Visualization of Roughness Indices in Amplitude-Frequency Space from Wavy Simulated Profiles

Rock surface roughness influences strength, stiffness, and fluid flow dynamics. Roughness algorithms, classified as either Euclidian or fractal, have been used to quantify roughness through computing roughness indices. Because of the complexity of the microtopography of the rock surface, it is difficult to put into context the meaning of a roughness index. The purpose of this study is to visualize roughness indices of simple simulated rough surfaces in amplitude-frequency space. We used a 1000 mm sine wave with varying amplitudes and frequencies to simulate the rough surface. Five Euclidian roughness algorithms were used to quantify the roughness. To visualize these methods, simulated wavy profiles were created using sine waves with specific bounds to capture both the waviness and unevenness of a profile. The findings highlight the superior performance of the Z2 and Mean Absolute Angle algorithms while indicating that care should be taken when using the Sinuosity to assess low frequency (<2 Hz) and low amplitude (<2 mm) profiles, and Root Mean Square, and Energy algorithms when assessing high frequency (>1 Hz) profiles.