Hybrid full-wave inversion based on a B-spline level set mesh deformation method of borehole seismic data for a subsalt imaging context

Oil and gas industry is particularly interested in subsalt imaging because salt bodies often serve as seals for hydrocarbon reservoirs especially on the flanks and underneath the salt body. Classical imaging or full-wave inversion have encountered many difficulties in imaging such subsalt regions. The high velocity contrast between the salt body and its surroundings, the shape of the salt body, and the strong attenuation of waves propagating in the salt make accurate imaging difficult.

Imaging from surface seismic data has already been addressed. We propose to apply the full-wave inversion approach to borehole seismic data.  These data are supposed to provide more informative seismic signals (one-way, transmitted waves, scattered field near receivers, …) and should better constrain the salt flanks and bottom imaging. Unfortunately, this inverse problem is severely ill-posed due to the lack of data redundancy.  Introducing geological prior information through the parameterization of the salt geometry using the level set method partly overcomes this problem. This approach implicitly defines the salt/sediments interface through a smooth function. This hybrid  full-wave inverse problem combines the classical field gradient and the level set geometric gradient, allowing us to retrieve respectively the physical parameters and the salt body geometry.

The forward wave equation for a heterogeneous elastic domain is solved using the spectral element method. This method allows us to have a better representation of the salt/sediments interface, thus a more accurate modeling of the scattered wavefield due to interactions at the interface. Regarding the level set inversion, we define the implicit function in a parametric framework. We use compactly supported B-spline basis functions for their ability to represent a wide range of geometries compared to radial basis functions, for instance.

During the level set inversion process, when the salt/sediments interface evolves, updating the physical model parameters near the interface becomes an issue. We propose to perform a continuous deformation of the medium while conserving the mesh topology. The interface nodes are moved consistently with the implicit level set function. Furthermore, this approach  preserves a meshed representation of the interface through the inversion process allowing a more accurate seismic modeling. The mesh deformation is obtained by geostatistical kriging of node locations, constrained by the updated interface position.

In short, we propose a hybrid full-wave inversion method to estimate both material parameter fields and geometric parameters of the salt/sediments interface. The method is validated on several elastic models using synthetic seismic well data in a subsalt imaging context.