Wavefield imaging using the energy norm

Abstract

For various wavefield types, one can formulate a measurement of the mechanical energy that satisfies conservation laws. Based on this formulation, one can derive an{\it energy norm} that is applicable to wavefield imaging. Extending the concept of the norm to an inner product, one can compare two related wavefields. Therefore, an imaging condition can be defined as the inner product between the source and receiver wavefields at every spatial location. In this regard, the imaging condition based on the energy inner product accounts for wavefield directionality in space and time, overcoming some problems present in the conventional imaging condition. I exploit the wavefield directionality information from the energy imaging condition to attenuate unwanted events in reverse time migrated (RTM) images. For acoustic wavefields, these unwanted events are characterized by the collinearity of the source and receiver raypaths, and they are described as RTM backscattering artifacts. For elastic wavefields, these events are characterized by the fact that source and receiver displacement fields have the same polarization and wave propagation directions. In both acoustic and elastic cases, one can to attenuate these artifacts and produce high quality images. Another application that uses the wavefield directionality is to enhance the full waveform inversion (FWI) gradient for acoustic wavefields. By enhancing wave events that are collinear and suppressing all other wave events, I am able to compute gradients that are more suitable for the inversion process. Numerical experiments show the efficacy of these applications for synthetic models that emulate the complexity of subsurface structures found in exploration seismology, such as salt bodies, diffractors, dipping layers and faults.