Generating random rough edges, surfaces, and volumes

Numerical methods of generating rough edges, surfaces, and volumes for subsequent simulations are commonly employed, but result in data with a variance that is downward biased from the desired value. Thus, it is highly desirable to quantify and to minimize this bias. Here, the degree of bias is determined through analytical derivations and numerical simulations as a function of the correlation length and the roughness exponent of several model power spectral density functions. The bias can be minimized by proper choice of grid size for a fixed number of data points, and this optimum grid size scales as the correlation length. The common approach of using a fixed grid size for such simulations leads to varying amounts of bias, which can easily be confounded with the physical effects being investigated.