Meantime a new Conversional formulation of the gradient based on the formula of objective functional with respect to Lamé cross-correlation of the derivatives of forward and constants and density is also proposed. Using dimensional backward particle displacement wavefield is derived from analysis (Baumstein et al., 2009), the gradient of the the second-order wave equations. During the process of objective functional computed by the new adjoint wave back-propagation of the data residuals, the adjoint wave equations and the corresponding formulation of gradient is equations are just the same as the forward ones. Without tested to be perfectly right, and it is no need to preprocess preprocessing the data residuals before back-propagation, the data residuals any more. Moreover, we need not convert one cannot obtain a properly scaled gradient when applying particle velocity to particle displacement, and the new the first-order velocity-stress differential equations. In this formulation of gradient reduces the calculation of spatial paper, based on the first-order elastic system in time derivatives of the adjoint wavefield, which improves the domain, we propose a new form of adjoint wave equations, computational efficiency to a certain extent.