Open AccessMoment Tensors and other Phenomenological Descriptions of Seismic Sources—I. Continuous Displacements
Author(s) -
Backus George,
Mulcahy Marjorie
Publication year - 1976
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1976.tb04162.x
Subject(s) - cauchy stress tensor , moment (physics) , strain rate tensor , cartesian tensor , tensor field , tensor (intrinsic definition) , viscous stress tensor , seismic moment , symmetric tensor , classical mechanics , mathematics , physics , tensor density , exact solutions in general relativity , mathematical analysis , geometry , geology , seismology , fault (geology)
If a seismic event involves no external bodies, its source can be described phenomenologically by a vector field or by any one of three kinds of symmetric second‐order tensor fields. The vector field is the equivalent force. The tensor fields are the stress‐free strain, the stress glut, and any other moment tensor density. A particular source uniquely determines all of its descriptions except the moment tensor densities, but the motion it produces determines only the equivalent force. The source can also be described by the polynomial moments of any of its four field descriptions, and for small sources exciting long waves, a good approximate description is obtained from a finite number of low‐degree moments of the equivalent force or the stress glut. ‘The’ seismic moment tensor is the zeroth degree moment tensor of the stress glut or any moment tensor density and also the first degree moment tensor of the equivalent force. The n ′th degree moments of any moment tensor density are uniquely determined by the motion if n = 0, 1 but not if n ≥ 2. In the Earth, the stress drop is not a moment tensor density, and its volume integral is not ‘the’ seismic moment tensor. In a later paper these conclusions are shown to be unaffected by relaxing the assumption of a continuous displacement field.