True-amplitude versus trace-normalized full waveform inversion

SUMMARY Full waveform inversion (FWI) is a powerful method to estimate high-resolution physical parameters of the subsurface by iteratively minimizing the misfit between the observed and synthetic seismic data. Standard FWI algorithms measure seismic misfit between amplitude-preserved seismic data (true-amplitude FWI). However, in order to mitigate the variations in sources and recording systems acquired on complex geological structures and the physics that cannot be modelled using an approximation of the seismic wave equation, the observed and synthetic seismic data are normalized trace-by-trace and then used to perform FWI. Trace-by-trace normalization removes the amplitude effects related to offset variations and only keeps the phase information. Furthermore, trace-by-trace normalization changes the true amplitude difference because of different normalization factors used for the corresponding synthetic and observed traces. In this paper, we study the performance of true-amplitude FWI and trace-normalized-residual-based FWI in the time domain. The misfit function of trace-normalized-residual-based FWI is defined such that the adjoint source used in gradient calculation is the trace-normalized seismic residual. We compare the two inversion schemes with synthetic seismic data simulated on laterally invariant models and the more complex 2-D Marmousi model. In order to simulate realistic scenarios, we perform the elastic FWI ignoring attenuation to noisy seismic data and to the synthetic data modelled using a viscoelastic modelling scheme. Comparisons of seismic data and adjoint sources show that trace-by-trace normalization increases the magnitude of seismic data at far offsets, which are usually more cycle-skipped than those at near offsets. The inverted results on linear-gradient models demonstrate that trace-by-trace normalization increases the non-linearity of FWI, so an initial model with sufficient accuracy is required to guarantee the convergence to the global minimum. The inverted results and the final seismic residuals computed using seismic data without trace-by-trace normalization demonstrate that true-amplitude FWI provides inverted models with higher accuracy than trace-normalized-residual-based FWI, even when the unknown density is updated using density–velocity relationship in inversion or in the presence of noise and complex physics, such as attenuation.

Tidal bending of ice shelves as a mechanism for large-scale temporal variations in ice flow

GPS measurements reveal strong modulation of horizontal ice shelf and ice stream flow at a variety of tidal frequencies, most notably a fortnightly (Msf) frequency not present in the vertical tides themselves. Current theories largely fail to explain the strength and prevalence of this signal over floating ice shelves. We show how well-known non-linear aspects of ice rheology can give rise to widespread, long-periodic tidal modulation in ice shelf flow, generated within ice shelves themselves through tidal flexure acting at diurnal and semidiurnal frequencies. Using full-Stokes viscoelastic modelling, we show that inclusion of tidal bending within the model accounts for much of the observed tidal modulation of ice shelf flow. Furthermore, our model shows that, in the absence of vertical tidal forcing, the mean flow of the ice shelf is reduced by almost 30 % for the geometry that we consider.