Nisar Ahmed

Deep learning (DL) algorithms are increasingly being used to address geophysical inverse problems, particularly when physical models are only partially known. This study introduces a supervised DL encoder–decoder approach based on a fully convolutional transformer architecture, where convolutional attention and wide‐focus modules are used to estimate reservoir elastic properties from seismic data. The DL method is evaluated against three physics‐based (PB) amplitude‐versus‐offset (AVO) inversion techniques: Bayesian linearized inversion, ensemble smoother with multiple data assimilation, and gradient‐based optimization. The DL model is trained on well‐log data to infer elastic properties from partial‐angle seismic stacks and interval velocity volumes, whereas the PB AVO inversion methods integrate geostatistical priors with seismic data through Bayesian inference, ensemble‐based data assimilation and gradient‐based optimization. Both approaches are applied to seismic and well‐log data from the Troll field in the North Sea. The network is trained using multiple well‐log datasets, using nearby seismic traces and interval velocity as input features, and then applied across the full three‐dimensional seismic volume. In contrast, the PB methods are applied to a two‐dimensional (2D) vertical section. The results are compared at training wells, multiple blind wells and along 2D sections of the predicted elastic properties. The DL approach demonstrates superior accuracy at training wells and competitive performance at blind wells, outperforming PB methods in some cases while producing comparable results in others. At blind well locations, the DL model produces under‐dispersed uncertainty estimates, indicating that it does not fully capture the variability represented by the PB methods. Results from real seismic field data highlight the complementary value of combining data‐driven and PB inversion strategies.

Seismic inversion contributes significantly to the estimation of subsurface properties based on seismic reflection data, serving as an essential step in reservoir modeling. Unlike conventional post-stack acoustic impedance inversion, this study presents a model-based nonlinear pre-stack inversion approach to estimate acoustic impedance, shear impedance, and density models, which are crucial for mapping subsurface lithofluid properties. The inversion algorithm comprises a convolutional model using a linearized amplitude versus offset approximation, the sum of squares of data misfit between theoretical model predictions and actual observations, and a Hessian-free conjugate gradient method and a nonlinear limited-memory quasi-Newton algorithm, which approximates second-order Hessian behavior, are employed to iteratively minimize the data misfit by fitting trial models to observed data. As the key novelty of this work, analytical adjoint-state gradients for acoustic (P-wave) and shear (S-wave) impedances are explicitly derived, which can eliminate the computational burden of finite-difference gradient approximations typically used in seismic inversion, while significantly improving the efficiency and scalability of large-scale seismic inversions. Meanwhile, Tikhonov and total variation regularization constraints are also applied to generate smooth estimated models for the ill-conditioned inverse problem. The proposed inversion technique is evaluated using a synthetic example based on one-dimensional well logs, a two-dimensional Marmousi model, and Troll field data from the Norwegian North Sea. Our investigations indicate that the estimated impedances and density models are accurate and stable, and the method provides good convergence to an optimal solution to the nonlinear inverse problem. A comparison of the sensitivity of the inversion results to the initial models is performed using Monte Carlo simulation and continuous ranked probability scores.

The amplitude-variation-with-offset inversion techniques are formulated to estimate elastic properties by fitting modeled seismic responses to observed data. Solving inverse seismic problems requires minimizing a target objective function for which gradient-based methods are frequently adopted. However, the efficiency and accuracy of these methods depend significantly on the approach used to compute the gradient of the target function. This work presents an explicit analytical gradient formulation of the exact Zoeppritz equation, discretized for multilayer media and derived using the adjoint-state method. The resulting expressions provide the gradient of a convolution-based objective function with respect to P-wave velocity, S-wave velocity, and density. The adjoint state-based solution improves computational efficiency by avoiding numerical approximations while maintaining high accuracy in calculating the gradient for seismic inversion. Additionally, using the exact Zoeppritz equation helps overcome the limitations associated with weak elastic property contrasts across subsurface layers. The least squares target function is minimized using a nonlinear limited-memory quasi-Newton algorithm. We demonstrate the effectiveness of the analytical gradient solution of the exact Zoeppritz equations in seismic inversion problems involving P-wave and S-wave velocity and density models. The inversion methodology is validated using 1D well logs-based and 2D synthetic seismic data with varying noise levels. Then it is applied to a 2D field data set from the Troll oil and gas field in the Norwegian North Sea. The results demonstrate that the proposed inversion framework provides stable and reliable estimates of elastic property models.

We develop a novel elastic amplitude-variation-with-offset (AVO) inversion process to estimate the fluid saturation and effective pressure or variations in these properties from time-lapse seismic data sets. These changes occur in oil and gas reservoirs caused by fluid injection or hydrocarbon production that leads to changes in the elastic wave properties, reflectivity, and seismic response. Our method is based on a seismic forward model that consists of a linearized AVO equation and a rock-physics model. The AVO equation links the elastic wave properties to seismic reflection amplitudes, whereas the rock-physics model maps the saturation and pressure into seismic velocities and density. The inversion approach relies on the gradient descent technique to estimate the unknown variables by searching for the minimum of the least-squares misfit between the observed and modeled data. The first-order gradient equations of the least-squares data misfit function with respect to effective pressure and water saturation are derived by using the adjoint-state method and the chain rule. The optimization method used to minimize the misfit function and obtain the best optimal solution is a limited-memory quasi-Newton algorithm. This inversion process allows us to incorporate prior constraints by using the logistic function to map the model variables to a bounded range. To achieve a stable solution to ill-posed inversion problems, optimal regularization weights are applied. The application of the developed workflow on 1D synthetic and real well-log data from the Edvard Grieg oil field simulating various saturation-pressure conditions during production demonstrates the validity of the approach with different noise levels. The inversion is then applied to a 2D synthetic data set modeled from the reservoir model of the Smeaheia field, a potential site for a large-scale offshore CO2 storage field located in the North Sea. Our results illustrate that our inversion method efficiently and accurately estimates reservoir saturation and pressure variations.

SUMMARY: Seismic inversion of amplitude versus offset (AVO) data in viscoelastic media can potentially provide high-resolution subsurface models of seismic velocities and attenuation from offset/angle seismic gathers. P- and S-wave quality factors (Q), whose inverse represent a measure of attenuation, depend on reservoir rock and pore fluid properties, in particular, saturation, permeability, porosity, fluid viscosity and lithology; however, these quality factors are rarely taken into account in seismic AVO inversion. For this reason, in this work, we aim to integrate quality factors derived from physically based models in AVO inversion by proposing a gradient descent optimization-based inversion technique to predict the unknown model properties (P- and S-wave velocities, the related quality factors and density). The proposed inversion minimizes the non-linear least-squares misfit with the observed data. The optimal solution is iteratively obtained by optimizing the data misfit using a second-order limited-memory quasi-Newton technique. The forward model is performed in the frequency–frequency-angle domain based on a convolution of broad-band signals and a linearized viscoelastic frequency-dependent AVO (FAVO) equation. The optimization includes the adjoint-state-based gradients with the Lagrangian formulation to improve the efficiency of the non-linear seismic FAVO inversion process. The inversion is tested on synthetic seismic data, in 1-D and 2-D, with and without noise. The sensitivity for seismic quality factors is evaluated using various rock physics models for seismic attenuation and quality factors. The results demonstrate that the proposed inversion method reliably retrieves the unknown elastic and an-elastic properties with good convergence and accuracy. The stability of the inverse solution especially seismic quality factors estimation relies on the noise level of the seismic data. We further investigate the uncertainty of the solution as a function of the variability of the initial models.

Seismic amplitude versus offset inversion has gained increased attention over the years and is a pragmatic tool applied to retrieve the seismic and petrophysical properties of the geological layers. The prediction of these petro-elastic properties plays an important role in litho-fluids identification and quantitative seismic reservoir characterization. However, imaging of these subsurface variables from the pre-stack seismic data requires minimizing the objective function and is generally solved by using a gradient-descent based optimization method. This method requires computing the gradients of the cost function with reference to the rock’s variables. We have introduced a model-based non-linear AVO inversion strategy that is based on the computation of the adjoint-state gradients. The forward seismic modelling is carried out by convolving the seismic wavelet with the reflectivity series modelled by using the linearized AVO approximation. The optimization method known as L-BFGS is implemented to attain the best optimal model. The novelty of this work is the adjoint-state solution of the linearized AVO equation. This inversion method has been successfully applied on single and multi-traced seismic data simulated with different seismic noise levels. The modelled examples show that the presented non-linear inversion method accurately extract the seismic properties including seismic (P and S) wave velocities and bulk density. Even at some realistic seismic noise levels, the true and extracted model show good agreement which demonstrates the wide application to solve the AVO inverse modelling problems.

Petrophysical evaluation and rock physics analysis are the important tools to relate the reservoir properties like porosity, permeability, pore fluids with seismic parameters. Nevertheless, the uncertainties always exist in the quantification of elastic and seismic parameters estimated through wireline logs and rock physics analysis. A workflow based on statistical relationships of rock physics and logs derived elastic and seismic parameters with porosity and the percentage error exist between them is given. The statistical linear regressions are developed for early Eocene Chorgali Formation between various petrophysically factors determined from borehole logging of well Ratana–03 drilled in tectonically disturbed zone and the seismic and elastic parameters estimated through rock physics modeling. The rock physics constraints such as seismic velocities, effective density and elastic moduli calculated from Gassmann fluid substation analysis are in harmony and close agreement to those estimated from borehole logs. The percentage errors between well logs and rock physics computed saturated bulk modulus (K _sat ), effective density (ρ _eff ), compressional and shear wave velocities (V _P and _V S) are 1.31%, 4.23 %, 5.25% and 4.01% respectively. The permeability of reservoir intervals show fairly strong linear relationship with the porosity, indicating that the reservoir interval of the Chorgali Formation is permeable and porous thus having large potential of hydrocarbon accumulation and production.