GNGTS 2017 - 36° Convegno Nazionale

GNGTS 2017 S essione 3.3 685 Hybrid Global and Bayesian CSEM Inversion G. Bernasconi 1 , G. Gentili 1 , L.Speranza 2 , J. Suffert 3 1 DEIB, Politecnico di Milano, Italy 2 Edison, Italy 3 Edison Norge EM geophysical methods can help the interpretation of seismic images, by providing information about the conductivity of the subsurface. In particular, “marine Controlled Source EM” (mCSEM) techniques use a transmitting antenna (TX), pulled by a vessel, and a network of receivers (RX) to reveal the presence of resistive bodies below the sea floor (Constable, 2010). The collected field can be expressed as the result of a forward problem: d = f ( m ) (1) where f represents the physical link between the model parameters m and the data d . The geophysical interpretation consists in recovering the model from the data, and this usually involves the solution of an inverse problem. CSEM inversion is often ill-posed, meaning that it has more than one valid solution, and it is highly non linear, giving birth to possible local minima in the residual space. Therefore, there is the need of constraints and/or a priori information, e.g. knowledge coming from geology or other geophysical methods (seismic), in order to drive the optimization procedure towards a unique realistic scenario, and to associate to this scenario a “probability/uncertainty” index. Within the mCSEM framework, we explore the pros and cons of two different inversion strategies, and then we propose a hybrid procedure which is able to exploit the advantages of both techniques. In a 1D scenario, the model is parameterized in layers with assigned thickness and resistivity; in 2D and 3D scenarios the model is described by the resistivity values of a grid of M points. Bayesian linearized inversion (BLI). The first approach is an iterative Bayesian linearized inversion, as presented in Tarantola (2005). The starting (a priori) model contains all the information coming from other domains. The uncertainty of the prior parameters is defined by a probability density function. When these probabilities are Gaussian, the procedure runs iteratively according to the formula (2) m k is the vector of the inversion parameters at iteration k , C D = C d + C fw is the covariance matrix that describes the uncertainties due to both the measurements ( C d ) and the forward modeling ( C fw ), C m is the covariance matrix that takes into account the uncertainties of the prior model, G k is the Jacobian matrix of the derivatives of the forward model equation with respect to the current model parameters, and λ is the update step size. In practice, the forward model equation is linearized around the current model m k , in order to have a mathematically tractable solution and uncertainty analysis. The iterative algorithm stops when . (3) The posterior covariance matrix of the model space, C m,post , describes the uncertainty of the solution . (4) The results of the BLI are robust and have a high synthetic to real correlation. The needed computing effort is usually affordable, especially when there is an efficient way to compute/ estimate the Jacobian matrix. On the other hand, the method is not global, and it can converge to local minima. Global inversion: simulated annealing (SA). Global inversionmethods have been designed in order to escape from local minima and to converge, after a certain amount of time, not always defined a priori, to the global minimum region. The Simulated Annealing algorithm was first