Avoiding Cycle Skipping

Low frequencies in the field data are essential for robust and effective inversion without cycle skipping issues. GeoStreamer multisensor acquisition provides these crucial low frequencies from the deep tow of the streamer. 

Full Waveform Inversion (FWI) inverts for the velocities that explain the observed data. This process is highly non-linear and the inversion can easily lead to the wrong solution. To mitigate this, conventional inversions require rich low frequency data and an initial model close to the true model. This article shows that by using the ‘Wasserstein distance’ or ‘W2 norm’, the observed and modeled data are compared in a different and more robust way than conventional FWI. This relaxes the requirement to have an accurate initial model and to have low frequency recordings. It could enable faster computation of a velocity model with less geological input or a detailed starting model.

Long-wavelength FWI updates in the presence of cycle skipping, The Leading Edge March 2019. Jaime Ramos-Martínez , Lingyun Qiu , Alejandro A. Valenciano, Xiaoyan Jiang, and Nizar Chemingui

Cycle-Skipping and FWI

When performing FWI, a data residual is minimized to update the velocity model. The residual is the difference between the acquired data and a synthetic modeled data using the velocity model. Cycle-skipping can occur when the phase match between the two data sets is greater than half a wavelength, causing erroneous model updates, which, in turn can lead to incorrectly imaged seismic data. Cycle-skipping mitigation remains the primary challenge for FWI’s implementation in all velocity regimes. Traditional least-squares solutions are performed on the residual of the waveforms, and thus know nothing about the requirements for phase alignment. PGS are implementing a method that uses a minimization of the so-called ‘Wasserstein distance’, which is the distance required to map one statistical representation to another through the use of distribution functions. This method reduces the half-cycle requirement of traditional FWI schemes. Relaxing this criterion enables the starting model for FWI to be less accurate, and therefore could conceivably reduce turnaround by by-passing the need to prepare a starting model for FWI that meets the half-cycle criterion.

With this method, the model is less affected by cycle-skipping issues and therefore should create a more reliable image, in an accelerated timeframe.

New FWI Applied to Data from the Ceará Basin, Brazil

The performance of the new solution is demonstrated on a GeoStreamer survey acquired offshore Brazil and illustrates how FWI successfully updates the earth model and resolves a high velocity carbonate section missing from the initial velocity model.

The new FWI algorithm was applied to a GeoStreamer survey acquired in the Ceará Basin, offshore Fortaleza, Brazil. The starting (a) and final (b) FWI models are shown for a line in the proximity of a well. The final FWI model matches the well trend capturing the spatial variability of the carbonates.
The new FWI algorithm was applied to a GeoStreamer survey acquired in the Ceará Basin, offshore Fortaleza, Brazil. The starting (a) and final (b) FWI models are shown for a line in the proximity of a well. The final FWI model matches the well trend capturing the spatial variability of the carbonates.