Paul T. Delaney

Formation and interpretation of dilatant echelon cracks

The relative displacements of the walls of many veins, joints, and dikes demonstrate that these structures are dilatant cracks. We infer that dilatant cracks propagate in a principal stress plane, normal to the maximum tensile or least compressive stress. Arrays of echelon crack segments appear to emerge from the peripheries of some dilatant cracks. Breakdown of a parent crack into an echelon array may be initiated by a spatial or temporal rotation of the remote principal stresses about an axis parallel to the crack propagation direction. Near the parent-crack tip, a rotation of the local principal stresses is induced in the same sense, but not necessarily through the same angle. Incipient echelon cracks form at the parent-crack tip normal to the local maximum tensile stress. Further longitudinal growth along surfaces that twist about axes parallel to the propagation direction realigns each echelon crack into a remote principal stress plane. The walls of these twisted cracks may be idealized as helicoidal surfaces. An array of helicoidal cracks sweeps out less surface area than one parent crack twisting through the same angle. Thus, many echelon cracks grow from a single parent because the work done in creating the array, as measured by its surface area, decreases as the number of cracks increases. In cross sections perpendicular to the propagation direction, echelon cracks grow laterally, each crack overlapping its neighbors, until the mechanical interaction of adjacent cracks limits this growth. Dilation of each crack pinches the tips of adjacent cracks into an asymmetrical form and introduces local stresses that can cause lateral growth along a curving, sigmoidal path. Sigmoidal echelon cracks may link at tip-to-plane intersections, leaving a step in the through-going crack wall. The geometry of dilatant echelon cracks may be used to infer spatial or temporal changes in the orientation of principal stresses in the Earth.

Surface deformation in volcanic rift zones

Abstract The principal conduits for magma transport within rift zones of basaltic volcanoes are steeply dipping dikes, some of which feed fissure eruptions. Elastic displacements accompanying a single dike emplacement elevate the flanks of the rift relative to a central depression. Concomitant normal faulting may transform the depression into a graben thus accentuating the topographic features of the rift. If eruption occurs the characteristic ridge-trough-ridge displacement profile changes to a single ridge, centered at the fissure, and the erupted lava alters the local topography. A well-developed rift zone owes its structure and topography to the integrated effects of many magmatic rifting events. To investigate this process we compute the elastic displacements and stresses in a homogeneous, two-dimensional half-space driven by a pressurized crack that may breach the surface. A derivative graphical method permits one to estimate the three geometric parameters of the dike (height, inclination, and depth-to-center) and the mechanical parameter (driving pressure/rock stiffness) from a smoothly varying displacement profile. Direct comparison of measured and theoretical profiles may be used to estimate these parameters even if inelastic deformation, notably normal faulting, creates discontinuities in the profile. Geological structures (open cracks, normal faults, buckles, and thrust faults) form because of stresses induced by dike emplacement and fissure eruption. Theoretical stress states associated with dilation of a pressurized crack are used to interpret the distribution and orientation of these structures and their role in rift formation.

Volume of magma accumulation or withdrawal estimated from surface uplift or subsidence, with application to the 1960 collapse of Kilauea Volcano

An elastic point source model proposed by Mogi for magma chamber inflation and deflation has been applied to geodetic data collected at many volcanoes. The volume of ground surface uplift or subsidence estimated from this model is closely related to the volume of magma injection into or withdrawal from the reservoir below. The analytical expressions for these volumes are reviewed for a spherical chamber and it is shown that they differ by the factor 2(1-v), where v is Poissons ratio of the host rock. For the common estimate v=0.25, as used by Mogi and subsequent workers, the uplift volume is 3/2 the injection volume. For highly fractured rocks, v can be even less and the uplift volume can approach twice the injection volume. Unfortunately, there is no single relation between the inflation of magma reservoirs and the dilation or contraction of host rocks. The inflation of sill-like bodies, for instance, generates no overall change in host rock volume. Inflation of dike-like bodies generates contraction such that, in contrast with Mogis result, the uplift volume is generally less than the injection volume; for v=0.25, the former is only 3/4 of the latter. Estimates of volumes of magma injection or withdrawal are there-fore greatly dependent on the magma reservoir configuration. Ground surface tilt data collected during the 1960 collapse of Kilauea crater, one of the first events interpreted with Mogis model and one of the largest collapses measured at Kilauea, is not favored by any one of a variety of deformation models. These models, however, predict substantially different volumes of both magma withdrawal and ground surface subsidence.

Deep magma body beneath the summit and rift zones of Kilauea Volcano, Hawaii

A magnitude 7.2 earthquake in 1975 caused the south flank of Kilauea Volcano, Hawaii, to move seaward in response to slippage along a deep fault. Since then, a large part of the volcanos edifice has been adjusting to this perturbation. The summit of Kilauea extended at a rate of 0.26 meter per year until 1983, the south flank uplifted more than 0.5 meter, and the axes of both the volcanos rift zones extended and subsided; the summit continues to subside. These ground-surface motions have been remarkably steady and much more widespread than those caused by either recurrent inflation and deflation of the summit magma chamber or the episodic propagation of dikes into the rift zones. Kilaueas magmatic system is, therefore, probably deeper and more extensive than previously thought; the summit and both rift zones may be underlain by a thick, near vertical dike-like magma system at a depth of 3 to 9 kilometers.

Volcanic spreading at Kilauea, 1976–1996

The rift system traversing about 80 km of the subaerial surface of Kilauea volcano has extended continuously since the M 7.2 flank earthquake of November 1975. Widening across the summit has amounted to more than 250 cm, decelerating after 1975 from about 25 to 4 cm yr−1 since 1983. Concurrently, the summit has subsided more than 200 cm, even as the adjacent south flank has risen more than 50 cm. The axes of the upper zones, about 10 km from the summit, subsided before 1983 at average rates of 9 and 4 cm yr−1, respectively, and at rates of 4 and 3 cm yr−1 since. The middle southwest rift zone is also subsiding and, at the other end of Kilaueas subaerial rift system, subsidence along the lower east rift zone has averaged 1–2 cm yr−1. Deformation of Kilaueas south flank has been continuous, although subject as well to displacements caused by major rift zone seismic swarms. Whereas horizontal strains across the subaerial south flank seem to have been generally compressive after 1975, they have been extensional since about 1980 or 1981, interrupted only by the east rift zone dike intrusion of 1983. Because the magnitudes of these contractions and extensions are much less than the extension across the rift system, the subaerial south flank is apparently sliding seaward on its basal decollement more than it is accumulating horizontal strains within the overlying volcanic pile. Kilauea suffers from gravitational spreading made even more unstable by accumulation of magma along the rift system at depths in excess of about 4–5 km in the presence hot rock incapable of withstanding deviatoric stresses. This seismicly quiescent zone decouples the south flank from the rest of Hawaiis volcanic edifice; the rift zones at lesser depths exhibit a more brittle and, therefore, sporadic extensional behavior. Judging from the modern extension record of the summit, which both predates the M 7.2 earthquake of 1975 and has outlived its 10-year period of aftershocks, Kilauea will continue to spread along its rift system as its south flank slips seaward to accommodate the accretion of magma and its relatively dense olivine-rich differentiate.

Motion of Kilauea Volcano during sustained eruption from the Puu Oo and Kupaianaha Vents, 1983–1991

Kilauea erupted almost continuously from January 1983 through 1991. Although the summit began subsiding during the rift zone dike intrusion that initiated this eruption, remarkably steady ground surface motions began in late 1983 after a magnitude 6.6 earthquake beneath the slopes of nearby Mauna Loa volcano and continued until the onset of brief upper east rift zone earthquake swarms in late 1990. During these 7 years the summit and upper rift zones subsided up to 10–11 and 4–8 cm yr−1, respectively, and summit baselines contracted up to 6 cm yr−1. Baselines directed northward from the summit to stations on Mauna Loa extended at rates up to 7 cm yr−1, and a baseline from south of the summit to Mauna Loa extended 4 cm yr−1. Much of this extension is inconsistent with deformation caused solely by summit magma reservoir collapse and more likely reflects rifting as the south flank of the volcano moved seaward from the summit and rift zones. Farther from the summit, baselines crossing the south flank extended up to 2 cm yr−1, and a south flank tide gauge rose 2 cm yr−1; the lower east rift zone, 40–50 km from the summit, subsided about 2 cm yr−1. Motion on Kilauea, then, is broadly consistent with slip along low-angle south flank faults, generating subsidence that is focused at the summit and along the rift system behind the faulting and uplift along the coastal south flank ahead of it. Dislocation models that combine these elements show that much of Kilaueas edifice migrated seaward, producing ground surface motions along the south flank of up to about 6 cm yr−1. The magnitude 6.1 earthquake of 1989 punctuated these motions along the eastern south flank, producing more than 25 cm of seaward displacement and, 15 km east of the epicenter, up to 24 cm of subsidence south of the lower east rift zone. Unlike the magnitude 7.2 south flank earthquake of 1975, the 1989 event was preceded neither by summit magma reservoir inflation nor by rift zone dike intrusions and accompanying compression of the south flank. Deformation was probably caused by the weight of the volcanic overburden and by ongoing dilation and slip within the rift system.

Geodetic analysis of dike intrusion and motion of the magma reservoir beneath the summit of Kilauea Volcano, Hawaii: 1970–1985

We use leveling and trilateration data collected on Kilauea volcano to constrain the location of deformation sources caused by magma accumulation, intrusion, and eruption. For the 13 inflationary epochs examined, combinations of an expanding point source and one or two opening rectangular dislocations mimic inflation of the summit reservoir and formation of dike(s), respectively. The combined model adequately accounts for the deformation data and is consistent with the seismicity observed during each epoch. For 10 deflationary epochs, however, the data require only a contracting point source. Confidence in these results is gained by noting that locations of the sources of both inflation and deflation are coincident, within the observed uncertainties of the data, the function of network geometry, and the inversion procedure. It appears, therefore, that magma accumulation at Kilauea volcano may be characterized by the growth of dikes during inflation of the summit reservoir. Drainage of the reservoir, on the other hand, is not accompanied by significant closure of dikes. In contrast to previous studies (e.g., Fiske and Kinoshita, 1969; Dvorak et al., 1983) that do not include the dislocation (or dike growth) component of summit magma accumulation and concluded that the source of inflation migrates over a 5 km2 area, we find that a single magmatic reservoir source accounts for data collected during all inflationary and deflationary epochs, results, which compare favorably with those obtained from the point ellipsoid model, can be used to estimate the distribution of stresses within the volcano in the near field of the source.

Physical processes of shallow mafic dike emplacement near the San Rafael Swell, Utah

Some 200 shonkinite dikes, sills, and breccia bodies on the western Colorado Plateau of south-central Utah were intruded from approximately 3.7 to 4.6 Ma, contemporaneous with mafic volcanism along the nearby plateau margin. Thicknesses of dikes range to about 6 m; the log-normal mean thickness is 85 cm. Despite the excellent exposures of essentially all dikes in strata of the Jurassic San Rafael Group, their number is indeterminate from their outcrop and spacing because they are everywhere greatly segmented. By our grouping of almost 2000 dike segments, most dikes are less than 2 km in outcrop length; the longest is 9 km. Because the San Rafael magmas were primitive and probably ascended directly from the mantle, dike lengths in outcrop are much less than their heights. The present exposures probably lie along the irregular upper peripheries of dikes that lengthen and merge with depth. Orientations of steps on dike contacts record local directions of dike-fracture propagation; about half of the measurements plunge less than 30°, showing that lateral propagation at dike peripheries is as important as the vertical propagation ultimately responsible for ascent. The San Rafael dikes, now exposed after erosion of about 0.5–1.5 km, appear to thicken and shorten upward, probably because near-surface vesiculation enhanced magmatic driving pressures. Propagation likely ceased soon after the first dike segments began to feed nearby sills or vented to initiate small-volume eruptions. Most of the dikes are exposed in clastic strata of the Jurassic San Rafael Group. They probably acquired their strikes, however, while ascending along well-developed joints in massive sandstones of the underlying Glen Canyon Group. Rotation of far-field stresses during the emplacement interval cannot account for disparate strikes of the dikes, which vary through 110°, most lying between north and N25°W. Rather, the two regional horizontal principal stresses were probably nearly equal, and so the dominant N75°E direction of dike opening was not strongly favored. Across the center of the swarm, about 10 to 15 dikes overlap and produce 15–20 m of dilation. Many are in sufficient proximity that later dikes should be thinner than earlier ones if neither the magma pressures nor regional stresses were changing during the emplacement interval. However, dike thicknesses vary systematically neither along the length of the swarm nor in proportion to the number of neighboring dikes. It appears that crustal extension during the magmatic interval relieved compressive stresses localized by intrusion.

A fault model for the 1989 Kilauea South Flank Earthquake from leveling and seismic data

The geometry of the fault that ruptured during the M6.1 south flank earthquake on Kilauea volcano in 1989 is determined from leveling data. The elastic dislocation, in a homogeneous elastic half-space, that best fits the data is found using a nonlinear inversion procedure. The best fitting model is a gently dipping thrust fault that lies at 4 km depth. This is significantly shallower than the 9 km hypocentral depth determined from the local seismic network. Two-dimensional finite-element calculations indicate that at least part of this discrepancy can be attributed to the focusing of the surface deformation by the upper few kilometers of compliant, low-density lavas. We conclude that it is important to include realistic elastic structure to estimate source geometry from geodetic data.

Sources of crustal deformation associated with the Krafla, Iceland, eruption of September 1984

A decade-long plate-boundary rifting episode in northern Iceland ended with the September 1984 fissure eruption of Krafla volcano. We apply a nonlinear inversion method to geodetic data collected before and after the eruption to infer the location, geometry, and strengths of deformation sources associated with the eruption. The net outflow of magma from a 3-km-deep magma chamber beneath the Krafla caldera was 30−120× 106 m³. A similar volume of magma, 50−70×106 m³, was emplaced in a 1-meter-wide, ∼9-km-long dike extending from the surface to ∼7 km depth. Furthermore, at least 110×106 m³ of magma erupted. Accordingly, a surplus of magma must have been expelled from a second reservoir, the location of which, although uncertain, is likely to lie at depths greater than ∼5 km beneath Krafla volcano. It would be difficult to detect this deeper source because of the narrow aperture of the geodetic networks.