@MASTERSTHESIS\{IMM2013-06635,
    author       = "C. L. Jensen",
    title        = "Characterization and modeling of structured noise in seismic reflection data",
    year         = "2013",
    school       = "Technical University of Denmark, Department of Applied Mathematics and Computer Science / {DTU} Co",
    address      = "Matematiktorvet, Building 303B, {DK-}2800 Kgs. Lyngby, Denmark, compute@compute.dtu.dk",
    type         = "",
    note         = "{DTU} supervisor: Klaus Mosegaard, and Thomas Mejer Hansen, {DTU} Compute",
    url          = "http://www.compute.dtu.dk/English.aspx",
    abstract     = "Obtaining reliable information about the noise in seismic reflection data can be difficult. Noise is often estimated from {''}expert knowledge{''} or other available information on which uncertainty is hard to quantify. I propose a method to characterize the noise directly from the data, without the need for external information, by using {4-D} data. It is shown, that the covariance of the residual of two {3-D} data sets (together constituting {4-D}) with identical geological subsurface is a good representation of the noise in the summed data set. The noise is characterized in the form of a positive definite semi-variogram model, and hence can be used in any probabilistic inversion. The method is demonstrated on both synthetic and real data by solving the linear least-squares problem ({LSQ,} Tarantola [2005]) without change of parameters, effectively removing the modeled noise from the data. Tests on the synthetic data with realistic noise levels show almost perfect removal of additive noise. A real {4-D} dataset from the Halfdan field in the North Sea with severe acquisition striping was also de-noised in this way. The data were mild- to moderately non-Gaussian, but the correlated noise was still convincingly attenuated. It is expected, that many commercial inversion algorithms use some form of linearized {LSQ}. Hence, the method developed here will easily integrate into existing software."
}