GNGTS 2019 - Atti del 38° Convegno Nazionale

758 GNGTS 2019 S essione 3.3 References Aleardi, M., Ciabarri, F., and Gukov, T. (2019). Reservoir Characterization Through Target-Oriented AVA- Petrophysical Inversions with Spatial Constraints. Pure and Applied Geophysics, 176(2), 901-924. Bodin, T., and Sambridge, M. (2009). Seismic tomography with the reversible jump algorithm. Geophysical Journal International, 178(3), 1411-1436. Buland, A., and Omre, H. (2003). Bayesian linearized AVO inversion. Geophysics, 68(1), 185-198. Tetyukhina, D., van Vliet, L. J., Luthi, S. M., and Wapenaar, K. (2010). High-resolution reservoir characterization by an acoustic impedance inversion of a Tertiary deltaic clinoform system in the North Sea. Geophysics, 75(6), O57-O67. Ursenbach, C. P., and Stewart, R. R. (2008). Two-term AVO inversion: Equivalences and new methods. Geophysics, 73(6), C31-C38. COMPARISON OF OBJECT FUNCTIONS FOR THE INVERSION OF SEISMIC DATA AND STUDY ON THE POTENTIALITIES OF THE WASSERSTEIN METRIC L. Stracca, E. Stucchi, A. Mazzotti Department of Earth Sciences, University of Pisa, Italy Introduction. The aim of an inverse problem is to find or estimate the unknown parameters of a model, knowing the data it generates and the forward modeling operator that defines the relationship between a generic model and its predicted data. In any inversion process, the main information to update the tested models is given by a certain object function that quantifies the misfit between the observed data to invert and the data predicted by the models themselves. This function has to be defined in order to measure the similarity between the predicted data and the observed ones, in order to drive the inversion procedure towards a satisfying solution, corresponding to the global minimum in the optimal case. In seismic data inversions, the most chosen object function is the L2 norm of the difference between the predicted and the observed data. This choice is justified by this function’s many advantageouses properties, such as: low computational cost, noise insensitivity, high resolution of the results. On the other hand, when applied to oscillating data, this same function is affected by the cycle-skipping problem: the overlap of signal portions with the same polarity (but different phase) generates local minima in the object function’s trend. When the starting model chosen at the beginning of the inversion process isn’t close enough to the true model, the process may converge to a local minima, returning an incorrect solution to the problem (Virieux and Operto, 2009; Sajeva et al., 2016). Misfit functions tested. In this study we tested different object functions that may be applied when inverting seismic data. The most important driving criterium for choosing the functions to compare is the possibility to avoid or significantly reduce the cycle-skipping problem. On the basis of the published literature the following objective functions were selected: Instantaneous envelope and phase misfit (Bozdag et al. , 2011), Adaptive Waveform Inversion (AWI; Warner and Guash, 2016) and quadratic Wasserstein metric (Engquist and Froese, 2014; Yang et al., 2018). The most of the attention during the development of this study was given to this last object function, as it was introduced only recently as a potential alternative to the L2 norm in the inversion of seismic data, and seems to perform well against the cycle-skipping. The Wasserstein distance is a transport metric and, given a cost function, computes the minimal value this function may return when a distribution (e.g. one of the predicted traces from a given velocity model) is converted in another one (the corresponding trace in the observed data).