Early-arrival waveform inversion for near-surface velocity and anisotropic parameters: modeling and sensitivity kernel analysis

Introduction

Full Waveform Inversion (FWI) (Tarantola, 1984; Pratt et al., 1998; Mora, 1987) iteratively updates model by trying to match input data with modeled data. It estimates subsurface velocity more accurately than conventional techniques, such as ray-based methods (White, 1989; Hampson and Russell, 1984; Olson, 1984), especially in geologically complex areas. This is because FWI predicts kinematics of recorded data more accurately by using finite-difference wave-equations, compared with ray-based methods using high frequency approximations of wave propagation. However, the dynamics of recorded data are not very accurately predicted by current FWI methods. In other words, successful field-data application of FWI usually relies more on matching kinematics of recorded data.

With longer-offset data ($>10$ km) commonly acquired these days, matching kinematics means matching data traveltime over the entire offset range. For such large offset ranges, anisotropic effects, if they exist, are no longer negligible. In the presence of anisotropy, if isotropic FWI is used, the inversion results will not correctly reflect the true subsurface attributes (Ghilami et al., 2011). More specifically, isotropic FWI of diving waves mostly recovers the horizontal velocity in anisotropic media. Migration using such a velocity will place reflectors at incorrect depths. To avoid this, anisotropic parameter estimation should be part of the inversion process. Such inversion can be carried out in several ways. One way is to perform single-parameter inversion for each parameter sequentially. Alternatively, joint inversion performs simultaneous inversion of multiple parameters, called joint inversion. Joint inversion is usually better, since the results of the first approach are sensitive to the order in which the inversion is performed. On the other hand, given the original definition of anisotropic parameters (Thomsen, 1986), direct changes in those parameters themselves usually result in very small changes in data kinematics, where as changes in velocity affect the data kinematics much more significantly (Plessix and Cao, 2011). For the purpose of simultaneous inversion, it is important to understand quantitatively how much the data kinematics change as a function of anisotropic parameters and velocity, and to come up with an effective parametrization of the model.

In this paper, I first describe the acoustic vertical transversely isotropic (VTI) wave-equation and the sensitivity kernel calculation. Then I use synthetic data examples to illustrate the sensitivity of the data kinematics to the anisotropic parameters and the velocity, in terms of both forward modeling and sensitivity-kernel calculation.

Early-arrival waveform inversion for near-surface velocity and anisotropic parameters: modeling and sensitivity kernel analysis