We have developed a stochastic full-waveform inversion that uses genetic algorithms (GA FWI) to estimate acoustic macro models of the P-wave velocity field. Stochastic methods such as GA severely suffer the curse of dimensionality, meaning that they require unaffordable computer resources for inverse problems with many unknowns and expensive forward modeling. To mitigate this issue, we have proposed a two-grid technique with a coarse grid to represent the subsurface for the GA inversion and a finer grid for the forward modeling. We have applied this procedure to invert synthetic acoustic data of the Marmousi model, and we have developed three different tests. The first two tests use a velocity model derived from standard stacking velocity analysis as prior information and differ only for the parameterization of the coarse grid. Their comparison indicates that a smart parameterization of the coarse grid may significantly improve the final result. The third test uses a linearly increasing 1D velocity model as prior information, a layer-stripping procedure, and a large number of model evaluations. All three tests return velocity models that fairly reproduce the long-wavelength structures of the Marmousi. First-break cycle skipping related to the seismograms of the final GA-FWI models is significantly reduced compared with that computed on the models used as prior information. Descent-based FWIs starting from final GA-FWI models yield velocity models with low and comparable model misfits and with an improved reconstruction of the structural details. The quality of the models obtained by GA FWI plus descent-based FWI is benchmarked against the models obtained by descent-based FWI started from a smoothed version of the Marmousi and started directly from the prior information models. Our results are promising and demonstrate the ability of the two-grid GA FWI to yield velocity models suitable as input to descent-based FWI.

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.

We have compared the performances of six recently developed global optimization algorithms: imperialist competitive algorithm, firefly algorithm (FA), water cycle algorithm (WCA), whale optimization algorithm (WOA), fireworks algorithm (FWA), and quantum particle swarm optimization (QPSO). These methods have been introduced in the past few years and have found very limited or no applications to geophysical exploration problems thus far. We benchmark the algorithms’ results against the particle swarm optimization (PSO), which is a popular and well-established global search method. In particular, we are interested in assessing the exploration and exploitation capabilities of each method as the dimension of the model space increases. First, we test the different algorithms on two multiminima and two convex analytic objective functions. Then, we compare them using the residual statics corrections and 1D elastic full-waveform inversion, which are highly nonlinear geophysical optimization problems. Our results demonstrate that FA, FWA, and WOA are characterized by optimal exploration capabilities because they outperform the other approaches in the case of optimization problems with multiminima objective functions. Differently, QPSO and PSO have good exploitation capabilities because they easily solve ill-conditioned optimizations characterized by a nearly flat valley in the objective function. QPSO, PSO, and WCA offer a good compromise between exploitation and exploration.

Determining the pressure dependence of dynamic moduli in unconsolidated sediments is still an open problem in applied geophysics. This is because several petrophysical parameters affect the elastic response of the granular medium during compression. Effective medium theories based on the Hertz–Mindlin contact law estimate the effective moduli from petrophysical parameters. Among them, the Pride and Berryman model assumes that new contacts between grains are progressively created during compression. Furthermore, the gaps around rattlers are distributed following a power law with distance and the global strain can change either linearly or quadratically with the local strain. This identifies two types of strain accumulation. Quadratic strain accumulation is associated with grain rotation. We simplified this model by assuming a flat distribution of gaps around rattlers and we applied this simplified model to published ultrasonic measurements. By means of these measurements, we studied how the strain-accumulation mechanism affects the coordination number during isotropic compression. The coordination numbers were estimated by applying a DEM-based correction to the average-strain model. We observe that the majority of the experimental trends lay between the linear and the quadratic accumulation trends. Based on this result, we assume that the strain accumulation is a combination of the two mechanisms and we propose a formula to estimate the contribution of each mechanism. Furthermore, we note that, in the studied datasets, rotation affects larger grains (diameter approximately 500 μm) more than smaller grains (diameter approximately 100 μm). If further validated, this correlation could guide the determination of pressure trends for sands.