To address the limitations of linear tsunami inversion, here, the Levenberg-Marquardt algorithm was applied to tsunami inversions, which allowed the use of nonlinear tsunami trace height data to estimate earthquake slip distributions. To the best of our knowledge, a completely nonlinear tsunami inversion has been used for the first time to investigate the source processes of historical earthquakes in which only tsunami trace heights are available. Using this inversion scheme and nonlinear long-wave equations, we estimated the slip distribution of the 1946 Showa-Nankai earthquake. The estimated slip distribution using only tsunami trace heights indicated a similar slip pattern to models previously proposed by linear tsunami inversions, although the amount of slip was substantially large. Another nonlinear inversion, which jointly used tsunami trace heights, tsunami waveforms, and crustal displacement data, imaged two slip asperities off Shikoku and the Kii Peninsula. The amount of slip in the asperities was still greater than that in the linear tsunami inversion analysis. However, it is still necessary to explain the tsunami trace heights. Our estimated earthquake magnitude was consistent with that obtained from the analysis of the seismic waveform inversion. The discrepancy in the estimated slip amount between the linear and nonlinear tsunami inversions may be related to uncertainties in the tsunami trace heights and/or tide gauge data.
