Physical Wavelet Defined On an Observation Plane And the Dreamlet

Wavefield or seismic data are special data sets. They cannot fill the 4-D space-time in arbitrary ways. The time-space distributions must observe causality which is dictated by the wave equation. Wave solutions can only exist on the light cone in the 4D Fourier space. Physical wavelet is a localized wave solution by extending the light cone into complex causal tube. In this study we establish the link between the physical wavelet defined by Kaiser using AST (analytic signal transform) and the dreamlet (drumbeat-beamlet). We prove that dreamlet can be considered as a type of physical wavelet defined on an observation plane (earth surface or a plane at depth z during extrapolation). Causality (or dispersion relation) built into the wavelet (dreamlet) and propagator is a distinctive feature of physical wavelet which is advantageous for applications in wavefield decomposition, propagation and imaging. One example of dreamlet decomposition on seismic data is given.