Seafloor topography inversion using least square collocation considering nonlinear term

The linear term of seafloor topography and satellite altimetry gravity data draws much attention and non-linear term tends to be ignored in current seafloor topography inversion. We proposed to use least square collocation (LSC) to estimate the linear term and non-linear term of seafloor topography and gravity data. A certain area in the sea of Japan was selected as the target sea area and corresponding bathymetry models were constructed by vertical gravity gradient anomaly (VGG) and gravity anomaly (GA) as the input data based on LSC. The accuracy of the inversion models was evaluated using shipboard sounding data as external checking points, and the spectral characteristics of the inversion models were analyzed. The results in the study area showed that the accuracy of the inversion models derived by the same GA and VGG based on LSC was improved by 2.5 times and 3.5 times at least, the relative accuracy was improved by 9.76% and 13.07%, compared with the least-square bathymetry models which only consider the linear term of seafloor topography and gravity data in the paper, which indicated that LSC greatly improved the quality of bathymetry inversion. The correlation coefficients between the inversion models and some other models, i. e. S&S V18.1, ETOPO1, GEBCO and BAT_VGG, were all above 0.95, which verifies the validity of the method (LSC) in the study area. The accuracy of the models by LSC was similar to S&S V18.1 and much higher than ETOPO1 and other bathymetry models in the study area. The inversion models could improve the relevant band information of ship measuring data effectively. The bathymetry models derived by VGG improved the relevant band information of shipboard sounding data more obviously than the bathymetry models by GA (the range of inversion waveband was 15 km to 160 km). In summary, the results in the study area verified the LSC’s feasibility and effectiveness.