Layer | Fill | Outline |
---|
Map layers
Theme | Visible | Selectable | Appearance | Zoom Range (now: 0) |
---|
Fill | Stroke |
---|---|
Collaborating Authors
Results
ABSTRACT We present a method, in realistic-size full-waveform inversion (FWI), to explicitly construct a projected Hessian matrix and its inverse matrix, which we subsequently used to solve FWI with a quasi-Newton method. Newtonโs method is practically unfeasible in solving realistic-size FWI problems because of the prohibitive cost (computing time and memory consumption) of calculating the Hessian matrix and the inverse Hessian. Therefore, the Gauss-Newton method and various quasi-Newton methods are proposed to approximate a Hessian matrix. Particularly, current quasi-Newton FWI (QNFWI) commonly uses the limited-memory BFGS (L-BFGS) method, which, however, only implicitly approximates an inverse Hessian. We repose FWI as a sparse optimization problem in a sparse model space, which contains substantially fewer model parameters that are constrained by structures of the model. With respect to fewer parameters in the sparse model, we can avoid the โlimited-memoryโ approximation and are able to explicitly compute and store a projected Hessian matrix that saves the computational time and required memory. We constructed such a projected Hessian matrix by adapting the classic BFGS method to a projected BFGS (P-BFGS) method in the sparse space. Using the projected Hessian matrix and its inverse, we can apply the P-BFGS method to solve FWI with a quasi-Newton method. In QNFWI with P-BFGS because we invert for a sparse model with much fewer parameters, the memory required to compute the projected Hessian is negligible compared to either forward modeling or gradient calculation. QNFWI with P-BFGS converges in fewer iterations than conjugate-gradient based methods and QNFWI with L-BFGS.
ABSTRACT Multiple problems, including high computational cost, spurious local minima, and solutions with no geologic sense, have prevented widespread application of full waveform inversion (FWI), especially FWI of seismic reflections. These problems are fundamentally related to a large number of model parameters and to the absence of low frequencies in recorded seismograms. Instead of inverting for all the parameters in a dense model, image-guided full waveform inversion inverts for a sparse model space that contains far fewer parameters. We represent a model with a sparse set of values, and from these values, we use image-guided interpolation (IGI) and its adjoint operator to compute finely and uniformly sampled models that can fit recorded data in FWI. Because of this sparse representation, image-guided FWI updates more blocky models, and this blockiness in the model space mitigates the absence of low frequencies in recorded data. Moreover, IGI honors imaged structures, so image-guided FWI built in this way yields models that are geologically sensible.
- Geophysics > Seismic Surveying > Seismic Processing (1.00)
- Geophysics > Seismic Surveying > Seismic Modeling > Velocity Modeling > Seismic Inversion (1.00)
Increasing the resolution of semblance-based velocity spectra, or semblance spectra, is useful for estimating normal moveout velocities, as increased resolution can help to distinguish peaks in the spectra. The resolution of semblance spectra depends on the sensitivity of semblance to changes in velocity. By weighting terms in the semblance calculation that are more sensitive to changes in velocity, we can increase resolution. Our implementation of weighted semblance is a straightforward extension of conventional semblance. Somewhat surprisingly, we increase resolution by choosing an offset-dependent weighting function that minimizes semblance. We test our method on synthetic and field data, and our tests confirm that weighted semblance provides higher resolution than conventional semblance.
- Geophysics > Seismic Surveying > Seismic Processing (1.00)
- Geophysics > Seismic Surveying > Seismic Modeling > Velocity Modeling (1.00)