Changing variable in the wave equation $\frac{\partial^{2} u}{\partial t^{2}}=c^{2} \frac{\partial^{2} u}{\partial x^{2}} $

Question

I am trying to implement reverse time migration (RTM). There is a direct wave equation: $$\frac{\partial^{2} u}{\partial t^{2}}=c^{2} \frac{\partial^{2} u}{\partial x^{2}}. $$

I solved it numerically. Now we need to solve this equation in reverse time. I can't figure out what will happen to the equation after changing the variable: $\,\,\,u(x,t)\,\to\,u(x,-t).$
Please tell me how to change the variable and a possible numerical scheme for solving the equation after changing the variable.