The Seismic Inverse Problem – active and now passive data for FWI.

The challenges in full wave form inversion (FWI) are many fold: non-linear objective functions, multiple local minima, awkward mathematics, bad starting velocity model guesses, extreme computational problems, and very large seismic data sets. The primary goal is to use a computer modeling system with all the right partial differentiable equations for the waves, including anisotropy and attenuation. Then simulate the earth with an initial starting velocity model. Once the simulation is complete, compare the computed seismic with the real data, and compute a meaningful error function. If the error is too high, find a method to update the velocity model and redo the simulation.

Recent changes in active and passive seismic recording systems allow for long time continuous recording. This passive data stream is now being recorded into the active data devices. So yet another input from the “Earth Computer” is now available. And the question to be asked is: how to process it?

The Laplace and Laplace Fourier methods for FWI have demonstrated for synthetic, and real seismic data sets a powerful results in final velocity models and depth migrations. To understand these FWI schemes the following results have been computed and will be presented. Using a 2D marine seismic line the FWI results for the smooth Laplace Domain, the Laplace Fourier, and Logarithmic Wave Form Inversion will be presented. These are then compared to the Frequency Domain Inversion method and each in sequence has a remarkable increase in quality. The final velocity model is used as input to the demonstrated RTM migration result.

In summary, FWI methods can be extended to include passive seismic activity if we can find ways to model that activity effectively. Using previous surface wave examples we extend the use of Rayleigh waves to actively help FWI find near surface shear velocities. The new methods are incorporated into the Laplace and Laplace Fourier FWI schemes.