On the interpretation of frequency response functions for oceanic gravity and bathymetry

Oceanic bathymetry and gravity comprise a geophysical system which is often characterized by a linear frequency response function or admittance. The actual behaviour of this system differs in important respects, however, from that of an ideal linear model. Three sources of such differences are considered in this study: the presence of noise in the data, non-linearity due to finite amplitude and intrinsic two-dimensionality of the data fields. The high positive correlation between admittance amplitude and coherence estimates obtained in a number of studies indicates that the noise is not normally distributed with zero mean, as generally assumed. Non-linear modification of the admittance results from the finite amplitude of the bathymetry and the non-linear elasticity of the lithosphere. The former effect increases with bathymetric roughness and is most pronounced for short-wavelength, uncompensated bathymetry; the latter is significant only if the deflection of the lithosphere is comparable to its elastic thickness, as for certain large seamounts in the Pacific Ocean which were emplaced on lithosphere near ridge crests. The most severe problem arises for features which are markedly two-dimensional. Features typical of observed oceanic seamounts are characterized by admittances along tracks which differ substantially from those appropriate to one-dimensional bathymetry. This difference occurs primarily in the long-wavelength portion of the admittance, rendering problematic the comparison of observed admittances (or gravity anomalies) with theoretical expressions.