Constrained Timeshift Estimation

Timeshift estimation is an unstable process and many sets of timeshift fields fit our data. Only a reduced set is physically sensible and this non-uniqueness is even more evident if try to map velocity changes. The results of common timeshift methods usually need to be filtered in order to look acceptable. This might give timeshifts that are not in accordance with our data. A superior approach is to find timeshifts while making sure that we are honouring both our prior information and the data optimally. In this paper timeshifts are estimated as solution to an inverse problem. All constraints are Gaussian so the resulting system is linear and easy to solve. This implies that the algorithm is suitable for full field datasets. The three addressed constraints: B-spline representation, lateral and vertical constraints are demonstrated on a North Sea dataset. A velocity anomaly is mapped with increasing clarity without matching quality being affected in any significant way.