Page - 1169 - in Book of Full Papers - Symposium Hydro Engineering

problem. Gradient and Newton methods involving the computation of the gradient and an approximation of the inverse Hessian operator have been successfully applied by [26, 27, 28]. Thus, motivating the application of the quasi-Newton limited memory Broyden-Fletcher-Goldfarb-Shanno (l-BFGS) method in this paper. The required model parameter gradient calculation is done using the adjoint state method as employed in [29]. Since the FWI is sensitive to the initial model, to enable convergence to the global minima, an initial model which contains the long wavelength part of the model to be resolved is required. Unlike in geophysical exploration, a priori information on the dam material parameters can often be gotten since most of these structures are man-made. Thus, the material properties at construction can be used as an upper bound as done in this case. (a) True model (b) Initial model Fig. 2 Distribution of seismic velocities (Vp , Vs)and density in the air, water, foundation and dam structure (true and initial model) A closer look at Fig. 2 shows that the true model in (a) and the initial model in (b) differ only by the inclusion of regions of degraded material properties in the true model. Therefore, the ‘as-built’ material properties of the dam are taken as the starting model. To probe the dam material, spike wavelets are sequentially emitted from each of the sources (e.g. air guns). Here, a low-pass filtered spike with upper corner frequency of 1kHz is applied as shown in Fig. 3. For each excitation shot the source wavelet propagates for a duration of 0:1s and the time interval (dt) used for the analysis is 3x10-5s which satisfies the Courant-Friedrichs-Lewy criterion for stability. 1169