Q-factor and velocity inversion from zero-offset VSP data

In this paper, we propose an inversion method to estimate the Q-factor and velocity using the Gauss-Newton method in a 1-D viscoelastic medium. To improve the computation efficiency, we derive an analytic expression of the Jacobi matrix. As the forward simulation is the base step of the inversion problem, we derive a transfer matrix to simulate forward modeling with a direct downgoing wave and an upgoing primary reflection of zero-offset VSP data. We give the workflow of both the forward and inversion method, and discuss the optimum initial value determination. Tests on synthetic VSP data show that the proposed method doesn't need a priori information of layers and can compress the influence of the upgoing wave at the interfaces. By applicating to field VSP data, we obtain Q and velocity curves which have almost the same distribution as those obtained from a well, which demonstrate that the effective method is powerful to predict the Q factor and the velocity of the earth.