Full waveform inversion using oriented time‐domain imaging method for vertical transverse isotropic media

Abstract

Full waveform inversion for reflection events is limited by its linearised update requirements given by a process equivalent to migration. Unless the background velocity model is reasonably accurate, the resulting gradient can have an inaccurate update direction leading the inversion to converge what we refer to as local minima of the objective function. In our approach, we consider mild lateral variation in the model and, thus, use a gradient given by the oriented time‐domain imaging method. Specifically, we apply the oriented time‐domain imaging on the data residual to obtain the geometrical features of the velocity perturbation. After updating the model in the time domain, we convert the perturbation from the time domain to depth using the average velocity. Considering density is constant, we can expand the conventional 1D impedance inversion method to two‐dimensional or three‐dimensional velocity inversion within the process of full waveform inversion. This method is not only capable of inverting for velocity, but it is also capable of retrieving anisotropic parameters relying on linearised representations of the reflection response. To eliminate the crosstalk artifacts between different parameters, we utilise what we consider being an optimal parametrisation for this step. To do so, we extend the prestack time‐domain migration image in incident angle dimension to incorporate angular dependence needed by the multiparameter inversion. For simple models, this approach provides an efficient and stable way to do full waveform inversion or modified seismic inversion and makes the anisotropic inversion more practicable. The proposed method still needs kinematically accurate initial models since it only recovers the high‐wavenumber part as conventional full waveform inversion method does. Results on synthetic data of isotropic and anisotropic cases illustrate the benefits and limitations of this method.

Least‐squares reverse time migration based on an efficient pure qP‐wave equation

“…While only considering the inaccurate anisotropic model, the imaging results generated by TTI LSRTM are influenced more by parameter ε , θ than δ , which can be illustrated by comparing Figure 17c with (b) and (d) of the same figure. These analyses are also consistent with previous studies (Alkhalifah & Plessix, 2014; Zhang & Alkhalifah, 2017; Zhu et al., 2018).…”

“…The reason for the aforementioned results is that the parameter ε mainly influences the lateral velocity of seismic wave propagation, the parameter δ has dominant effect on the P-wave move out velocity relative to the axis of symmetry and mildly influences the propagation of seismic wave, and the dip angle has significant influence on the traveltime and raypath tracing of seismic waves (Mu, Huang, Yang, et al, 2020). Furthermore, compared to Figure 15, the imaging results in These analyses are also consistent with previous studies (Alkhalifah & Plessix, 2014;Zhang & Alkhalifah, 2017;Zhu et al, 2018).…”

Transmission + reflection anisotropic wave‐equation traveltime and waveform inversion

“…Assuming a mainly horizontal earth, Fig. shows the radiation patterns for the anisotropic parameters , ε and δ for a horizontal reflector, which are consistent with the patterns presented by Zhang and Alkhalifah (). The radiation pattern of is independent of the angle which is similar to the isotropic case.…”

Multiscale phase inversion for vertical transverse isotropic media

“…where the first term on the right side represents the gradient for updating the anisotropic model, the second term generates the crosstalk artefacts introduced by the products of the L v p0 and L . To reduce the crosstalk between v p0 and , one strategy is that v po is updated only with the near-offset data in the first iterations, then is updated with v p0 with full-offset data in the later iteration (Zhang and Alkhalifah, 2017). In a similar way, the rolling-offset strategy gradually extends the offset range with an increasing number of iterations to mitigate the local minimum problem (AlTheyab and Schuster, 2015).…”