Fractal Interrelationships in Field and Seismic Data

Size scaling interrelationships are evaluated in this study using a fractal model. Fractal models of several geologic variables are examined and include fracture patterns, reflection travel times, structural relief, drainage, topographic relief and active fault patterns. The fractal properties of structural relief inferred from seismic data and structural cross sections provide a quantitative means to characterize and compare complex structural patterns. Studies were conducted using seismic data from the Granny Creek oil field in the Appalachian Plateau. Previous studies of the field reveal that subtle detached structures present on the limb of a larger structure are associated with enhanced production from the field. Vertical increases of fractal dimension across the zone of detachment provide a measure of the extent to which detachment has occurred. The increases of fractal dimension are greatest in the more productive areas of the field. A result with equally important ramifications is that fracture systems do not appear to be intrinsically fractal as is often suggested in the literature. While examples of nearly identical patterns can be found at different scales supporting the idea of self-similarity, these examples are often taken from different areas and from different lithologies. Examination of fracture systems at different scales in the Valley and Ridge Province suggest that their distribution become increasingly sparse with scale reduction, and therefore are dissimilar or non-fractal. Box counting data in all cases failed to yield a fractal regime. The results obtained from this analysis bring into question the general applicability of reservoir simulations employing fractal models of fracture distribution. The same conclusions were obtained from the analysis of 1D fracture patterns such as those that might appear in a horizontal well. Field studies of near-surface structure yielded results consistent with those obtained from the analysis of seismic data; structural relief exhibits fractal behavior. Along strike variations in the fractal dimension of structural cross sections were systematic and provided a quantifiable measure of visible changes in mapped surface structure. Links between the fractal characteristics of structural relief to the patterns of accompanying fracture systems were not uncovered. Several variations in fracture pattern are encountered, however, the degree to which these variations are the result of scale change, has not been evaluated. The methods of fractal analysis can be applied to characterize fracture patterns, however, the presence of scale-variance requires that such analysis be carried out at a common scale. Detailed investigations of surface topography in the Valley and Ridge area reveal a linear relationship between variations in the fractal dimensions of structural and topographic relief. Much of this interrelationship is undoubtedly related to structurally controlled variations in lithology across the surface. However, significant topographic changes occur across the Parsons CSD (cross-strike structural discontinuity) in areas where the large scale structure is invariant, and suggests that variations in the intensity of fracturing are the predominant erosional control in these areas. The fractal characteristics of topography in the Plateau revealed little variance, and provided no hint as to the presence of faults forming the margin of the Rome Trough. This is not surprising since seismic data reveal that the deep structures of the Trough were largely inactive during deposition of the Pennsylvanian age sediments exposed at the surface across the area. The dependence of topographic development on local structure was also investigated in an active tectonic area in central Japan. Analysis reveals a positive correlation between the fractal dimensions of active faults in the region and those of associated topographic relief. The fault zones are zones of weakness along which movement has occurred. Consequently, these zones are more easily weathered and eroded, contributing significantly to the topographic expression of the region. Exceptions to the relationship suggest that other factors may exert significant control on the development of topography in those regions, or that the active faults in those regions have not been detected or mapped. These relationships may be useful for earthquake hazard assessments. The investigations conducted under this contract have carried fractal analysis from the stage of simple identification of fractal behavior to that of establishing interrelationships between the fractal characteristics of complex variables, and between fractal properties and geologic processes. Changes in the fractal characteristics of seismic reflection events, for example, allow one to quantify the relative abundance of detached structures. The fractal characteristics of surface topography can be used to predict those of near-surface structure. Future work is suggested by the results of work conducted under this contract. The ability to predict fracture behavior on the basis of larger scale structural interrelationships observable in seismic data or mapable in the field has not been solved. Further study incorporating stochastic and scale invariant descriptions of fracture patterns may reveal predictable relationships between the complexity of fracture networks and surrounding structure.