This paper presents the results of a global and regional stochastic analysis of near-ridge abyssal hill morphology. The analysis includes the use of Sea Beam data for the estimation of stochastic parameters up to order 4. These parameters provide important quantitative physical information regarding abyssal hills, including their rms height, azimuthal orientation, characteristic width, aspect ratio, Hausdorff dimension, skewness, tilt, and peakiness. The global data set consists of 64 Sea Beam swaths near the Rivera, Cocos, and Nazca spreading sections of the East Pacific Rise, the Mid-Atlantic Ridge, and the Central Indian Ridge. In one form of analysis, the parameters are averaged among spreading rate bins. Each of the spreading rate subsets can be identified as unique from the others in at least one aspect. The slowest spreading rate subset (Mid-Atlantic data) exhibit the largest scales (rms height and characteristic width and length) of abyssal hills. These parameters generally decrease as spreading rate increases up to the fast spreading rate data (Pacific-Cocos) but increase going from fast to very fast (Pacific-Nazca) spreading rate data. This indicates some complexity in the relationship between spreading rate and abyssal hill morphology. The plan view aspect ratio is nearly twice as large for the fast spreading rate data than for any of the other subsets and is smallest for the very fast spreading rate data. The fractal dimension is nearly identical for all spreading rate subsets. The vertical skewness is positive for the slow and medium spreading rate data, indicating larger peaks than troughs, and negative for the fast spreading rate data, indicating larger troughs than peaks. The kurtosis, or peakiness is everywhere larger than the Gaussian value of 3 and tends to be larger in the Atlantic than the Pacific. The tilting parameter provides substantial evidence indicating steeper inward facing slopes in the medium and fast spreading rate data, but only marginal evidence for it in the slow spreading rate data. From an analysis of correlations among parameters it is found that subsets sometimes behave differently from the entire data set.

In particular, while over the global data set the characteristic width exhibits a well-resolved positive trend when plotted versus rms height, these parameters exhibit a more gradual positive trend in the Mid-Atlantic data and a negative trend in the Pacific-Cocos data. In addition, the plan view aspect ratio, while generally uncorrelated with rms height for the global data set, is positively correlated with rms height for the Pacific-Cocos data set. These results emphasize a strong uniqueness of the Pacific-Cocos data relative to the rest of the data global set. The Pacific-Cocos data consist of 27 swaths concentrated between the Siqueiros and Orozco fracture zones. These data provide very good abyssal hill coverage of this well-mapped and well-studied region and form the basis of a regional analysis of the correlation between ridge morphology and stochastic abyssal hill parameters. In this analysis, it is found that abyssal hill parameters are correlated with the depth of the adjacent ridge axis, indicating that the relative abundance in magma supply, which likely controls the ridge axis depth, may also be an important influence on the formation of abyssal hills. ¿ American Geophysical Union 1991