Applications of adjoint modeling

An adjoint model backpropagates a special field from the receiver back through the medium to the source. The field is initialized by the forward model mismatch with measurements—i.e., we run our forward model through a medium whose properties are only known approximately, then compare the forward-propagated field with the measured field at all receiver points. Because we do not know the medium properties perfectly, there is mismatch. The special field back-propagated by the adjoint model is initialized by that mismatch. The special field yields the gradient of the medium properties with respsect to the mismatch, enabling steepest descent methods to be used to invert the mismatch for the unknown refinements to the medium properties that would reproduce the measurements. An adjoint modeling approach to obtaining the gradients needed for the inversion requires two modeling runs, one run of the forward model, and one run of the adjoint model. We will review methods for deriving an adjoint model for some underwater acoustic applications, and demonstrate how an adjoint model can be used in inversion problems. We will also discuss connections to similar methods used in similar fields.