Elastic full-waveform inversion with probabilistic petrophysical model constraints

Abstract

Full-waveform inversion (FWI) based on the minimization of data residuals may not enhance our understanding of the subsurface and can at times lead to misleading subsurface models. Additionally, unconstrained multiparameter FWI may also lead to models that do not represent realistic lithology for independently derived parameters. We have developed a method for elastic FWI that explicitly imposes petrophysical restrictions to guide models toward realistic and feasible lithology, that is, to subsurface models consistent with the seismic data and with the underlying petrophysics. We exploit petrophysical information, such as that provided by well logs, to constrain the inversion and to avoid implausible models. We achieve this goal by confining the inverted models to a feasible region defined by a probability density function instead of imposing lithologic facies as a function of position. Inside this feasible petrophysical regime, the inverted models do not need to obey a specific trend, that is, we do not link the parameters with explicit and potentially inaccurate petrophysical relations. Instead, we define a petrophysical basin of attraction that confines models to a feasible region validated by regional lithologic and petrophysical information. We find through elastic models that incorporating probabilistic petrophysical constraints into the inversion objective function leads to models that are superior to models obtained either without constraints or with approximate analytic constraints. In addition, we discover that these constraints can help in mitigating common issues affecting elastic FWI, such as the artifacts produced by interparameter crosstalk and limited acquisition coverage.

Characterising ice slabs in firn using seismic full waveform inversion, a sensitivity study

“…Here we follow the approach of Aragao and Sava (2020) who define the data residual as;with the objective function then defined aswhere a , x and t are, respectively, the experiment index, space coordinates and time, || 2 indicates the L2 (least-squares) norm, W u ( a , x , t ) are trace weights, e s ( a , x , t ) the (synthetic) source wavefield and d ( a , x , t ) are the observed data. The model that minimises the objective function is considered to the best solution to the inversion (Pratt, 1999).…”

“…The model that minimises the objective function is considered to the best solution to the inversion (Pratt, 1999). We use a gradient-based method to update the model iteratively following the approach outlined in Aragao and Sava (2020). For more information on the numerical approach, see the description there.…”

“…We use an adjoint method (Plessix, 2006) and a gradient-based method (Tarantola, 1988) to update the model between iterations. We use the Madagascar framework (Fomel and others, 2013), provided by the Center for Wave Phenomena, to implement this approach (Aragao and Sava, 2020). To minimize the impact of cycle skipping, we start iterations for the low-frequency wavefield, filtered between 3 and 10 Hz, running a minimum of five iterations for each frequency band until the OF updates suggest model convergence.…”

“…In our FWI, we use a gradient approach to define the fit between recorded and modelled data (Aragao and Sava, 2020). To minimise the OF with respect to the model parameters ( m ), the OF is differentiated,…”