Least-squares migration has been shown to improve image quality compared to the conventional migration method and it is one of the hot spot of present research. However most of the present LSRTM method is established based on the second-order scalar acoustic equation, therefore it is not suitable for the first-order velocity-stress equation. In this abstract, we extend the LSRTM method to the first-order velocity-stress equation. Firstly, we linearize the first-order wave equation and define the cost function. Then we derived the adjoint wave equation, and the iterative solution is derived using adjoint-state method. We found that the adjoint state equation based on first-order acoustic equation is very different from its forward modeling equation. Finally, the theory framework of the first-order LSRTM is established. Numerical tests on synthetic data demonstrate that our method is convenient to handle variable-density media, and has higher simulation accuracy.
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