| Full-waveform inversion(FWI)is a powerful technique,which utilizes the waveform information of seismic data to reconstruct the seismic parameters of the subsurface,including P-wave/S-wave velocities,density and anisotropic parameters.Recent studies based on synthetic data have demonstrated that this technique has a huge potential to provide higher-resolution velocity models and accurate event locations for microseismic data.However,FWI with microseismic data also faces additional challenges as the source parameters,i.e.the location and the moment tensor,are unknown.The process of FWI is to minimize a norm distance between predicted data and recorded data.The predicted data are the solution of a forward problem,which solves a wave equation.In this thesis,I formulate the velocity-stress elastic wave equation into a pseudo-conservative form,which makes the forward operator self-adjoint.We use a moment tensor source for the microseismic data simulation.The forward and adjoint wavefields are computed by solving an elastic Vertical Transverse Isotropy(VTI)wave equation with a high-order staggered-grid finite-difference algorithm.I have also implemented a perfectly matched layer absorbing boundary condition to prevent spurious reflections from the model boundaries from contaminating the modelled wavefields.In this thesis,I utilized a nonlinear conjugate gradient(NCG)method to minimize the objective function of FWI.Besides,I provided a detailed introduction to the adjoint-state method in the context of waveform modelling of microseismic data in VTI media.In addition,I also developed an elastic FWI algorithm,in which the gradients of the parameters of sources and media are obtained with the adjoint-state method.Numerical tests have demonstrated that this algorithm can successfully invert the 2D velocity field as well as the source parameters(location,origin time,and moment tensor)from microseismic data. |
