March 2023

I present a method for computing reflection angle gathers using time-shift extended least-squares reverse-time migration. The method is aimed at producing image gathers that can be interpreted in terms of angle-dependent reflection coefficients, also under complex overburdens. It is based on a two-step procedure involving an iterative inversion to estimate a time-shift extended representation of the subsurface reflectivity, followed by a transform of this reflectivity to the reflection angle domain. Using a formulation in terms of time-shift extended imaging allows to naturally handle complex wave-field effects like multi-pathing. The main building blocks of the method include an adjoint pair of time-shift extended linearized modelling and imaging operators, an effective time-shift extended-domain preconditioner and a transform from the time-shift domain to the reflection angle domain that properly handles amplitudes. The method is demonstrated on a synthetic data example.

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