The optimal checkpointing algorithm (Griewank and Walther, 2000) minimizes the computational complexity of the adjoint state method. Applied to reverse time migration, optimal checkpointing eliminates (or at least drastically reduces) the need for disk i/o, which is quite extensive in more straightforward implementations. This paper describes optimal checkpointing in a form which applies both t...

Hydrocarbon production modifies the stress conditions in the subsurface and changes the model parameters previously estimated from the prospect. The capability to remotely monitor the changes in the reservoir using seismic data has strategic importance since it allows us to infer fluid movement and evolution of stress conditions, which are key factors to enhance recovery and reduce uncertainty ...

The adjoint method is an elegant approach for the computation of the gradient of a cost function to identify a set of parameters. An additional set of differential equations has to be solved to compute the adjoint variables, which are further used for the gradient computation. However, the accuracy of the numerical solution of the adjoint differential equation has a great impact on the gradient...

An adjoint model for a 2D finite element Galerkin shallow water model is developed using the Independent Set Perturbation Adjoint method (ISP-Adjoint, [33]). Its performance in a full 4-D VAR setup with a limited area is assessed by comparing with the adjoint model derived by the automatic differentiation approach, where it is used for optimising the initial conditions. It is shown that ISP-Adj...

In this study, we investigate the method for adjoint-based optimal control of linear and non-linear equations. In particular, we are interested in the formulation of the unsteady adjoint method based on the high-order spectral difference method. For the linear equation, we consider the simple 1D advection equation. For the non-linear equation, we consider the 1D viscous Burger’s equation. In bo...