Application of Probabilistic Calibration of Geostatistical Parameters in Seismic Travel Time Inversion-Paper

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The study presents a probabilistic method for seismic travel-time tomography to estimate subsurface P-wave velocities while quantifying uncertainty. Unlike deterministic inversion, which produces a single velocity model, the approach generates multiple plausible models by combining borehole measurements with seismic travel-time data.<br /><br />First, Bayesian Kriging estimates the velocity field’s mean and spatial covariance parameters from borehole logs. These estimates guide sequential Gaussian simulation, which generates geostatistically realistic prior models. An extended Metropolis sampler then updates the models using observed travel times, producing posterior velocity realizations. Their mean and standard deviation summarize the estimated field and its uncertainty.<br /><br />The method was tested on a synthetic offshore soil model with six boreholes and 625 source–receiver travel times. One borehole (BH3) was withheld for validation. Posterior models, informed by both borehole and seismic data, showed less variability than prior models based only on boreholes and better reproduced the known velocity pattern. At the withheld location, posterior predictions were closer to the original borehole log and had lower uncertainty.<br /><br />The results suggest that integrating geostatistical priors with travel-time observations can improve velocity estimates between boreholes and provide a practical way to assess uncertainty in offshore geotechnical site characterization.

Keywords

seismic travel-time tomography

P-wave velocity

Bayesian Kriging

sequential Gaussian simulation

Metropolis sampler

posterior velocity realizations

uncertainty quantification

borehole logs

offshore geotechnical site characterization

subsurface velocity model