The mean and standard deviation (STD) of gradient magnitude of ground noise is directly proportional to the STD of noise . To investigate the mathematical relationship between statistical distribution of ground noise (represented by coarse background located by NNES) and the gradient magnitude of ground noise, we used random normal array that mimics the data structure of our image sample and generated its Scharr gradient image for statistical analysis. (a) Normal-like distribution of Scharr gradient. Simulated 800*800 ground noise image subject to normal distribution (i), (ii), and (iii) are processed by Scharr operator and the gradient distribution is shown. The gradient distribution is not influenced by the mean yet by the STD of native data of the simulated ground noise. (b and c) The mean of noise gradient is not influenced by the mean of the noise, but the STD of noise. The mean of noise gradient is directly proportional to the STD of native noise. (d and e) The STD of the noise gradient is only influenced by STD of the noise as well. The STD of the noise gradient is directly proportional to the STD of native noise.