Defense in Geophysics
Student: Pedro Bautista Canas
Program: Geophysics
Title: "Vs Profile Estimation in Seismic Downhole Tests using Levenberg-Marquardt Inversion"
Advisor: Prof. Dr. George Sand Leão Araújo de França
Judging Committee:
- Prof. Dr. George Sand Leão Araújo de França - Presidente e Orientador - IAG/USP
- Prof. Dr. Giuliano Sant'Anna Marotta - UnB
- Prof. Dr. Dionísio Uendro Carlos – UNESP
Other Members:
- Prof. Dr. Carlos Alberto Mendonça - IAG/USP
- Prof. Dr. Walter Eugênio de Medeiros - UFRN
- Prof. Dr. Emilson Pereira Leite - UNICAMP
- Prof. Dr. Carlos Alberto Moreno Chaves - IAG/USP
Abstract:
This study presents a novel non-linear inversion method for estimating shear wave velocity profiles (Vs) from Downhole seismic tests. Unlike conventional sequential interpretation methods, which accumulate errors with depth and are highly sensitive to arrival-time uncertainties, the proposed approach simultaneously estimates layer velocities and seismic ray geometry using the Levenberg-Marquardt algorithm, considering Snell's Law in the forward problem. The inversion framework incorporates first-order Tikhonov regularisation to attenuate instabilities in the velocity profile, alongside a weighting scheme based on observational uncertainty. Based on maximum likelihood principles, this scheme prioritises the fitting of data with lower uncertainty and compensates for the order of magnitude of the observed data. Combined with Jacobi preconditioning, this approach ensures greater numerical stability and computational efficiency. The method was validated using noise-free synthetic models, datasets with random noise, and numerical wave propagation simulations representing more realistic geological conditions. In all cases, the approach consistently recovered the main velocity contrasts and ray geometry, maintaining low relative errors even in the presence of noise and stratigraphic interfaces that do not coincide with the receiver positions. Compared to traditional methods, such as the Interval Method (IM), Modified Interval Method (MIM), and Refracted Ray Method (RRM), the proposed methodology demonstrated greater robustness, stability, and physical consistency, constituting a reliable alternative for interpreting Downhole seismic tests and for geotechnical subsoil characterisation.
Keywords: Seismic downhole test, Non-linear inversion, Levenberg–Marquardt, Shear wave velocity, Geotechnical site characterisation