GNGTS 2017 - 36° Convegno Nazionale

GNGTS 2017 S essione 3.3 687 Layer nr. Medium Thickness [m] Resistivity [Ohm.m] 0 Air Half space Infinite 1 Sea 1000 0.33 2 Sediments 100 → m1 1 3 Resistive anomaly 100 → m2 30 → m3 4 Sediments Half space 1 multidimensional domain. In practice the first “high temperature” phase permits to place the current point within the global minimum region. Then, in a second phase, when the temperature decreases, the point remains trapped in the optimal region and converges (usually slowly) to the global solution. SA is classified as a global inversion technique: on the other hand its main drawbacks are the high computational cost and the lack of a direct accuracy index of the solution. Hybrid inversion method. The consecutive execution of Bayesian and global inversions steps can be exploited to reach the minimum residual in a shorter time with respect to a global inversion run. Moreover, when performing a Bayesian step, it becomes available also the uncertainty of the current solution. The actual strategy of switching between the two methods is here derived experimentally, on a synthetic example. We present also some analysis tools that permit a fast visual inspection of the inversion evolution, and of the solution accuracy. Examples and analysis tools. The tutorial example is a 1D resistivity layered model, described in Tab. 1. The values indicated with m 1 , m 2 and m 3 are the inversion parameters. The starting model is m 1 = 70 m, m 2 =80 m, and m 3 =2 Ohm.m. We plot the model distance versus residual (Bosisio et al. , 2014) to inspect the behavior of the convergence: in practice, we define a reference point in the model space (reference model) and, for every set of parameters (candidate model) used to compute a new residual, we add a dot to the panel at the Euclidean distance of the candidate from the reference point and the residual (left side of Figs. 2 and 3). The total number of forward model computations for candidate points is around 6000 when following the Corana SA procedure, and around 150 with the Bayesian approach, including the numerical computation of the derivatives and the execution of a line search procedure at each iteration in order to optimize the step size λ in Eq. (2) (Vandone et al. , 2014). Fig. 3 right shows the candidate points for the SA in the model space, colored with the residual: the area with minimum residual (dark blue) is elongated along the m 1 direction, so that there could be local minima trapping the BLI evolution. On the other side, BLI provides a conditioning analysis of the Jacobian matrix at the final step of the inversion, and the accuracy Fig. 2 - Bayesian inversion evolution. Tab. 1 - 1D resistivity model.