Postseismic rebound due to creep of the lower lithosphere and asthenosphere

Postseismic surface deformations are attributed to the inelastic flow of the subcrustal regions of the Earth following an earthquake. A multilayer representation of the Earth's rheological properties is used in conjunction with a finite element computational scheme to calculate time dependent displacements and strains subsequent to a strike slip earthquake. The deviatoric stress strain relations for the uppermost layer is assumed elastic. Lower layers are assumed to be, in order of increasing depth, a standard, linear, three element, viscoelastic solid; a linear viscoelastic fluid; and another elastic solid. Physically these layers correspond to the upper lithosphere, lower lithosphere, asthenosphere, and lower mantle, respectively. Elastic dilatational properties are assumed throughout. Appreciable postseismic displacements, possibly approaching meters, for large earthquakes, arise from viscoelastic relaxation following sudden coseismic slip. Furthermore, compared to the simpler case of an elastic lithosphere over a viscoelastic asthenosphere and the near fault postseismic shear, strain is increased, by a factor of two or more in some cases, by the presence of a viscoelastic lower lithosphere. Also, the duration of postseismic straining is increased by the relatively slow relaxation of this layer

Computer simulation of earthquakes

Two computer simulation models of earthquakes were studied for the dependence of the pattern of events on the model assumptions and input parameters. Both models represent the seismically active region by mechanical blocks which are connected to one another and to a driving plate. The blocks slide on a friction surface. In the first model elastic forces were employed and time independent friction to simulate main shock events. The size, length, and time and place of event occurrence were influenced strongly by the magnitude and degree of homogeniety in the elastic and friction parameters of the fault region. Periodically reoccurring similar events were frequently observed in simulations with near homogeneous parameters along the fault, whereas, seismic gaps were a common feature of simulations employing large variations in the fault parameters. The second model incorporated viscoelastic forces and time-dependent friction to account for aftershock sequences. The periods between aftershock events increased with time and the aftershock region was confined to that which moved in the main event

A multilayer model of time dependent deformation following an earthquake on a strike-slip fault

A multilayer model of the Earth to calculate finite element of time dependent deformation and stress following an earthquake on a strike slip fault is discussed. The model involves shear properties of an elastic upper lithosphere, a standard viscoelastic linear solid lower lithosphere, a Maxwell viscoelastic asthenosphere and an elastic mesosphere. Systematic variations of fault and layer depths and comparisons with simpler elastic lithosphere over viscoelastic asthenosphere calculations are analyzed. Both the creep of the lower lithosphere and astenosphere contribute to the postseismic deformation. The magnitude of the deformation is enhanced by a short distance between the bottom of the fault (slip zone) and the top of the creep region but is less sensitive to the thickness of the creeping layer. Postseismic restressing is increased as the lower lithosphere becomes more viscoelastic, but the tendency for the width of the restressed zone to growth with time is retarded

Postseismic viscoelastic surface deformation and stress. Part 1: Theoretical considerations, displacement and strain calculations

A model of viscoelastic deformations associated with earthquakes is presented. A strike-slip fault is represented by a rectangular dislocation in a viscoelastic layer (lithosphere) lying over a viscoelastic half-space (asthenosphere). Deformations occur on three time scales. The initial response is governed by the instantaneous elastic properties of the earth. A slower response is associated with viscoelastic relaxation of the lithosphere and a yet slower response is due to viscoelastic relaxation of the asthenosphere. The major conceptual contribution is the inclusion of lithospheric viscoelastic properties into a dislocation model of earthquake related deformations and stresses. Numerical calculations using typical fault parameters reveal that the postseismic displacements and strains are small compared to the coseismic ones near the fault, but become significant further away. Moreover, the directional sense of the deformations attributable to the elastic response, the lithospheric viscoelastic softening, and the asthenospheric viscoelastic flow may differ and depend on location and model details. The results and theoretical arguments suggest that the stress changes accompanying lithospheric relaxation may also be in a different sense than and be larger than the strain changes

Postseismic deformation due to subcrustal viscoelastic relaxation following dip-slip earthquakes

The deformation of the Earth following a dip-slip earthquake is calculated using a three layer rheological model and finite element techniques. The three layers are an elastic upper lithosphere, a standard linear solid lower lithosphere, and a Maxwell viscoelastic asthenosphere-a model previously analyzed in the strike-clip case (Cohen, 1981, 1982). Attention is focused on the magnitude of the postseismic subsidence and the width of the subsidence zone that can develop due to the viscoelastic response to coseismic reverse slip. Detailed analysis for a fault extending from the surface to 15 km with a 45 deg dip reveals that postseismic subsidence is sensitive to the depth to the asthenosphere but is only weakly dependent on lower lithosphere depth. The greatest subsidence occurs when the elastic lithosphere is about 30 km thick and the asthenosphere lies just below this layer (asthenosphere depth = 2 times the fault depth). The extremum in the subsidence pattern occurs at about 5 km from the surface trace of the fault and lies over the slip plane. In a typical case after a time t = 30 tau (tau = Maxwell time) following the earthquake the subsidence at this point is 60% of the coseismic uplift. Unlike the horizontal deformation following a strike slip earthquake, significant vertical deformation due to asthenosphere flow persists for many times tau and the magnitude of the vertical deformation is not necessarily enhanced by having a partially relaxing lower lithosphere

Geophysical interpretation of satellite laser ranging measurements of crustal movement in California

As determined by satellite laser ranging the rate of contraction of a 900 kilometer baseline between sites located near Quincy in northern California and San Diego in southern California is about 61 to 65 mm/yr with a formal uncertainty of about 10 mm/yr. The measured changes in baseline length are a manifestation of the relative motion between the North America and Pacific tectonic plates. This long baseline result is compared to measurements made by more conventional means on shorter baselines. Additional information based on seismicity, geology, and theoretical modelling is also analyzed. Deformation lying within a few tens of kilometers about the major faults in southern California accounts for most, but not all of the observed motion. Further motion is attributable to a broader scale deformation in southern California. Data suggesting crustal movements north of the Garlock fault, in and near the southern Sierra Nevada and local motion at an observatory are also critically reviewed. The best estimates of overall motion indicated by ground observations lie between 40 and 60 mm/yr. This lies within one or two standard deviations of that deduced by satellite ranging but the possibility of some unresolved deficit cannot be dismissed. The long time scale RM2 plate tectonic model of Minster and Jordan predicts a contraction between 47 and 53 mm/yr depending on the extension rate of the Basin and Range. Thus the ground based observations, satellite laser ranging (SLR) results, and RM2 rates differ at about the 10 mm/yr level and are consistent with one another within the data and model uncertainties

Regional analysis of earthquake occurrence and seismic energy release

The historic temporal variation in earthquake occurrence and seismic energy release on a regional basis throughtout the world were studied. The regionalization scheme employed divided the world into large areas based either on seismic and tectonic considerations (Flinn-Engdahl Scheme) or geographic (longitude and latitude) criteria. The data set is the wide earthquake catalog of the National Geophysical Solar-Terrestrial Data Center. An apparent relationship exists between the maximum energy released in a limited time within a seismic region and the average or background energy per year averaged over a long time period. In terms of average or peak energy release, the most seismic regions of the world during the 50 to 81 year period ending in 1977 were Japanese, Andean South American, and the Alaska-Aleutian Arc regions. The year to year fluctuations in regional seismic energy release are greater, by orders of magnitude, than the corresponding variations in the world-wide seismic energy release. The b values of seismic regions range from 0.7 to 1.4 where earthquake magnitude is in the range 6.0 to 7.5

Postseismic viscoelastic deformation and stress. Part 2: Stress theory and computation; dependence of displacement, strain, and stress on fault parameters

A viscoelastic model for deformation and stress associated with earthquakes is reported. The model consists of a rectangular dislocation (strike slip fault) in a viscoelastic layer (lithosphere) lying over a viscoelastic half space (asthenosphere). The time dependent surface stresses are analyzed. The model predicts that near the fault a significant fraction of the stress that was reduced during the earthquake is recovered by viscoelastic softening of the lithosphere. By contrast, the strain shows very little change near the fault. The model also predicts that the stress changes associated with asthenospheric flow extend over a broader region than those associated with lithospheric relaxation even though the peak value is less. The dependence of the displacements, stresses on fault parameters studied. Peak values of strain and stress drop increase with increasing fault height and decrease with fault depth. Under many circumstances postseismic strains and stresses show an increase with decreasing depth to the lithosphere-asthenosphere boundary. Values of the strain and stress at distant points from the fault increase with fault area but are relatively insensitive to fault depth

Postseismic surface deformations due to lithospheric and asthenospheric viscoelasticity

A model is proposed for post seismic surface deformations attributing them to lithospheric and asthenospheric viscoelasticity. The model predicts that the deformations due to lithospheric viscoelasticity depend on the ratio of the effective shear modulus acting long after the lithospheric viscoelastic relaxation to that acting immediately following the earthquake. While such deformations are generally smaller than those associated with asthenospheric viscoelasticity, they occur on a shorter time scale and may be in opposite direction to both the motion occurring at the time of the earthquake and that occurring as the asthenospheric relaxation occurs

Waveguide CO2 laser gain: Dependence on gas kinetic and discharge properties

Using a simple rate equation approach the gas kinetic and discharge properties of waveguide CO2 lasers were examined. The dependence was calculated of the population inversion and laser small signal gain on gas pressure, gas mixture, pumping rate (discharge current), tube bore diameter, and wall temperature. At higher pressures the gain is optimized by using more helium rich mixtures and smaller bore diameters. The dependence of laser tunability on the gas kinetic properties and cavity losses was determined, it was found that for loss cavities the laser tunability may substantially exceed the molecular fullwidth at half maximum. The more helium rich gas mixtures give greater tunability when cavity losses are small and less tunability when cavity losses are large. The role of the various gases in the waveguide CO2 laser is the same as that in conventional devices, by contrast with conventional lasers, the waveguide laser transition is homogeneously broadened. The dependence of gain on gas pressure and other kinetic and discharge properties differs substantially from that predicted by scaling results from conventional low pressure lasers