Flux-normalized elastodynamic wavefield decomposition using only particle velocity recordings

Abstract

We present a new approach to apply wavefield decomposition, illustrated for an energy flux-normalized elastodynamic case. We start by considering a situation where two horizontal boreholes are closely separated from each other. By recording only the particle velocities at both depth levels (for example with conventional 3-component geophones) and expressing the one-way wavefields at one depth level in terms of the fields at the other depth level, an inverse problem can be formulated and solved. This new approach of multi-depth level(MDL) wavefield decomposition is illustrated with a synthetic 2D finite difference example, showing correct one-way wavefield retrieval. We then modify the methodology for a special case with a single receiver array just below a free surface, where the problem is naturally constrained by the (Dirichlet) boundary condition at the free-surface. Again, it is shown that correct elastodynamic wavefield decomposition takes place, for both P- and S-waves.