Basics of averaging of the Maxwell equations for bulk materials

Volume or statistical averaging of the microscopic Maxwell equations (MEs), i.e. transition from microscopic MEs to their macroscopic counterparts, is one of the main steps in electrodynamics of materials. In spite of the fundamental importance of the averaging procedure, it is quite rarely properly discussed in university courses and respective books; up to now there is no established consensus about how the averaging procedure has to be performed. In this paper we show that there are some basic principles for the averaging procedure (irrespective to what type of material is studied) which have to be satisfied. Any homogenization model has to be consistent with the basic principles. In case of absence of this correlation of a particular model with the basic principles the model could not be accepted as a credible one. Another goal of this paper is to establish the averaging procedure for bulk MM, which is rather close to the case of compound materials but should include magnetic response of the inclusions and their clusters. In the vast majority of cases the consideration of bulk materials means that we consider propagation of an electromagnetic wave far from the interfaces, where the eigenwave in the medium has been already formed and stabilized. In other words, in this paper we consider the possible eigenmodes, which could exist in the equivalent homogenized media, and the necessary math apparatus for an adequate description of these waves. A discussion about boundary conditions and layered MM is a subject of separate publication and will be done elsewhere

Crustal subsidence observed by GRACE after the 2013 Okhotsk deep-focus earthquake

Coseismic gravity changes stem from (1) vertical deformation of layer boundaries with density contrast (i.e., surface and Moho) and (2) density changes of rocks at depth. They have been observed in earthquakes with M-w exceeding similar to 8.5 by Gravity Recovery and Climate Experiment (GRACE) satellites, but those of M8 class earthquakes have never been detected clearly. Here we report coseismic gravity change of the 24 May 2013 Okhotsk deep earthquake (M(w)8.3), smaller than the detection threshold. In shallow thrust faulting, factor (2) is dominant, while factor (1) remains secondary due to poor spatial resolution of GRACE. In the 2013 Okhotsk earthquake, however, factor (2) is insignificant because they occur at depth exceeding 600km. On the other hand, factor (1) becomes dominant because the centers of uplift and subsidence are well separated and GRACE can resolve them. This enables GRACE to map vertical ground movements of deep earthquakes over both land and ocean