• near surface
• high resolution
• global optimization
• actual data
• Rayleigh wave
• robust inversion

We propose a new method, two-grid full waveform inversion (FWI) of Rayleigh waves, for the prediction of 2-D shear wave velocity (Vs) models, which employs a genetic algorithm as the optimization tool and a finite difference code as the forward modeling engine. To limit the computing time required by the genetic algorithm, in the implementation of the FWI we make use of a two-grid parameterization of the subsurface model, one fine grid and one coarse grid. Forward modeling is performed on the fine grid to avoid numerical dispersion, while the genetic algorithm inverts for the unknown velocities and density at the nodes of the coarse grid. The coarser the grid, the less the unknowns to be inverted for, at the expense of the final model resolution. In general, we look for obtaining Vs models that contain the long-wavelength features of the velocity structures. A frequency marching strategy is included in the inversion to accelerate the convergence. The use of a genetic algorithm, which is a global optimization method, allows us to relax the requirement of local optimization methods of having a “good” starting model from which to launch the inversion. We show that fair results can be retrieved even in the case of null a-priori information.
Before illustrating the two-grid genetic algorithm FWI method, some of the complexities of the surface wave modeling are shown. The modeling is realized by a 2-D elastic finite difference modeling code. The efficient attenuation of wave energy at absorbing boundaries, the influence of topography and the effect of the 3-D to 2-D correction of seismic data are discussed. Furthermore, the reliability of the modeling code is confirmed by the good matches between its results and those produced by other finite difference, reflectivity and spectral element modeling codes.
Next, several synthetic data inversion examples are given. By applying our method, we are able to fairly predict complex near-surface Vs models, such as those containing sharp velocity contrasts, velocity inversions, lateral velocity variations and an irregular topographic surface. We invert for all Vs, compressional wave velocities (Vp) and density.
Then, we show that the velocity models obtained via our stochastic approach are adequate initial models for FWI with a local optimization method for further refinement. The local optimization FWI we use is the one developed by the TOAST (Toolbox for applied seismic tomography) project team and made available as an open-source code. Increases of the fine details of the velocity models are derived.
After that, some further synthetic tests are presented to evidence the impacts that several forward modeling approximations and assumptions have on FWI. In particular, we discuss issues such as the limited number of points per wavelength employed in the modeling, the use of elastic instead of visco-elastic modeling, the 2-D instead of 3-D wave propagation and whether Vp and density can be excluded from the inversion because of their limited influence on surface waves compared with Vs. We find that the consequence of the various assumptions is, quite obviously, the deterioration of the genetic algorithm FWI result. Still, in the test cases we examined, the data misfits are always satisfactory and the main structural features of the subsurface models are somewhat predicted, even in the case of null a-priori information.
Our two-grid genetic algorithm FWI code is parallelized by using Open MPI – C++ and each synthetic data test mentioned above requires about one hour of computation time on a distributed system with 545 threads.
The major project is concluded with the application of our inversion method to two field data sets.
One field data set was acquired in Grenoble, France in September 2013, in the framework of the InterPACIFIC project, with 48 vertical-component geophones, spaced 1 m in the in-line direction, and with an 8-kg sledgehammer as the energy source. Three shot gathers, one split-spread and two off-ends, are used in the inversion. Though no a-priori information is used, the inversion fairly predicts most parts of the observed data and nearly all the mismatches between predicted and observed traces are within half-periods. By calculating the mean of the predicted 2-D model, a pseudo 1-D model is obtained and then compared with nearby borehole data. Though the small features are difficult to be found due to our two-grid strategy, the pseudo 1-D model fairly matches the main features shown by the borehole data.
The other field data set was acquired in Luni, Italy in March 2017, with 36 vertical-component geophones, spaced 1 m in the in-line direction, and with a seismic gun as the energy source. Again, three shot gathers, one split-spread and two off-ends, are used in the inversion. In this case, the Rayleigh waves are strongly dispersed and thus, to strengthen the inversion, we make use of both the envelopes and the waveforms of the traces in the data misfit computation. With no a-priori information used, the inversion nicely predicts the surface wave data corresponding to the fundamental mode and partly predicts the data likely related to the 1st higher mode. The predicted model can be roughly considered as a two-layer model, slightly dipping, with a general velocity increase and with a small velocity inversion between 1 m and 2 m depth.
Finally, as it is customary for our Doctorate, the Appendixes report the results and the conclusions of the minor project, which includes the computation of high-resolution dispersion spectra and receiver deghosting of marine seismic data by using a frequency domain sparse Radon transform code we developed.