Mapping and modeling of radial fracture patterns on Venus

Abstract

Abstract. Synthetic aperture radar images indicate numerous radial fracture systems on Venus. The formation of these systems has been attributed either to surface deformation related to subsurface dike emplacement or to fracturing caused by domical uplift above an ascending magma plume. We evaluate the dike emplacement hypothesis by investigating the relationship between the process of subsurface dike emplacement and the geometric attributes of radial fracture patterns, assuming the surface fracture patterns correspond to the patterns of dikes about a magma chamber below the volcanic summit. We select a radial fracture system for mapping and model its formation using a two-dimensional analysis which idealizes the chamber as a pressurized hole in an elastic plate subject to a remote biaxial stress field. Radial fractures correspond to maximum principal stress trajectories, and the pattern of these trajectories is controlled primarily by four variables: the chamber radius, the magma pressure, the remote differential stress, and the remote principal stress direction. We find that stress trajectories also depend on the remote mean stress and that the location of isotropic points in the trajectory pattern can be used to interpret the mean stress state. These models are used to estimate the remote loading conditions under which dikes were emplaced. The mapped fracture pattern is consistent with dikes emplaced under remote differential stress conditions ranging from 2 to 8 MPa, calculated over a range of possible emplacement depths from 1 to 9 km. This is consistent with regional stress states on Earth.

Calculation of dike trajectories from volcanic centers

“…It is Figure 2. (top) Circular hole of radius R and internal pressure P in an elastic body subject to a biaxial stress at infinity split into an isotropic mean stress field M and a deviatoric stress field of magnitude S. (bottom) Circular hole of overpressure ÁP in an elastic body subject to a deviatoric remote stress of magnitude S. important then to remember both that the stresses s ij in equation (8) denote the deviations from the mean compression and not the true stresses of equation (7) and that the source pressure ÁP is the source overpressure P + M and not the actual source pressure P. Koenig and Pollard [1998] criticize McKenzie et al [1992] for setting the remote mean stress equal to zero by using (8) and thus ignoring the effect of mean stress on trajectories. In fact, there is no problem here provided the pressure P in McKenzie et al [1992] is understood to be the overpressure relative to the mean stress and not the actual pressure (the paper does not explicitly define P).…”

“…[32] A second example is furnished by Koenig and Pollard [1998] study of a dike swarm on Venus. While they achieved a reasonably good fit between principal-stress trajectories and the Figure 8.…”

“…The far-field stresses are s xx 1 = M À S, s yy 1 = M + S, and s xy 1 = 0; the terms involving P are just isotropic dilation from a source with overpressure P + M (which take the simple form s rr = À(P + M )(R/r) 2 , s qq = (P + M )(R/r) 2 , s r q = 0 in cylindrical coordinates); the remaining terms involving S represent the perturbation to the far-field stress due to the presence of the hole and are required to satisfy the constant-pressure boundary conditions s rr = ÀP and s r q = 0 on r = R. Koenig and Pollard [1998] calculate their principal-stress trajectories from equation (7).…”

“…Thus the swarm patterns exhibiting a transition from radial to subparallel propagation suggest that a regional stress field existed in the crust at the time the dikes were injected. For example, calculations considering the superposition of the stress field due to a pressurized source and a biaxial regional stress field showed that reasonable agreement in pattern could be obtained by judicious choice of the relative magnitudes of the stresses [Baer and Reches, 1991;McKenzie et al, 1992;Koenig and Pollard, 1998]. The transition from radial to subparallel geometry is located where the regional stress field begins to dominate that due to the pressurized source.…”

“…[3] This concept of principal-stress trajectories has been applied to dike swarms, which form characteristic geometrical patterns [e.g., Odé, 1957;Muller and Pollard, 1977;Baer and Reches, 1991;McKenzie et al, 1992;Koenig and Pollard, 1998]. These patterns are observed on both Earth and Venus and are considered to be the result of subhorizontal propagation in different directions from a shallow source region (see Ernst et al [1995] for a review).…”