Geodetic measurements and mechanical models of rifting in onshore segments of mid-ocean ridges



NSF Geophysics EAR 0810134

Kurt L. Feigl University of Wisconsin-Madison


Timothy Masterlark University of Alabama


Abstract

The research supported by this proposal is an international collaboration between U.S. scientists from the University of Wisconsin and the University of Alabama-Tuscaloosa and their Icelandic colleagues that is aimed at quantifying the role of magmatism in accommodating spreading at mid-oceanic ridges. The investigators are performing an impulse-response experiment, in which the impulse is the injection of magma at the rift, and the response is the deformation recorded by geodesic and seismological methods. The research focuses on extension related to an intrusive event from the northern volcanic zone of Krafla in Iceland in 1975-1984, where the width of the axial valley was increased by several meters due to the intrusion of dikes, resulting in a century?s worth of spreading at the long-term average rate of about two centimeters per year. After the magma supply diminishes, the extension continues over years or decades, and finally slows as the stresses relax. The research is addressing the following questions: (1) What is the geometry of the magmatic plumbing? (2) How does the magmatic pressure in the plumbing evolve with time? (3) What are the material properties of the rift structure? Providing quantitative answers to these questions requires answering a more fundamental question: which constitutive relation (rheology) best describes the rock below the lithosphere? Accordingly, the primary goal of the research is determining the constitutive relations and rheologic properties governing rifting. The research is contributing to the understanding of the mechanics of rifting at mid-ocean ridges, a fundamental process in plate tectonics. The research is fostering the training of a doctoral graduate student and is supporting the research efforts of an early career scientist. Research results and the modeling protocols developed during this study will be disseminated among the geological community. From a societal standpoint, the research is leading to a broader understanding of magmatic and seismological hazards associated with rifting events. The research is supported by the Geophysics Program and Marine Geology and Geophysics Programs of the National Science Foundation (NSF).

Introduction


Between 1978 and 1989, the rift between North America and Eurasia widened by more than 4 meters (Figure 1). This amount represents over 200 years of spreading at the long-term average rate of ~2 cm/yr. This simple observation implies that the process of rifting at mid-ocean ridges is episodic in time and localized in space. In other words, such rifting events are transients. They accommodate plate divergence through a combination of diking, faulting, and stretching. At slow-spreading ridges such as the Mid Atlantic Ridge (MAR) with ample magma supply, episodic dike injections accommodate most of the plate motion [e.g., Buck et al., 2005]. Under these conditions, the ensuing rifting episode concentrates magmatic and seismic activity near the rift axis during a brief time [Abdallah et al., 1979; Ruegg et al., 1979; Tarantola et al., 1979; Ruegg and Kasser, 1987; Bergman and Solomon, 1990; Vigny et al., 2004; Buck et al., 2005; Cattin et al., 2005; Kendall et al., 2005; Tentler, 2005; Keir et al., 2006; Sigmundsson, 2006; Wright et al., 2006; Rowland et al., 2007; Tentler and Temperley, 2007]. After such an event, the extension around the rift continues over a time scale of years to decades as the stresses relax (Figure 2). Conceptually, one can imagine a pulse of strain gradually propagating away from the rift axis and creating stress and strain fields that are functions of both time and space. Measuring and modeling them can test hypotheses for the rifting process. Such is the objective of the proposed research.

As transients, rifting episodes provide rare and precious opportunities to perform a rheological experiment. The dike intrusion constitutes the impulse. The subsequent deformation constitutes the response. By modeling the impulse (stress), measuring the response (strain), and interpreting the constitutive relation between the two, we can infer the rheology. For example, if the relaxation time constant [Turcotte and Schubert, 2002] of the stress and strain fields is of the order of 1 to 10 years, then we would infer a viscosity of the order of 1018 to 1019 Pa⋅s, assuming a simple Maxwell viscoelastic rheology and a rigidity of ~30 GPa. Because measuring the response with geodesy is easier on dry land than at sea, the list of relevant natural laboratories is short:

„    Krafla in Iceland    1975-1984    Sigmundsson [2006]
„    Asal in Djibouti    1978    Cattin et al. [2005]
„    Dabbahu in Ethiopia    2005    Wright et al. [2006]

 Although all three events were observed using modern geodetic and seismologic techniques, the Icelandic case has the largest observational data set. Accordingly, we propose a measuring and modeling study in the Northern Volcanic Zone (NVZ) of Iceland to address the following questions:

„    What is the geometry of the magmatic plumbing?
„    How does the magmatic pressure in the plumbing evolve with time?
„    Which constitutive relation (rheology) best describes the rock below the lithosphere?
„    What are the material properties of the rift structure?

In our conceptual model, the magmatic ŅplumbingÓ includes: a deep magma chamber (~20 km depth), a shallow chamber (~3 km depth), and rift-parallel dikes propagating from the chambers [de Zeeuw-van Dalfsen et al., 2004]. During the rifting episode, magma moves from the deep chamber into the shallow one, which inflates and causes uplift at the land surface. The magma then flows outwards along the dikes, causing deflation of the shallow magma chamber and subsidence of the overlying caldera [Buck et al., 2006; Sigmundsson, 2006]. After the magma injection ceases, the resulting pulse of extensional strain propagates slowly away from the rift, as sketched in Figure 2. The pulse would arrive at a benchmark 50 km away from the rift axis some 5 years later, based on a very simple 1-dimensional diffusive model [Foulger et al., 1992]. It is the details of the deformation fieldÕs distribution in space and evolution in time that will provide strong constraints on our modeling effort. For example, the rate of extension across a 100-km wide transect was at least 4 cm/yr in 2000, according to the GPS and INSAR measurements described below. This rate is still twice as fast as the 19 mm/yr value predicted for the divergence of North America and Eurasia from the NUVEL-1A plate motion model [DeMets et al., 1990; DeMets et al., 1994]. Assuming that the long-term, far-field rate is accommodated by rifting episodes that each produce 4 m of opening, one would expect a recurrence time of 200 years between two such episodes. Accordingly, the instantaneous rate of extension will continue to decrease in the years to come, presumably to values well below the long-term average. In other words, the available geodetic measurements can measure the post-rifting transient in the NVZ study area. Thus, the proposed impulse-response experiment is feasible.


The primary goal of the proposed research is to understand the processes driving plate divergence by evaluating which constitutive laws and rheologic material properties govern spreading at mid-oceanic ridges. Specifically, we will test six hypotheses:

I.    The deformation in NVZ after the 1979-1984 Krafla rifting episode had not reached a steady state in 2000, implying that post-rifting stress relaxation occurs on a time scale of decades.
II.    An episode of magma injection at the rift axis is a necessary and sufficient initial condition to describe the stress and strain observed on time scales shorter than a century. 
III.    The effective viscosity is several orders of magnitude smaller in the asthenospheric upper mantle than in the lithospheric lower crust.
IV.    The 3-dimensional distribution of material properties modulates the stress and strain fields
V.    The viscoelastic constitutive relation involves a non-linear (e.g., power-law) dependence of strain rate on deviatoric stress.
VI.    The deformation field as observed by geodetic measurements is relatively insensitive to changes in viscosity caused by temporal changes in temperature over time scales less than ~100 yr.

To test these hypotheses, we will measure, model, and intepret the deformation following the 1979-1984 Krafla Fires rifting episode in Iceland. The measuring component of the project will analyze the rich observational set that has already been acquired. In particular, the measurements include geodetic time series from: (1) interferometry using satellite radar images (INSAR) and (2) Global Positioning System (GPS) surveys. The modeling component will employ 3D finite element modeling (FEM) to account for: (1) the timing and geometry of the magma chambers, dikes and faults; (2) the spatial distribution of material properties; and (3) the constitutive (rheological) relations between stress and strain. We plan to continue our collaboration with our colleagues in Iceland, particularly Freysteinn Sigmundsson of the Nordic Volcanological Center (NVC) at the University of Iceland, as described in his letter of support.





Figure 1. Displacements as large as 4 meters in the Northern Volcanic Zone of Iceland during the Krafla Fires rifting episode. The benchmarks were surveyed by electronic distance measurements in March 1978 and March 1989. From Tryggvason [1991] as reproduced by Sigmundsson [2006].



Figure 2. Conceptual sketch of displacement and velocity as a function of time over three cycles of periodic rifting. For a point at distance x from the rift axis at time t, the cumulative displacement U(x, t) is the sum of the displacements from all previous rifting episodes Σ °i=1 u(x, t + iT) that recur with period T. In this case, a dike with half-width U0 = 1 m intrudes at x = 0 every T = 100 years. The displacement u(x, t) (solid line) and velocity du/dt (dashed line) for each individual rifting pulse are calculated from the solution to the stress-diffusion equation (1) derived by Foulger et al. [1992] for a location at  x = 50 km from the rift axis and a stress diffusivity of κ = 1.1 m2/s.



Figure 3. Profile of rift-perpendicular component of GPS velocity for three different time intervals. The fastest rates occur in the first measurement interval (1987 Š1990) during the post-rifting phase. The strike of the profile is perpendicular to the rift axis and centered at Krafla. Modified from Volksen [2000] as reprinted in Sigmundsson [2006].



Figure 4. Range change for the time interval 1993 and 1999 extracted from the interferogram of Figure 8, along a profile perpendicular to the rift axis and centered at Krafla. Since the (descending) ground track of the satellite is off the east end of the profile, the decrease in range toward the east indicates motion toward the radar satellite. The bump in the profile corresponds to deflation at Krafla central volcano. The unit vector from Krafla to ERS is [E, N, U] = (+0.39, Š0.11, +0.91), implying that the (full) rate of extension is 51 mm/yr, assuming horizontal motion perpendicular to the rift axis.



Figure 5. Map showing location of volcanic systems along the plate boundary in the Northern Volcanic Zone (NVZ) in Iceland. The main branches of the Tjšrnes Fracture Zone, the Gr’msey seismic zone and the Hœsav’k-Flatey faults are delineated by epicenters of 1995-2003 (dark red dots), provided by the Icelandic Meteorological Office. Light red dots are epicenters of events during the Krafla rifting episode. Fissure swarms (dark stripes), central volcanoes (shown by thin, closed lines), and calderas are from Einarsson and S¾mundsson [1987]. Small black box outlines area covered by the INSAR observations. (Inset) Arrows indicate the direction of plate spreading. Large swath outlines the area covered by SAR images acquired by the ERS and ENVISAT satellites in their orbital track 9. Figure and caption adapted from Buck et al. [2006].



Figure 6. INSAR maps (interferograms) showing observed (a) and modeled (e) values of phase change around the Krafla rift segment between 1993 and 1999. The location is outlined in Figure 2. The best-fit models include location of a dike modeled as a tensile dislocation (purple line) and two spherical magma chambers modeled with the Mogi [1958] formulation (black stars). The residual field (i) is the difference between the observed and modeled fields. One fringe represents 28 mm of change in range. Background shading is radar amplitude (backscatter). Figure from Zeeuw-van Dalfsen et al. [2004].



Figure 8. INSAR map (interferogram) showing observed values of phase change around the Krafla rift segment between 1993 and 1999. The location is outlined in Figure 2. One fringe represents 28 mm of change in range, shown increasing to the right on the color bar below. Range change along profile through Krafla (second white line from top) is shown in . The epochs in this pair are 1993-JUN-26 (ERS-1 orbit number 10174) and 1998-AUG-18 (ERS-2 orbit number 17398). The orbital separation is less than 2 m, corresponding to an altitude of ambiguity over 5400 m. The Doppler separation is 0.14 PRF. The time separation is over 5 years. Although these three values are exceptional, several dozen other interferograms in the NVC data set show equally clear fringes.

Geodetic Measurements and Numerical Models of Rifting in Northern Iceland for 1993Š1999
by Brett Brady Carr
A thesis submitted in partial fulfillment of the requirements for the degree of
Master of Science (Geophysics) at the
UNIVERSITY OF WISCONSIN-MADISON 2008






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