1. A seismic imaging system using Laplace-domain wave equation in acoustic-elastic coupled media, comprising: a scaled gradient calculating hardware circuit calculating a scaled gradient direction of an objective function by multiplying a gradient of the objective function and an accumulated gradient, wherein the accumulated gradient is calculated using a vertically accumulated square sum of original gradient values by summing an accumulated gradient of a previous vertical layer and a square of the gradient of the objective function, and the objective function is defined by a residual of logarithmic wavefield in Laplace domain; a modeling parameter updating hardware circuit updating model parameters for a discretized finite element equation for the acoustic-elastic coupled media from a Laplace-transformed acoustic wave equation, a Laplace-transformed elastic wave equation and continuity conditions at an interface between an acoustic media and an elastic media of the acoustic-elastic coupled media; an iteration control hardware circuit controlling the scaled gradient calculating circuit and the modeling parameter updating hardware circuit to repeat processing iteratively until a stopping criteria is met; and an imaging hardware circuit converting Lamè constants into P-wave velocity, S-wave velocity, and density and generating a submarine subsurface image showing the distribution of P-wave and S-wave velocities.