Abstract
This paper investigates the capability of acoustic Full Waveform Inversion (FWI) in building Marmousi velocity model, in time and frequency domain. FWI is an iterative minimization of misfit between observed and calculated data which is generally solved in three segments: forward modeling, which numerically solves the wave equation with an initial model, gradient computation of the objective function, and updating the model parameters, with a valid optimization method. FWI codes developed in MATLAB herein FWISIMAT (Full Waveform Inversion in Seismic Imaging using MATLAB) are successfully implemented using the Marmousi velocity model as the true model. An initial model is obtained by smoothing the true model to initiate FWI procedure. Smoothing ensures an adequate starting model for FWI, as the FWI procedure is known to be sensitive on the starting model. The final model is compared with the true model to review the number of recovered velocities. FWI codes developed in MATLAB herein FWISIMAT (Full Waveform Inversion in Seismic Imaging using MATLAB) are successfully implemented usingMarmousi velocity model astrue model. An initial model is derived from smoothing the true model to initiate FWI procedure. Smoothing ensures an adequate starting model for FWI, as the FWI procedure is known to be sensitive onstarting model. The final model is compared with the true model to review theamount of recovered velocities.
Highlights
Exploration industries commonly use seismic imaging tools, which allow waves to propagate through subsurface rock structure and reveal possible crude oil and natural gas bearing formations
Full Waveform Inversion (FWI) is an inverse method that generally employ the least squares objective function to minimize the difference between observed seismic data and synthetic seismic gathers by updating the initial model parameters until convergence (Margrave et al, 2011)
The FWISIMAT algorithm used in the study, performs an iterative search for a velocity model that minimizes the residuals between the data computed in the velocity model and the observed data, i.e. the final result is a “best fit” model
Summary
Exploration industries commonly use seismic imaging tools, which allow waves to propagate through subsurface rock structure and reveal possible crude oil and natural gas bearing formations. FWI is an inverse method that generally employ the least squares objective function to minimize the difference between observed seismic data and synthetic seismic gathers by updating the initial model parameters until convergence (Margrave et al, 2011). As to the forward modelling, second order finite difference method is employed due to its high efficiency This discretization scheme includes absorbing boundary conditions applied on the edges of the velocity medium. Let unl ,m be the wave-field at the time l∆t and spatial position (n∆x, m∆z) , vn,m be the velocity at (n∆x, m∆z) Equation 2 can be discretized using central difference scheme as follows: unl +,m1.
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