This paper describes computational analysis of the problem of estimating physical parameters of an object, buried in the seafloor, by acoustic probing. A ROV-mounted directive acoustic source sends a train of pulses at the object and the reflected echoes are registered by a separately located vertical receiver array. The fitness function then estimates the misfit between the experimentally observed and model-predicted time-series. Only model computations have been performed i.e. no experimental data have been used. Seven parameters describing the range, depth, roll, yaw, pitch, density and the sound speed of a box-shaped scatterer have been studied. The nonlinear global optimization problem has been solved with the Differential Evolution algorithm, DE. The local behaviour of the object function has been studied by evaluations of the second derivative at the global minimum. The Neighbourhood Algorithm Bayes, NAB, has been used to estimate the probability density function of the ensemble of parameter vectors.