Effects of Physical Processes and Sampling Resolution on Fault Displacement Versus Length Scaling: The Case of the Cantarell Complex Oilfield, Gulf of Mexico

Abstract

In this paper, we first review some factors that may alter the fault D max /L ratio and scaling relationship. The three main physical processes are documented as follows: (1) The D max /L ratio increases in an individual segmented fault, whereas it decreases in a fault array consisting of two or more fault segments. This effect occurs at any scale during fault growth and in any type of rock. (2) Vertical restriction decreases the D max /L ratio along the fault strike due to mechanical layers. (3) The D max /L ratio increases or decreases due to fault reactivation depending on the type of reactivation. Thus, using data from the normal faults of the Cantarell oilfield in the southern Gulf of Mexico, we document that the displacement (D max ) and length (L) show a weak correlation of linear or power-law scaling, with exponents that are much less than 1 (n & 0.5). This scaling relation is due to the combination of the physical processes mentioned above, as well as sampling effects, such as technique resolution. These results indicate that sublinear scaling (n & 0.5) can occur as a result of more than one physical process during faulting in a studied area. In addition to the physical processes associated with brittle deformation in the studied area, the sampling resolution dramatically affects the exponents of the D max -L scaling.

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“…(2022) and Xu et al. (2016) found that more segmented faults show a lower D max / L ratio, while individual fault segments accumulated more displacement for a given fault length, and this could be due either to an advanced maturity in the fault's evolution or to the fact that such fault grew in isolation and had no chances of linkage; Finally, in case where the fault experiences a reactivation in the opposite sense of slip (and this would be the case if we assume both the inflation first proposed by P. H. Schultz (1976), and the piecemeal caldera collapse suggested by Luzzi et al. (2021)), reverse faults reactivated as normal can show lower values of D max / L ratios (Kim & Sanderson, 2005).…”

“…(2022) and Xu et al. (2016) found that more segmented faults show a lower D max / L ratio, while individual fault segments accumulated more displacement for a given fault length, and this could be due either to an advanced maturity in the fault's evolution or to the fact that such fault grew in isolation and had no chances of linkage;…”

“…• Mechanical discontinuities (e.g., due to different materials in contact) can act as barriers for the propagation in depth, while laterally the length of the fault can keep growing, therefore causing a vertical fault restriction (Martin & Watters, 2022;Nicol et al, 1996;Wilkins & Gross, 2002); 2022) and Xu et al (2016) found that more segmented faults show a lower D max /L ratio, while individual fault segments accumulated more displacement for a given fault length, and this could be due either to an advanced maturity in the fault's evolution or to the fact that such fault grew in isolation and had no chances of linkage;…”

“…A power law relationship between displacement and length can be observed in the commonly used Equation : $$${D}_{\mathrm{max}}=\gamma {L}^{c}$$$ where γ is a constant depending on several factors (e.g., lithology, regional stress), and the exponent c depends on the nature of the scaling: a linear scaling law corresponds to c = 1 , while in the case of scale‐dependent geometries c is defined by values ≠ 1 (Kim & Sanderson, 2005). In cases where the scaling exponent is greater than 1 (e.g., 1.5 or 2), the power law can be defined as superlinear; on the other hand, if the c value is less than 1 (e.g., 0.5), the power law is defined as sublinear (Callihan & Klimczak, 2019; Xu et al., 2016).…”

“…(e.g., 1.5 or 2), the power law can be defined as superlinear; on the other hand, if the c value is less than 1 (e.g., 0.5), the power law is defined as sublinear (Callihan & Klimczak, 2019;Xu et al, 2016).…”