Full-waveform inversion

Full Wave form Inversion
1. Introduction:
Full wave form Inversion (FWI) is a recent method used for geotechnical site characterization. It involves deriving of quantitative images related to subsurface obtained from seismic measurements. Thus it is also suitable for imaging the shear wave (S-wave) and compressive wave (P-wave) velocities of soil particles (Biondi, B. and Almomin, A., 2012). In FWI, an optimization model is used to solve out the optimal earth module in order to meet the recorded seismic measurements in a predefined space. Echoes which are outcomes from geological discontinuities are utilized to facilitate the subsurface (Chi, B., Dong, L. and Liu, Y., 2014). Some physical parameters like velocities of seismic waves, mass density are used in geotechnical applications. It involves solving full wave equation to restore the parameters models of subsurface.
2. Working and Implementation of FWI Method:
Optimal model of the subsurface is determined in FWI. By performing successive iterations on the misfit function to decrease its value present between recorded and synthetic data. With the solution of “forward problem” it explains the seismic data which was recorded. In the first iteration, these variable inputs are assigned to the first model. This initial model is predicted based upon the information received after performing calculations through conventional seismic imaging methods. Then, the data which is obtained from measurement of seismic graphs is noted and recorded (Baeten G., et al. 2013).
Inputs to the iteration model are initial velocity model and recorded data. Following steps are to be performed for each iteration i;
1) Forward modeling:
Synthetic field is to be obtained from the given initial velocity model having the source and receiver locations equal with the recorded data. For the first iteration, velocity gradient model is used and for remaining iteration...