SEISMIC RANGE EQUATION

The seismic range equation is the seismic equivalent to the radar range equation. It unites the relevant factors in a marine data gathering system (source, subsurface, target, and receiving system) into a single formulation and provides a systematic approach to seismic data analysis, which we have used to improve seismic data processing for marine basins around the world. While most of the concepts contained in the seismic range equation are well known, this is the first time all have been put together, described in such detail, and used effectively (by way of modeling) to improve processing. A wavelet's amplitude spectrum can be calculated using the seismic range equation, and its phase spectrum can be calculated by considering the phase contributions from source to receiver. An amplitude-versus-offset (AVO) example supports our approach. Source array geometry and the outgoing waveforms from the array elements are required. The receiving system's load impedance and the hydrophone array's geometry, sensitivity, and impedance are also required. Subsurface factors and target strength can be determined by assuming a horizontally layered subsurface and ray theory. The required layer thicknesses, P-wave velocities, and densities can be generated by hand, statistically, or from well data. Well data are not required at the location of interest. The Zoeppritz equations furnish all P-wave reflection and transmission coefficients along a raypath. Seismic data at the location of interest can be used to estimate an attenuation constant (effective Q).