Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userFull waveform inversion using triangular waveform adapted meshes
77
0
0.0
(
0
)
Added by
Keith Roberts
Publication date
2021
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
In this article, continuous Galerkin finite elements are applied to perform full waveform inversion (FWI) for seismic velocity model building. A time-domain FWI approach is detailed that uses meshes composed of variably sized triangular elements to discretize the domain. To resolve both the forward and adjoint-state equations, and to calculate a mesh-independent gradient associated with the FWI process, a fully-explicit, variable higher-order (up to degree $k=5$ in $2$D and $k=3$ in 3D) mass lumping method is used. By adapting the triangular elements to the expected peak source frequency and properties of the wavefield (e.g., local P-wavespeed) and by leveraging higher-order basis functions, the number of degrees-of-freedom necessary to discretize the domain can be reduced. Results from wave simulations and FWIs in both $2$D and 3D highlight our developments and demonstrate the benefits and challenges with using triangular meshes adapted to the material proprieties. Software developments are implemented an open source code built on top of Firedrake, a high-level Python package for the automated solution of partial differential equations using the finite element method.
rate research
Read More
The Hessian matrix plays an important role in correct interpretation of the multiple scattered wave fields inside the FWI frame work. Due to the high computational costs, the computation of the Hessian matrix is not feasible. Consequently, FWI produces overburden related artifacts inside the target zone model, due to the lack of the exact Hessian matrix. We have shown here that Marchenko-based target-oriented Full Waveform Inversion can compensate the need of Hessian matrix inversion by reducing the non-linearity due to overburden effects. This is achieved by exploiting Marchenko-based target replacement to remove the overburden response and its interactions with the target zone from residuals and inserting the response of the updated target zone into the response of the entire medium. We have also shown that this method is more robust with respect to prior information than the standard gradient FWI. Similarly to standard Marchenko imaging, the proposed method only requires knowledge of the direct arrival time from a focusing point to the surface and the reflection response of the medium.
Seismic full-waveform inversion (FWI) techniques aim to find a high-resolution subsurface geophysical model provided with waveform data. Some recent effort in data-driven FWI has shown some encouraging results in obtaining 2D velocity maps. However, due to high computational complexity and large memory consumption, the reconstruction of 3D high-resolution velocity maps via deep networks is still a great challenge. In this paper, we present InversionNet3D, an efficient and scalable encoder-decoder network for 3D FWI. The proposed method employs group convolution in the encoder to establish an effective hierarchy for learning information from multiple sources while cutting down unnecessary parameters and operations at the same time. The introduction of invertible layers further reduces the memory consumption of intermediate features during training and thus enables the development of deeper networks with more layers and higher capacity as required by different application scenarios. Experiments on the 3D Kimberlina dataset demonstrate that InversionNet3D achieves state-of-the-art reconstruction performance with lower computational cost and lower memory footprint compared to the baseline.
We describe a novel framework for estimating subsurface properties, such as rock permeability and porosity, from time-lapse observed seismic data by coupling full-waveform inversion, subsurface flow processes, and rock physics models. For the inverse modeling, we handle the back-propagation of gradients by an intrusive automatic differentiation strategy that offers three levels of user control: (1) at the wave physics level, we adopted the discrete adjoint method in order to use our existing high-performance FWI code; (2) at the rock physics level, we used built-in operators from the $texttt{TensorFlow}$ backend; (3) at the flow physics level, we implemented customized PDE operators for the potential and nonlinear saturation equations. These three levels of gradient computation strike a good balance between computational efficiency and programming efficiency, and when chained together, constitute a coupled inverse system. We use numerical experiments to demonstrate that (1) the three-level coupled inverse problem is superior in terms of accuracy to a traditional decoupled inversion strategy; (2) it is able to simultaneously invert for parameters in empirical relationships such as the rock physics models; and (3) the inverted model can be used for reservoir performance prediction and reservoir management/optimization purposes.
Full waveform inversion (FWI) delivers high-resolution images of the subsurface by minimizing iteratively the misfit between the recorded and calculated seismic data. It has been attacked successfully with the Gauss-Newton method and sparsity promoting regularization based on fixed multiscale transforms that permit significant subsampling of the seismic data when the model perturbation at each FWI data-fitting iteration can be represented with sparse coefficients. Rather than using analytical transforms with predefined dictionaries to achieve sparse representation, we introduce an adaptive transform called the Sparse Orthonormal Transform (SOT) whose dictionary is learned from many small training patches taken from the model perturbations in previous iterations. The patch-based dictionary is constrained to be orthonormal and trained with an online approach to provide the best sparse representation of the complex features and variations of the entire model perturbation. The complexity of the training method is proportional to the cube of the number of samples in one small patch. By incorporating both compressive subsampling and the adaptive SOT-based representation into the Gauss-Newton least-squares problem for each FWI iteration, the model perturbation can be recovered after an l1-norm sparsity constraint is applied on the SOT coefficients. Numerical experiments on synthetic models demonstrate that the SOT-based sparsity promoting regularization can provide robust FWI results with reduced computation.
Seismic full-waveform inversion (FWI), which uses iterative methods to estimate high-resolution subsurface models from seismograms, is a powerful imaging technique in exploration geophysics. In recent years, the computational cost of FWI has grown exponentially due to the increasing size and resolution of seismic data. Moreover, it is a non-convex problem and can encounter local minima due to the limited accuracy of the initial velocity models or the absence of low frequencies in the measurements. To overcome these computational issues, we develop a multiscale data-driven FWI method based on fully convolutional networks (FCN). In preparing the training data, we first develop a real-time style transform method to create a large set of synthetic subsurface velocity models from natural images. We then develop two convolutional neural networks with encoder-decoder structure to reconstruct the low- and high-frequency components of the subsurface velocity models, separately. To validate the performance of our data-driven inversion method and the effectiveness of the synthesized training set, we compare it with conventional physics-based waveform inversion approaches using both synthetic and field data. These numerical results demonstrate that, once our model is fully trained, it can significantly reduce the computation time, and yield more accurate subsurface velocity models in comparison with conventional FWI.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
