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Propagating seismic waves are dispersed and attenuated in the subsurface due to the conversion of elastic energy into heat. The absorptive property of a medium can be described by the quality factor Q . In this study, the first-order pressure-velocity viscoacoustic wave equations based on the standard linear solid model are used to incorporate the effect of Q . For the Q model inversion, an iterative procedure is then proposed by minimizing an objective function that measures the misfit energy between the observed data and the modeled data. The adjoint method is applied to derive the gradients of the objective function with respect to the model parameters, that is, bulk modulus, density, and Q -related parameter τ . Numerical tests on the crosswell recording geometry indicate the feasibility of the proposed approach for the Q anomaly estimation.

Time Domain Waveform Inversion for the Q Model Based on the First-Order Viscoacoustic Wave Equations