GNGTS 2018 - 37° Convegno Nazionale

716 GNGTS 2018 S essione 3.3 References Bodin, T., and Sambridge, M. (2009). Seismic tomography with the reversible jump algorithm. Geophysical Journal International, 178(3), 1411-1436 . Bodin, T., Sambridge, M., Tkalčić, H., Arroucau, P., Gallagher, K., and Rawlinson, N. (2012). Transdimensional inversion of receiver functions and surface wave dispersion. Journal of Geophysical Research: Solid Earth, 117(B2). Dadi, S., Gibson, R., and Wang, K. (2016). Velocity log upscaling based on reversible jump Markov chain Monte Carlo simulated annealingRJMCMC-based sonic log upscaling. Geophysics, 81(5), R293-R305. Mandolesi, E., Ogaya, X., Campanyà, J., and Agostinetti, N. P. (2018). A reversible-jump Markov chain Monte Carlo algorithm for 1D inversion of magnetotelluric data. Computers & Geosciences, 113, 94-105. Malinverno, A., and Briggs, V. A. (2004). Expanded uncertainty quantification in inverse problems: Hierarchical Bayes and empirical Bayes. Geophysics, 69(4), 1005-1016. Sambridge, M., Gallagher, K., Jackson, A., and Rickwood, P. (2006). Trans-dimensional inverse problems, model comparison and the evidence. Geophysical Journal International, 167(2), 528-542. Zhu, D., and Gibson, R. (2016). Seismic inversion and uncertainty analysis using a transdimensional Markov chain Monte Carlo method. In SEG Technical Program Expanded Abstracts 2016 (pp. 3666-3671). Society of Exploration Geophysicists. SOME STRATEGIES TO MAKE GLOBAL METHODS SUITABLE TO SOLVE HIGH-DIMENSIONAL AND ILL-CONDITIONED GEOPHYSICAL OPTIMIZATION PROBLEMS M. Aleardi Earth Sciences Department, University of Pisa, Italy Introduction. Geophysical optimisation problems are often non-linear, multi-dimensional, and characterised by objective functions with complex topologies (i.e. multiple local minima). Global methods are often used to solve these problems, but they are affected by the curse of dimensionality problem, that is their ability to explore the model space exponentially decreases as the dimensions of the model space increase. In addition, their limited exploitation capabilities make global search algorithms unable to converge in ill-conditioned optimization problems or in cases with highly correlated model parameters. In this work, I test three different strategies that could be used to partially attenuate the previous issues. The first strategy uses Legendre polynomials to reparametrize the subsurface model. More in detail, the subsurface model is expanded into series of Legendre polynomials that are used as basis functions. In this framework the unknown parameters become the series of expansion coefficients associated to each polynomial. The aim of this peculiar parameterization is three-fold: Efficiently decreasing the number of unknowns, inherently imposing a 1D spatial correlation to the recovered subsurface model, and finally searching for maximally decoupled parameters. This approach is applied to 1D seismic-petrophysical inversion in which the objective function to minimize is a weighted sum of data misfit and a-priori model information. The second strategy combines the global algorithm with a 1D edge-preserving smoothing (EPS) filter to solve the non-linear amplitude versus angle (AVA) inversion. In this case the simple L2 norm misfit between observed and predicted seismic gather is used as the objective function to minimize. The third example concerns a 2D cross-hole tomography. Due to the severe ill-conditioning and the non-linearity of this inverse problem, the 2D EPS filter is used in conjunction with model constraints in the objective function. In particular, following Zhang and Zhang (2012) the objective function is a weighted sum of L2 norm data misfit and an