GNGTS 2018 - 37° Convegno Nazionale

GNGTS 2018 S essione 3.3 717 edge-preserving regularization that impose sparseness constraints into the first order derivatives of model parameters. Note that EPS filters are extensively applied to reduce the noise of geophysical subsurface images while preserving structural and stratigraphic discontinuities and/or edges (i.e. for sharpening seismic stack images for interpretation; AlBinHassan et al. 2006). In the context of global search methods, EPS filters drive the optimization in a suitably preconditioned model domain instead of relying completely on the random perturbation. This will decrease the ill-conditioning of the inversion because the modified model space is designed to be smaller than the complete suite of solutions. In all the following tests the firefly algorithm (FA) is used as the optimization tool. This is a quite new global search method inspired by the swarm intelligence that was proposed by Yang (2008). Over the last decade, this optimization strategy has been extensively applied in engineering applications but found very limited applications to geophysical optimization problems. In all cases the predictions yielded by the proposed strategies are compared with those provided by the more standard approach in which only the L2 norm misfit function and where no preconditioning strategies are applied in the optimization framework. In all the following tests, I focus the attention to synthetic data optimizations with the aim to maintain the discussion at a simple level and to draw general conclusions. 1D Seismic-petrophysical inversion. I apply the Legendre parameterization to seismic- petrophysical inversion aimed at inferring the petrophysical properties of porosity ( ϕ ), water saturation ( Sw ), and shaliness ( Sh ) from pre-stack seismic data. This exercise is based on actual well log data pertaining to a clastic, gas saturated reservoir located in a shale-sand sequence. The full Zoeppritz equations constitute the elastic convolutional forward modelling, and the theoretical equations based on granular media models constitute the rock-physic model. I consider an angle range between 0-45 degrees and a 45-Hz Ricker wavelet with a sampling rate of 0.002 s as the source signature, which is assumed perfectly known during the inversion. To realistically simulate a field dataset, I add to the synthetic observed data Gaussian random noise with zero mean, resulting in a signal-to-noise (S/N) ratio equal to 10. I also use the logit transformation to transform to the bounded petrophysical variables to variables with support in ℝ. In this case, the vector m expressing the subsurface model parameters can be written as: (1) This results in a total of p ×3 subsurface model parameters. Basing on Legendre polynomials, I reparametrize the subsurface model as follows: (2.1) (2.2) (2.3) where Q represent the Legendre polynomials, N expresses the total number of Legendre polynomials considered, whereas s n are the numerical coefficients to be determined; the vector y =[ y 1 , y 2 , y p ] represents the considered vertical interval of p time samples linearly converted into the [-1,1] interval; s prior is the prior petrophysical model vector equal to the average values of petrophysical properties derived from borehole information. Finally, L s and L m are the standard and modified logit transformations. Note that this peculiar parameterization inherently imposes a 1D constraint to the vertical variability of petrophysical properties. Obviously, the wavelength