Natural fractures serve a very important function in the transport of fluid through rocks, as well as in the flow of electrical charge and heat. The creation of numerically synthesized fractures can aid the study of the physical processes connected with fractures. Synthetic fracture is the term used to describe fractures that are created numerically in such a way that they share the same mean geometrical characteristics as specific natural fractures measured by profiling, by a process known as tuning. We have modified methods for producing synthetic rough surfaces whose geometric properties are tuned to mimic natural fracture surfaces in rocks in order to create synthetic fractures that are statistically identical to those found in rocks. One important such modification has been the incorporation of a method that allows the surfaces to be matched at long wavelengths and unmatched at short wavelengths, with the degree of matching varying smoothly in between, as it does for real fractures. We have compared numerically synthetic fractures created using the new method with fractures created using an existing technique that uses a mismatch wavelength as a sudden discontinuity between matched and unmatched behavior, as well as data from fractures in real rocks. This comparison has shown that the new technique provides much more realistic numerically synthesized fractures than previous methods. Synthetic fractures created with the new method have been used in normal closure and fluid flow modeling, and the results are reported in a companion paper.