. This configuration maintains local stationarity and supplies consistent inputs for statistical simulation and data augmentation.

Fig. 13

Pseudo-well no.1 generated for Well A within the interval between horizons A and B (vertical axis in the time domain (TWT, ms) after time–depth conversion). From left to right, the tracks display V_P (blue), Rho (black), V_S (red), and Sw (color-filled). The pseudo-logs are initially generated in the depth domain using calibrated rock-physics relationships and a statistical workflow, and subsequently converted to the time domain using the well-tie-derived time–depth relationship. This ensures consistency with seismic-domain inversion results while preserving the depth-dependent trends and variability of the observed well data.

Fig. 14

Predicted 3D acoustic impedance volumes generated from neural network inversion between Inline 54–612 and Crossline 1600–1900. The seismic volume is displayed over a broader time window of TWT 480–650 ms, while the target A–B inversion interval corresponds to 510–592 ms. (a) Result from the MLFN, trained with seismic attributes and augmented well data. (b) Result from the RBFN for the same interval, providing a comparable impedance distribution with slightly lower continuity relative to the MLFN.

Fig. 15

Cross-plots validating the predictive performance of neural network models for acoustic impedance inversion. (a) The MLFN yields a CC of 87% and an NRMSE of 0.493 across 1008 samples, with actual values on the horizontal axis and predicted values on the vertical axis (color-coded by pseudo-well). The close alignment confirms the model’s reliable predictive performance for reproducing impedance in geologically complex, data-limited settings. (b) The RBFN achieves a CC of 79% and an NRMSE of 0.613 for the same dataset, demonstrating stable performance and utility in data-limited conditions, albeit with slightly lower accuracy than the MLFN.