HR: 0800h
AN: U41A-0714    [Abstracts]
TI: Seismological Constraints on Geodynamics
AU: * Lomnitz, C
EM: cinna@prodigy.net.mx
AF: Institute of Geophysics, Nat'l U of Mexico, Mexico, DF 04510 Mexico
AB: Earth is an open thermodynamic system radiating heat energy into space. A transition from geostatic earth models such as PREM to geodynamical models is needed. We discuss possible thermodynamic constraints on the variables that govern the distribution of forces and flows in the deep Earth. In this paper we assume that the temperature distribution is time-invariant, so that all flows vanish at steady state except for the heat flow $J_{q}$ per unit area (Kuiken, 1994). Superscript 0 will refer to the steady state while x denotes the excited state of the system. We may write $\sigma$$^{0}$=(J${_q}^{0}$$\cdot$X${_q}^{0}$)/T where $X_{q}$ is the conjugate force corresponding to $J_{q}$, and $\sigma$ is the rate of entropy production per unit volume. Consider now what happens after the occurrence of an earthquake at time t=0 and location (0,0,0). The earthquake introduces a stress drop $\Delta$P(x,y,z) at all points of the system. Response flows are directed along the gradients toward the epicentral area, and the entropy production will increase with time as (Prigogine, 1947) $\sigma$$^{x}$(t)=$\sigma$$^{0}$+$\alpha$${_1}$/(t+$\beta$)+$\alpha$${_2}$/(t+$\beta$)$^{2}+etc A seismological constraint on the parameters may be obtained from Omori's empirical relation N(t)=p/(t+q)$\space$ where N(t) is the number of aftershocks at time t following the main shock. It may be assumed that p/q$\sim\alpha_{1}/\beta$ times a constant. Another useful constraint is the Mexican-hat geometry of the seismic transient as obtained e.g. from InSAR radar interferometry. For strike-slip events such as Landers the distribution of $\Delta$P is quadrantal, and an oval-shaped seismicity gap develops about the epicenter. A weak outer triggering maximum is found at a distance of about 17 fault lengths. Such patterns may be extracted from earthquake catalogs by statistical analysis (Lomnitz, 1996). Finally, the energy of the perturbation must be at least equal to the recovery energy. The total energy expended in an aftershock sequence can be found approximately by integrating the local contribution over volume V: $\int$${_V}$$\sum$${_k}$$\nu$${_k}^{2}$(grad$\Delta$P)$^{2}$dV$\space$ where the $L_{ik}$ are Onsager coefficients and $\nu_k}$ is the stoichiometric coefficient of phase k. This enables us to calibrate the process. Note that there are contributions to the excited state that include material flows $J_{k}^{x}$ (flows of water and electrons into the epicentral area), in addition to the excited heat flow values $J_{q}^{x}$. A geodynamic model of the earthquake process would be essential for earthquake prediction. Kuiken, G.D.C., Thermodynamics of Irreversible Processes (John Wiley & Sons, New York, 1994). Lomnitz, C., On thermodynamics of planets, Geophys. J. Roy. Astr. Soc., 5, 157-161, 1961. Lomnitz, C., Search of a worldwide catalog for earthquakes triggered at intermediate distances, Bull. Seismol. Soc. Am., 86, 293-298, 1996.
DE: 7207 Core and mantle
DE: 3919 Equations of state
DE: 1212 Earth's interior--composition and state (8105)
DE: 1507 Core processes (8115)
SC: Union [U]
MN: 2004 AGU Fall Meeting