Simultaneous inversion for velocity and attenuation by waveform tomography

Abstract

Seismic waveform tomography can invert for the velocity and attenuation ( 1 − Q ) variations simultaneously. For this simultaneous inversion, we propose two strategies for waveform tomography. First, we analyze the contributions of the real part and the imaginary part of the gradients, associated with the velocity and attenuation parameters respectively, and determine that the combination of the real part of the gradient subvector for the velocity parameter and the imaginary part of the gradient subvector for the attenuation parameter would produce an optimal inversion result. Second, we attempt to balance the sensitivities of the objective function to the velocity and the attenuation parameters. Considering the magnitude differences between these twotype parameters in the simultaneous inversion, we apply preliminarily a normalization to both the velocity model and the attenuation model. However, for balancing their sensitivities, we further adjust the corresponding model updates using a tuning factor. We determine this tuning parameter adaptively, based on the sensitivities of these two parameters, at each iteration. Numerical tests demonstrate the feasibility and reliability of these two strategies in full waveform inversion.

Waveform Tomography of Two-Dimensional Three-Component Seismic Data for HTI Anisotropic Media

“…Besides the magnitude and units differences, we also take account the sensitivity differences to the objective function during the inversion. To balance these updates to the normalized models, the gradient sub-vectors for the rest of the parameters can simply be amplified to the parameter exerting a dominant role in the simultaneous inversion by their corresponding positive tuning factors Gao and Wang 2016). Subsequently, together with the step length, the objective function will decrease toward the optimal solutions along the composite gradient vectors.…”

“…Apart from the aforementioned methods, the subspace method is also a choice for multiple parameter inversion (Kennett et al 1988;Houseman 1994, 1995;Wang 2016) wherein the parameters are divided into different parameter classes. One may also choose to balance the differences of different parameters using a tuning factor to make the misfit function decrease along the optimal composite gradient direction (Wang 1998;Gao and Wang 2016). Adding constraints, such as Total Variation regularization, to the misfit function is also helpful for reducing leakage of imprints between different parameters (Ramos-Martínez et al 2017).…”

A sequential inversion with outer iterations for the velocity and the intrinsic attenuation using an efficient wavefield inversion

“…As the observed data are influenced by a variety of subsurface parameters including velocity, density, anisotropy, and intrinsic attenuation, FWI has the potential to recover these parameters, but with different sensitivities and tradeoff. With the help of the viscoacoustic assumption, FWI can provide inversion results for both the velocity and the attenuation models (Kamei and Pratt, 2008;Malinowski et al, 2011;Gao and Wang, 2016). However, multiparameter FWI has always been a challenge, because parameter update tradeoff may cause inaccurate inversion results (Tarantola, 1994).…”

“…The velocity and the intrinsic attenuation are both independent of the scattering angle with varying magnitude of data sensitivities. Suggestions to balance the sensitivities of the velocity and the intrinsic attenuation in a simultaneous inversion have been proposed (Malinowski et al, 2011;Gao and Wang, 2016). Simultaneous inversion calculates the gradients of different parameters using the same background models, and updates all the parameters at once in every iteration.…”

“…In multiparameter waveform inversion, EWI demonstrates its effectiveness in recovering a good velocity model, so a sequential inversion for any other parameter will suffer less from the cross-talk issue (Song et al, 2019a;Song and Alkhalifah, 2020a). For viscoacoustic media, as the velocity is the dominant parameter controlling the wave propagation, and it has a larger influence on the data, we first update the velocity model through the selected frequency band (Gao and Wang, 2016). Then, we keep the updated velocity fixed, and then update the attenuation model.…”