Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The adjoint state method is a numerical method for computing the gradient of a function or operator in a numerical optimization problem. It has applications in geophysics and seismic imaging. The adjoint state space is chosen to simplify the physical interpretation of equation constraints. It may take the form of a Hilbert space. Adjoint state techniques allow the use of integration by parts, resulting in a form which explicitly contains the physically interesting quantity. An adjoint state equation is introduced, including a new unknown variable.

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