Two-grid genetic algorithm full-waveform inversion

Abstract

Full-waveform inversion (FWI) tries to estimate velocity models of the subsurface with improved accuracy and resolution compared to conventional methods. To be successful, it needs input data that is rich in low frequencies and possibly characterized by long source-to-receiver offsets. The correct solution of the inverse problem by means of local methods is facilitated if the starting model lies in the “valley” of the cost-function global minimum. We explore the possibility of relaxing this requirement by using genetic algorithms, a stochastic optimization method, as the driver of the FWI (GA FWI). However, stochastic methods are affected by the “curse of dimensionality,” meaning that they require huge and sometimes even unaffordable computer resources for inverse problems with many unknowns and costly forward modeling. Therefore, we need to adopt proper stratagems in the inversion and limit our goal to the estimation of a velocity macromodel that is of a model with only the long-wavelength velocity structures, which could eventually act as the starting model for a local, higher-resolution gradient-based inversion. To this end, in the GA FWI we parametrize the subsurface with two grids: (1) a coarse grid with widely spaced nodes, that is unknowns, for the inversion, and (2) a fine grid with shorter spacing for the modeling. As a side result, we can also have an estimate of the uncertainty at the solution nodes of the grid. The approach we discuss is 2D acoustic in the time domain, with finite difference forward modeling. The examples we show refer to the Marmousi model and to a marine field data set

A new hybrid optimization approach using PSO, Nelder-Mead Simplex and Kmeans clustering algorithms for 1D Full Waveform Inversion

“…Reducing the number of parameters (unknowns) consequently reduces the computational cost and enables the application of the most diverse algorithms. The main strategy used in 2D problems is know as two grids [ 20 ], where there is an inversion grid (coarse) and a modeling grid (fine). The first grid is where the parameters are optimized, that is, these are the parameters that the inversion process changes in the search for a solution and has a low sampling rate (few parameters).…”

A Global-Local Experience of 2D Acoustic FWI on a Real Data Set

“…The initial model used in this work is obtained by a global optimization procedure that uses the genetic algorithms on a coarse inversion grid (Tognarelli et al 2015) (Mazzotti et al 2017). The coarse grid 80th EAGE Conference & Exhibition 2018 11-14 June 2018, Copenhagen, Denmark consists of 4840 nodes, organized in 40 rows.…”

“…The GA parameters are set as follow: 4800 individuals, a selection rate of 0.42 (to limit the computational time for each generation) and a mutation rate of 0.1%. The search range for GA is 800 m/s centred on the 1D velocity model obtained as a horizontal mean of the model computed in Mazzotti et al 2017. Figure 2a shows the best GA model after approximately 600 generations.…”

Using orthogonal Legendre polynomials to parameterize global geophysical optimizations: Applications to seismic‐petrophysical inversion and 1D elastic full‐waveform inversion

“…The fine grid can be derived from the coarse grid by means of a simple bilinear interpolation (Mazzotti et al . ; Sajeva et al . ) or by means of more sophisticated sparse model reparameterizations combined with spline interpolation (Datta and Sen ).…”