4) Anisotropy


Considering the historic focus our group had, anisotropy imaging and estimation are still important areas of our research. Though we as a community know how to image anisotropy and characterize it, we tend to have a feel for the parameters, yet we still struggle in estimating the anisotropy parameter in complex media. We have resorted to assumptions, additional information including wells to constrain the problem. 
Thus, our objectives in anisotropy can be summarized in the following:
  a. Efficient effective modeling and migration: The cost of TI and tilted orthorhombic extrapolation is about 4-5 times the isotropic. This additional cost makes imaging and later FWI an expensive task. We have developed and will continue to develop what we refer to as effective anisotropic models. These models result in accurate anisotropic wavefields kinematically, as well as amplitudes, using isotropic extrapolators. The effective models are built using high frequency asymptotic approaches (Alkhalifah, Ma, Waheed, and Zuberi, 2012; Waheed and Alkhalifah, 2013, 2014; Wang, Alkhalifah, and Waheed, 2014; Ibiz, Alkhalifah, and Waheed, 2014).
  b. High frequency asymptotic based methods: We are focused on developing efficient eikonal and ray tracing methods for high order anisotropies including orthorhombic anisotropy. Such eikonal solvers are 4-5 times more efficient than the conventional methods (Waheed and Alkhalifah, 2012, 2013, 2014; Ma and Alkhalifah, 2012).
  c. Parameter estimation: We develop approximate traveltime representations for complex backgrounds to help simplify the parameter estimation process. We have covered media from TI, to HTI, to Orthorhombic,  and tilted (Alkhalifah 2010, 2011a, 2011b; Stovas and Alkhalifah, 2012, 2013; Waheed, Alkhalifah and Stovas, 2013; Waheed and Alkhalifah, 2013; Masoudi and Alkhalifah, 2014).
  d. New models: From DTI to effective media, we have promoted simplifying anisotropy to the practical level (Alkhalifah and Sava, 2010, 2011; Wang and Alkhalifah 2014).
  e. Image gathers: They provide valuable information for parameter estimation and AVO, and thus, their accurate representation is necessary. We have tackled this problem from many angles (and angle gathers) including with wavefield (Alkhalifah and Fomel, 2010) and the extended imaging condition (Sava and Alkhalifah, 2012, 2013).