Curvelet processing and imaging: 4D adaptive subtraction

With burgeoning world demand and a limited rate of discovery of new reserves, there is increasing impetus upon the industry to optimize recovery from already existing fields. 4D, or time-lapse, seismic imaging holds great promise to better monitor and optimise reservoir production. The basic idea behind 4D seismic is that when multiple 3D surveys are acquired at separate calendar times over a producing field, the reservoir geology will not change from survey to survey but the state of the reservoir fluids will change. Thus, taking the difference between two 3D surveys should remove the static geologic contribution to the data and isolate the time-varying fluid flow component. However, a major challenge in 4D seismic is that acquisition and processing differences between 3D surveys often overshadow the changes caused by fluid flow. This problem is compounded when 4D effects are sought to be derived from legacy 3D data sets that were not originally acquired with 4D in mind. The goal of this study is to remove the acquisition and imaging artefacts from a 4D seismic difference cube using Curvelet processing techniques. The denoising problem In this paper, we argue that computing 4D difference cubes can be recast into the framework of solving a generic denoising problem that estimates the model m from noisy data d = m + n with Gaussian noise n. The solution of this inverse problem can be written in terms of the following variational problem mˆ mi