To find the sparse solution to an underdetermined system of equations of the source location problem, we propose to use the alternating direction method of multipliers(ADMM). The single measurement of sparse representation problem has been widely studied. Generally we enforce sparsity by imposing penalties based on the $l_1$-norm. However, when the equations are multiple measurement vectors which have the same, but unknown, sparsity structure, the sparse representation problem can not be formulated easily. By using ADMM we just need to solve three subproblems and each subproblem can be easy to solve. What is more, this formulation of the model with $l_p$-norm ($p\geq1$) can be solved. We can use the shrinkage operator to solve these subproblems. The convergence of ADMM with three separable variables of pairwise linear constraints also has been proven. This method is effective by experiments using the observation of the earthquake rupture.