Fig. 6

a Travel-time residuals obtained by the MCMC-based static array positioning method are shown in time series. Top panel shows the projected travel-time residuals by the colored cross symbols and the black symbols are summation of the NTDs modeled as S-NTD and the equivalent deep gradients. Middle panel shows the projected travel-time residuals subtracting the equivalent deep gradients by the colored cross symbols. The black, red, and blue curves show S-NTD, L-NTD, and summation of L-NTD and the contributions of the shallow gradients. Bottom panel shows the final travel-time residuals subtracting NTDs. b Projected travel-time residuals subtracting L-NTD are shown on the sea-surface platform track