We propose a new approximation method to compute the matrix-vector product of the Hessian matrix and perturbation vector. The new method is based on the central finite-difference approximation (FDA), the Born perturbation and the limit of a function, which does not require to construct and invert the perturbed modelling operator during the linear conjugate-gradient procedures. In addition, we do not have to perform a number of numerical tests to find an appropriate approximation interval. As a result, the new method is more efficient than the conventional method based on the forward FDA. Numerical examples for the Marmousi-2 model show that the new method yields almost the same inversion results as those obtained by the conventional method using the FDA.


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