Postseismic Motion Research Articles

Time‐dependent models of vertical deformation for the Yellowstone‐Hebgen Lake Region, 1923–1987

Results of repeated levelings have been used to determine the patterns of elevation change associated with the Yellowstone caldera, and apparent viscoelastic rebound following the magnitude 7.3 earthquake near Hebgen Lake in 1959. Models with alternative treatments for nonuniform height change were utilized. Area‐wide levelings in 1923, 1975–1977, and 1987 in Yellowstone National Park allowed derivation of uplift velocities for the periods before and after 1976. Maximum uplift velocity for the earlier period was 14 mm/yr, causing 90 cm of height change from 1923 to 1984. Recent annual levelings on the east side of the caldera show a cessation of uplift in 1984–85, and the beginning of rapid subsidence; −19 mm/yr from 1985 to 1989. The long‐term uplift correlates closely with the caldera rim. After structuring the leveling observations to be insensitive to the 1959 coseismic deformation (−6 m) at Hebgen Lake, the broader spatial pattern of postseismic rebound was resolved, showing uplift of at least 32 cm. As a group, the relevelings converging at nearby West Yellowstone were accomplished at various times, which allowed selection of a best model to fit the temporal character of postseismic motion. The preferred model has a 2‐year decay period indicating that uplift stopped by 1970. Supplementary indications of the uplift near Hebgen Lake were obtained by comparing Global Positioning System data to earlier levelings, facilitated by a new precise geoid by D. G. Milbert and W. T. Dewhurst (submitted manuscript, 1990).

Postseismic Movements after the 1891 Great Nobi Earthquake

Postseismic Movements after the 1891 Great Nobi Earthquake

Earthquake deformation cycle in the Andean Back Arc, western Argentina

Repeated leveling surveys conducted in 1938, 1967, 1975–1976, 1978–1979, 1980, and 1981 provide information on preseismic, coseismic, and postseismic movements associated with the Ms ∼ 7.4 1977 Caucete, Argentina, earthquake sequence. The spatial pattern and amount of uplift (∼1 m) that accompanied the earthquake suggest 4 m of slip on a north‐south trending, west dipping fault, buried 17 km below the surface, with a dip of 35°, a downdip width of 24 km, and a length of 80 km. These fault parameters are generally consistent with the seismic focal mechanism, the moment of the double main shock, and the distribution of aftershocks. Vertical movements during the first preseismic period (1938–1967), while an order of magnitude smaller, have a spatial pattern similar to the observed coseismic movements. The second period of preseismic deformation (1967–1976) is characterized by movements opposite those which accompanied the earthquake (∼2±1 cm of relative subsidence). During the first postseismic interval (1978–1980), deformation continued in the same sense as the coseismic movements (an additional 10±1 cm of relative uplift). Subsequent postseismic movements (1980–1981) were opposite in sense to the coseismic deformation (∼12±1 cm of relative subsidence). We suggest that the preseismic movements for the 1938–1967 time period result from reverse slip (∼50 cm) on a downdip section of the 1977 earthquake fault. This slip may have been induced by a Ms ∼ 7.5 earthquake that occurred near San Juan in 1944 or may represent coseismic slip for a M ∼ 6.5 earthquake that occurred in 1941. Deformation during the second preseismic period (1967–1976) is interpreted as being due to steady strain accumulation on the fault (∼9 mm yr−1). The initial postseismic movements (1978–1980) are roughly consistent with afterslip on the 1977 earthquake fault (∼40 cm) in the same sense as the coseismic slip. The second phase of postseismic deformation may represent the period of rapid postseismic recovery (i.e., strain accumulation) observed previously in interplate areas. There is some evidence that strain accumulation following the earthquake began on the updip section of the fault. This process of strain accumulation may be responsible for the fact that the 1977 main shock initiated at the updip end of the coseismic fault. Assuming that the time predictable model of earthquake occurrence is applicable to this area, we estimate that the next earthquake on the 1977 earthquake fault will occur in 200–600 years.

The effects of post-seismic motions on the moment of inertia of a stratified viscoelastic earth with an asthenosphere

Summary. We give the analytical formulation for calculating the transient displacement of fields produced by earthquakes in a stratified, selfgravitating, incompressible, viscoelastic earth. We have evaluated the potential of viscous creep in the asthenosphere in exciting the Chandler wobble by a four-layer model consisting of an elastic lithosphere, a two-layer Maxwell viscoelastic mantle, and an inviscid core. The seismic source is modelled as an inhomogeneous boundary condition, which involves a jump condition of the displacement fields across the fault in the lithosphere. The response fields are derived from the solution of a two-point boundary value problem, using analytical propagator matrices in the Laplace-transformed domain. Transient flows produced by post-seismic rebound are found to be confined within the asthenosphere for local viscosity values less than 1OZoP. The viscosity of the mantle below the low-viscosity channel is kept at 1OZ2P. For low-viscosity zones with widths greater than about 100 km and asthenospheric viscosities less than lOP, we find that viscoelasticity can amplify the perturbations in the moment of inertia by a factor of 4-5 above the elastic contribution within the time span of the wobble period. We have carried out a comparative study on the changes of the inertia tensor from forcings due to surface loading and to faulting. In general the global responses from faulting are found to be much more sensitive to the viscosity structure of the asthenosphere than those produced from surface loading.

Deformation of the Mitaka Rhombus: Strain buildup following the 1923 Kanto earthquake, central Honshu, Japan

Frequently repeated surveys of a local network near Tokyo provide considerable detail on the horizontal strain changes immediately adjacent to the rupture zone of the M = 8.1 Kanto earthquake. Changes in the three independent tensor strain components are determined for 35 epochs during 1916–1980 to a precision of about ±1.5 μstrain. No significant shear or elongational strain changes preceded the earthquake; a change in dilational strain is marginally significant. Postseismic movements are large, accumulating to 40% or more of the coseismic strain drop. They have at least two time scales. A distinct short‐term transient lasting less than a year is explained well by slip or localized deformation that occurs downdip of the coseismic rupture plane and has a time constant of about 3 months. More complex, longer‐period postseismic movements continue for at least another 10 years. Their precise duration, as well as the transition to presumably steadier interseismic deformation, is obscured by notable irregularities in the strain buildup at Mitaka. As a result, neither the interseismic strain rate nor the occurrence time of the next Kanto earthquake can be reliably estimated from these observations.

Releveling evidence for crustal deformation in the United States

Abstract We have reduced and analyzed over 90% of existing U.S. National Geodetic Survey releveling observations, in order to evaluate the implications of these measurements for contemporary crustal movements. The data are displayed both in profile form (movement versus distance along route) and, where adequate coverage is available, as maps of apparent elevation change. Our analysis involves: 1. (1) evaluating the reliability of the leveling measurements using modified geodetic checks as well as through comparison with independent measurements of crustal movement (e.g., tide and lake level measurements, seismological evidence, tilt and strain observations); 2. (2) interpreting what appear to be real movements in light of other geological and geophysical information on crustal dynamics. Empirical analysis of the U.S. releveling data base indicates that apparent tilts of less than 3 microradians are pervasive and must be regarded as typical signal levels and/or as typical levels of systematic error. Systematic leveling errors are suggested in some cases by close correlations between apparent elevation change and topography, disagreements between leveling and tide gauge measurements, and internal inconsistencies in leveling circuits. Apparent movements which correlate with topography are observed in many areas of the U.S. Such apparent movements often reach 35 mm per 100 m of relief. Disagreements between leveling and tide gauge measurements along the east and west coasts and internal inconsistencies in leveling circuits suggest errors reaching 1 mm/km which can accumulate monotonically for distances exceeding 1000 km. Regional maps of apparent elevation change for the Eastern U.S. show serious inconsistencies with similar maps for adjacent portions of Canada suggesting that such maps may be more indicative of systematic leveling errors than real crustal movements. The largest signals (apparent tilts greater than 4.5 microradians) are for the most part associated with: 1. (1) coseismic and postseismic movements of major (M>6) dip-slip earthquakes, 2. (2) regions of contemporary magmatic activity, 3. (3) subsidence due to fluid withdrawal, 4. (4) topography-correlated apparent movements. Coseismic movements reported for eleven U.S. earthquakes are roughly consistent with simple models of elastic rebound. At least some postseismic movements appear consistent with after-slip on the fault or an extension of the fault that ruptured during the earthquake, although other explanations have been proposed (e.g., viscoelastic relaxation of the lithosphere-asthenosphere). Deformations possibly associated with contemporary magmatic processes are not restricted to volcanically active areas (e.g. Hawaii) having been observed in the Rio Grande rift and in Yellowstone National Park as well. Subsidence due to fluid withdrawal, well known in areas of intense pumping, is considerably more widespread than previously reported occuring throughout much of the Atlantic and Gulf coastal plains, along the Mississippi Valley and within many smaller sedimentary basins which have been exploited for groundwater. The association of many of the largest signals with real surface movements further demonstrates the ability of historic leveling to detect relatively subtle deformation.

Anelastic response of the Earth to a dip slip earthquake

The deformation of the earth's surface immediately following an earthquake is well modeled by a dislocation in an elastic half space. Some time after the event, however, the elastic stresses begin to relax due to flow in the more fluid regions of the upper mantle (the asthenosphere). This relaxation causes further slow displacements observable at the earth's surface. This paper examines the pattern and timing of these postseismic motions for a vertical dip slip fault and a 30° dip thrust fault. A variety of rheological models are studied. These models encompass variations in asthenosphere thickness, mesosphere viscosity, fault depth, and, most important, power law flow. Both Newtonian (n = 1) and non‐Newtonian (n = 3) Maxwell rheologies are considered for the asthenosphere and mesosphere. The results for a vertical dip slip fault show that a peripheral upwarp develops within a distance of a few lithosphere thicknesses from the rupture zone on the downthrown side of the fault (a comparable downwarp develops on the upthrown side). These peripheral warps grow to a maximum height of about 5% of the total fault slip some time after the earthquake event and then collapse at much greater times. The vertical motions for a 30° dip thrust fault show that after the earthquake a general uplift occurs in the region near the rupture zone. Horizontal displacements propagate asymmetrically away from the rupture zone, the largest displacements occurring in the overthrust plate. The principal result of the comparison of n = 1 and n = 3 rheological laws is that the basic pattern of uplifts and horizontal motions is very similar: the major difference is the time dependence of the development of the pattern. In spite of the complex geometrical structure of the subduction zone the displacements ui(1)(t) for Newtonian rheology are nearly the same as ui(3)(t′) for the non‐Newtonian rheology if t′ ∼ t3. Thus although the qualitative pattern of the displacements is not diagnostic of power law flow, the great difference in time dependence allows a clear discrimination of the two flow laws.

Vertical movements following a dip‐slip earthquake

Fault motion during a dip‐slip earthquake induces elastic stresses in the earth which are well modeled by elastic dislocation theory. Shortly after the earthquake, flow in the asthenosphere begins to relax these stresses and leads to postseismic motions observable at the earth's surface. Recent work has led to apparently contradictory results on the sign of the vertical motion following a dip‐slip earthquake: some workers find downwarping in the region overlying a thrust fault; others find upwarping. This controversy is now resolved by a finite element study of postseismic rebound following a thrust earthquake on a 30° dip fault in an initially planar elastic lithosphere which overlies a Maxwell viscoelastic asthenosphere. If the fault penetrates less than 0.68 of the way through the lithosphere, downwarping follows the earthquake. If the fault penetrates more than 0.68 of the lithosphere, upwarping results. The magnitude as well as the sign of the postseismic rebound is a sensitive indicator of the ratio between the thickness of the elastic lithosphere and the fault depth. Observations of postseismic rebound may thus be used to measure lithosphere thicknesses at time scales on the order of years.

A model for the earthquake cycle in underthrust zones

The time‐dependent surface deformation due to thrust faulting in an elastic plate overlying a viscoelastic half space is examined and compared with geodetic measurements of earthquake‐related crustal movements from Japan. The model fault is two‐dimensional, and the half‐space rheology is that of a Maxwell solid whose instantaneous response to applied loads is purely elastic but which subsequently flows to relieve imposed shear stresses. A characteristic feature of shallow‐angle underthrusting shown by these computations is that buried slip produces predominantly land uplift, while asthenospheric relaxation due to surface faulting results principally in surface downwarping. These distinctive patterns, also reflected in the measured deformation, are particularly useful in formulating a viable model for the entire earthquake cycle. For the model constructed in this way, coseismic faulting in the upper part of the plate transfers a load to the lower lithosphere and asthenosphere, inducing postseismic slip downdip of the seismic rupture and relaxation in the asthenosphere, these transients eventually merging into the steady buried slip and smoother asthenospheric flow that characterize the interseismic phase of the deformation cycle. Aseismic slip and asthenospheric relaxation cause the load supported by the plate‐bounding fault to be gradually transferred back to the shallow locked segment of the fault, effecting the strain buildup for a subsequent earthquake, and the cycle is repeated. No explicit account of plate‐driving forces is made; their net effect is presumed to be the steady buried slip that persists throughout the cycle and provides the energy that drives it. Characteristic features of the observed deformation in southwest Japan, site of the 1946 Nankaido earthquake, and in the South Kanto district, where the great 1923 earthquake occurred, are matched by this model using conventional values of lithospheric thickness (60 km) and asthenospheric viscosity (1021 P, or 1020 N s/2), although the model is not strongly tied to these exact values. Postseismic movements are adequately explained by episodic slip that occurs below the coseismic rupture, is 10–30% of the seismic slip, and acts in the same sense. Superimposed on these movements are the lesser effects of asthenospheric relaxation, which in the South Kanto district contribute significantly to the postseismic vertical level changes because post‐1923 buried slip is comparatively small and involves largely strike slip movements. Interseismic subsidence in both regions is explained well by asthenospheric relaxation and less significant deformation effects due to steady aseismic slip on the lower part of the plate boundary.