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Although full waveform inversion (FWI) is a promising method to provide subsurface material properties and has been extensively studied, there are still needs to improve FWI particularly in case of multi-parameters. In this study, we propose a multi-parameter acoustic FWI strategy that can recover both velocity and density. The strategy is developed analyzing the characteristics of acoustic FWI based on a couple of parameterizations in acoustic wave equation for heterogeneous media. Our strategy consists of two stages. In the first stage, density is fixed at an arbitrary value, and velocity is only restored updating the bulk modulus based on the wave equation parameterized by bulk modulus and density. In this case, although the bulk modulus can be wrong, the inferred velocity can be reasonable. In the second stage, both velocity and density are inverted based on the wave equation parameterized by velocity and density. For the second stage, bulk modulus rather than velocity itself is updated, which is performed by using a chain rule to compute the gradient of bulk modulus. Our FWI uses the finite-element method and the back-propagation method. Numerical examples for synthetic data of the SEG/EAGE overthrust model show that our hierarchical strategy for acoustic FWI yields better results than the conventional method.

bulk, deep learning, density, density estimation, density model, Figure, formation evaluation, FWI, geophysics, inversion, inversion result, machine learning, method, model, neural network, Overthrust model, reservoir simulation, result, stage, strategy, velocity, velocity model, Waveform Inversion, well logging

SPE Disciplines: Reservoir Description and Dynamics > Reservoir Characterization > Seismic processing and interpretation (1.00)

Technology:

- IT > AI > Representation & Reasoning > Uncertainty (0.42)
- IT > AI > Representation & Reasoning > Mathematical & Statistical Methods (0.35)
- IT > AI > Machine Learning > Neural Networks (0.35)

For a robust elastic waveform inversion algorithm, we propose incorporating a denoise function into gradients in the

SPE Disciplines: Reservoir Description and Dynamics > Reservoir Characterization > Seismic processing and interpretation (1.00)

In this paper, we propose a new objective function that incorporates both simultaneous-source technique and robust norm in the frequency domain. The proposed objective function is defined to measure the residual of the super-shot consisting of encoded shot gathers. Although the objective function does not exactly simulate the ordinary

SPE Disciplines: Reservoir Description and Dynamics > Reservoir Characterization > Seismic processing and interpretation (1.00)

To make the

Since seismic modeling is conducted repeatedly in seismic inversion, efficiency and accuracy of inversion are affected by seismic modeling algorithm used in it. One of the main factors influencing accuracy of seismic modeling can be the boundary condition used to remove edge reflections arising from finite-size models. For elastic modeling and inversion algorithms free from edge reflections, we propose using the logarithmic grid set. In the logarithmic grid set, the origin is located in the middle of surface of a given model and grid interval increases logarithmically with distance from the origin. The logarithmic grid set enables us to incorporate huge boundary areas with fewer grid points than in the conventional grid set, so that edge reflections are not recorded within the recording duration. For elastic modeling and inversion in the logarithmic grid set, wave equations and source position are first transformed to the logarithm-scaled coordintate. To convert field data from the conventional grid set to the logarithmic grid set and transform inversion results from the logarithmic grid set to the conventional grid set, interpolation algorithms are needed. In the elastic modeling algorithm, the cell-based finite-difference method, which properly describes the free-surface boundary conditions, is used. For inversion process, we apply the gradient method based on the back-propagation method, the pseudo-Hessian matrix, and the conjugate-gradient method. We also employ the frequency-marching method. Numerical examples generated for the modified version of the Marmousi-2 model showed that the elastic modeling and inversion algorithms designed in the logarithmic grid set yield reasonable results.

algorithm, boundary, boundary condition, deep learning, equation, Figure, formation evaluation, geologic modeling, geophysics, grid, inversion, Inversion Algorithm, machine learning, method, neural network, recording duration, reflection, reservoir simulation, result, seismic modeling, Wave Equation, Waveform Inversion