The “direct wave root” is an evanescent wave which is observed below the sea floor when the direct water wave is incident on the sea floor from above at supercritical angles. For shallow borehole receivers, it is the largest amplitude arrival on large offset seismograms. The wave has been studied and observed in electromagnetics and acoustics but this paper is the first report of the “direct wave root” in marine seismology.
Theoretically, an expression for the “direct wave root” can be obtained from a branch line integral in the complex ray parameter plane for the transmission problem between two acoustic half-spaces. Synthetic seismogram analysis based on the discrete wavenumber (or reflectivity) method can be applied to study the more realistic cases of elastic bottoms, gradients beneath the sea floor, and intrinsic attenuation. Steep gradients below the sea floor give amplitude-depth relations which are not exponential. Attenuation (Q = 40) affects amplitudes less than 1 dB.
Observations of the “direct wave root” have been made at the Deep Sea Drilling Project Site 504B in the Costa Rica Rift area and the observed properties are consistent with theory. It is proposed that more detailed measurements of the decay of the “direct wave root” amplitude with depth be used to obtain high resolution measurements of upper crustal elastic properties at seismic frequencies.