Waveform inversion

2) Waveform inversion


No doubt that in the seismic arena this is the subject of the decade, as we still face many challenges in its application to real life. The high nonlinearity of the objective we seek to invert, the nonuniqeness of the model especially in the multi parameter, and the cost are among the biggest challenges as we seek to converge to a global solution for these problems. 
Thus, our objective in this matter:
  a. Maneuver the nonlinearity in a practical way: we are currently emphasizing a focus on the model, rather than the data in what we refer to as Full model wavenumber inversion (FMWI). The real source of nonlinearity is the gap between the low model wavenumber responsible for propagating the wavefield and the high ones responsible for the scattering. Of course, data and acquisition have a huge impact on the matter as we seek low frequencies and large offsets, but as academicians we have little control over that, and as a result our focus is filtering in the model domain. We also have utilized alternative objective functions that admit low wavenumber (Choi and Alkhalifah 2010, 2011, 2012, 2013, 2014; Alkhalifah and Choi 2012, 2013).
  b. Getting the low wavenumbers within FWI: We mix MVA and FWI naturally through a new objective function. Thus, a mix of MVA or RFWI with FWI in a more natural way can help improve the coverage of the model wavenumbers needed (Alkhalifah and Wu, 2013 2014; Wu and Alkhalifah 2013, 2014).
  c. Utilizing transmissions free of nonlinearity: Using unwrapped phase in a frequency domain implementation allows us to mitigate the nonlinearity associated with the classic cycle skipping. We focus on transmissions through Laplace damping the wavefield (Choi and Alkhalifah 2012, 2013; Alkhalifah and Choi, 2013).
  d. Efficiency: Simultaneous sources implementation is at the heart of improving the efficiency of FWI. We also try to effectively and optimally parallelize FWI using GPU implementations as well as CPU (Choi and Alkhalifah 2012, 2013; Wu and Alkhalifah, 2013, 2014).
  e. Better physics: Practical multi parameter and anisotropic inversion is at the heart of a successful real data application of FWI. A key issue here is developing the proper parameterization that could reduce the expected tradeoff between the parameters. As a result, we analyzed radiations patterns and sensitivity kernels for many multi parameter setups (Djebbi and Alkhalifah, 2013, 2014; Alkhalifah and Plessix, 2014).
  f. Getting the near surface right: The more stable transmission part of FWI with reasonable offsets has the potential in resolving the near surface better than tomography approaches. We utilize a combination of the unwrapped phase and Laplace damping as well as smart first arrival ambiguity resolution to invert for the near surface. Our implementations have shown credible results for real data (Choi and Alkhalifah 2012, 2013; Saragiotis, Keho, Choi, and Alkhalifah, 2012).