Deformation due to a pressurized horizontal circular crack in an elastic half-space, with applications to volcano geodesy

We consider deformation due to sill-like magma intrusions using a model of a horizontal circular crack in a semi-infinite elastic solid. We present exact expressions for vertical and horizontal displacements of the free surface of a half-space, and calculate surface displacements for a special case of a uniformly pressurized crack. We derive expressions for other observable geophysical parameters, such as the volume of a surface uplift/subsidence, and the corresponding volume change due to fluid injection/withdrawal at depth. We demonstrate that for essentially oblate (i.e. sill-like) source geometries the volume change at the source always equals the volume of the displaced material at the surface of a half-space. Our solutions compare favourably to a number of previously published approximate models. Surface deformation due to a ‘point’ crack (that is, a crack with a large depth-to-radius ratio) differs appreciably from that due to an isotropic point source (‘Mogi model’). Geodetic inversions that employ only one component of deformation (either vertical or horizontal) are unlikely to resolve the overall geometry of subsurface deformation sources even in a simplest case of axisymmetric deformation. Measurements of a complete vector displacement field at the Earth's surface may help to constrain the depth and morphology of active magma reservoirs. However, our results indicate that differences in surface displacements due to various axisymmetric sources may be subtle. In particular, the sill-like and pluton-like magma chambers may give rise to differences in the ratio of maximum horizontal displacements to maximum vertical displacements (a parameter that is most indicative of the source geometry) that are less than 30 per cent. Given measurement errors in geodetic data, such differences may be hard to distinguish

Finite source modelling of magmatic unrest in Socorro, New Mexico, and Long Valley, California

We investigate surface deformation associated with currently active crustal magma bodies in Socorro, New Mexico, and Long Valley, California, USA. We invert available geodetic data from these locations to constrain the overall geometry and dynamics of the inferred deformation sources at depth. Our best-fitting model for the Socorro magma body is a sill with a depth of 19 km, an effective diameter of 70 km and a rate of increase in the excess magma pressure of 0.6 kPa yr^(−1). We show that the corresponding volumetric inflation rate is ∼6×10^(−3) km^3 yr^(−1), which is considerably less than previously suggested. The measured inflation rate of the Socorro magma body may result from a steady influx of magma from a deep source, or a volume increase associated with melting of the magma chamber roof (i.e. crustal anatexis). In the latter case, the most recent major injection of mantle-derived melts into the middle crust beneath Socorro may have occurred within the last several tens to several hundreds of years. The Synthetic Interferometric Aperture Radar (InSAR) data collected in the area of the Long Valley caldera, CA, between June 1996 and July 1998 reveal an intracaldera uplift with a maximum amplitude of ∼11 cm and a volume of 3.5×10^(−2) km^3. Modelling of the InSAR data suggests that the observed deformation might be due to either a sill-like magma body at a depth of ∼12 km or a pluton-like magma body at a depth of ∼8 km beneath the resurgent dome. Assuming that the caldera fill deforms as an isotropic linear elastic solid, a joint inversion of the InSAR data and two-colour laser geodimeter data (which provide independent constraints on horizontal displacements at the surface) suggests that the inferred magma chamber is a steeply dipping prolate spheroid with a depth of 7–9 km and an aspect ratio in excess of 2:1. Our results highlight the need for large radar look angles and multiple look directions in future InSAR missions

Коронавірусні пахощі

It is shown that epidemic dynamics and total number of people with a viral disease in a closed community critically depend on the duration of the period of virus contagiousness. The time that an infected person remains infectious is limited either by his/her isolation or by a natural decrease in virus activity. From laboratory data on changes in virus COVID-19 activity over time and on the basis of studying the epidemic dynamics in various communities, it follows that if the isolation of an infected person is not effectively used to combat the epidemic, then the individual, on average, remains contagious for 9—10 days after being infected. Modeling shows that in this case approximately 15 % of the closed community population will be finally infected (including asymptomatic cases). Since only about 20 % of those infected go to the doctor and are registered in the statistics, it should be expected that the number of registered cases would be about 3 % of the population. Currently, only Israel has reached this threshold