Simultaneous inversion of velocity and reflectivity

We introduce an inversion approach to simultaneously invert for both velocity and reflectivity. The core of the inversion workflow is a novel wave-equation that provides the full acoustic wavefield, which is parameterized in terms of velocity and vector reflectivity. A key aspect is the separation of the low- and high-wavenumber components of the gradient based on inverse scattering theory, enabling the sensitivity kernels to update the velocity and the vector reflectivity, respectively. The estimation problem is essentially a multi-parameter inversion where the crosstalk trade-offs between the two parameters are minimized with scale separation. Our adjoint state-based inversion is equivalent to performing Full Waveform Inversion (FWI) and Least-Squares Reverse Time Migration (LS-RTM) using the full acoustic wavefield within the same framework. The final inverted reflectivity is an accurate estimate of the true earth reflectivity, compensated for acquisition and poor illumination effects, and with reduced image crosstalk from multiples. The new approach reduces the turnaround time of imaging projects by combining velocity model building (FWI) and imaging (LS-RTM) into a single inversion process with minimum data preprocessing from an inaccurate initial model. We demonstrate the benefits of our scheme using synthetic and field data examples.