Development of 2D Full Waveform Inversion algorithm of seismic data

Abstract

Full Waveform Inversion (FWI) is an advanced and emerging seismic imaging technique that exploits the full wavefield information present in the data. FWI is an optimization problem where the misfit between the recorded and generated data is iteratively minimized. This project attempts to create a robust forward acoustic wave propagation engine with appropriate boundary conditions and a non-linear waveform inversion algorithm using the Gauss-Newton (GN) and Non-Linear Conjugate Gradient (NLCG) methods for the 2D seismic dataset. Both the acoustic wave propagation modeling and the waveform inversion are formulated in the frequency domain. The forward model is created using the fourth-order finite difference approximation of the scalar wave equation on staggered-grid. The boundaries are incorporated with Perfectly Matching Layers (PMLs) to suppress undesired reflections from edges. The forward modeling was posed as a sparse linear system and is solved for each frequency by LU decomposition. The seismogram in the time domain was retrieved by applying a Fourier transform to the generated data. The waveform inversion is implemented in a least-square sense, i.e., the objective function defined as L2 norm of data residuals is minimized. A term containing the prior information about the model parameters is also incorporated in the objective function for stability. The inversion is done initially using the Gauss-Newton method, where the Hessian (the second-order derivative of the objective function) is approximated in terms of the first-order derivative of the forward operator. And later implemented using the Non-Linear Conjugate Gradient method, where the model is updated in the opposite of gradient direction. The forward modeling results establish the reliability and robustness of the created forward engine. We start with a simple two-layer model and compare the arrival time of the reflection event of generated seismogram with the calculated arrival time. A comparison of data generated using the algorithm and data generated using Madagascar is also provided. The waveform inversion is done at discreet frequencies; hence it is computationally less expensive as compared to the time domain approach. The inversion results on synthetic models with buried boxes at different depths with anomalous velocities are presented using both GN and NLCG methods. Both methods are also tested on a checkerboard velocity model for a rigorous investigation of the robustness of the algorithms.