The compensated linear-vector dipole: A possible mechanism for deep earthquakes

Abstract

Models of earthquake sources that have no volume change, no net force, and no net torque as criteria for the radiation of first motions, have five degrees of freedom in their spatial orientation. The usual double‐couple model has only three degrees of freedom. The most general source of high‐frequency seismic motions must be a linear combination of a double couple and another source called the compensated linear‐vector dipole. A radiation pattern of amplitudes of first motions on the focal sphere cannot be uniquely decomposed into the radiation patterns due to the two sources.

Moment tensor decompositions revisited

“…Although the moment tensor decomposition is not unique and many other decompositions have been proposed, the decomposition of Knopoff and Randall (1970) proved to be useful for physical interpretations and became widely accepted. This decomposition was further developed and applied by Sipkin (1986), Jost and Herrmann (1989), Hudson et al (1989), Kuge and Lay (1994), Vavryčuk (2001Vavryčuk ( , 2005Vavryčuk ( , 2011 and others.…”

“…In order to identify which type of seismic source is physically represented by the retrieved moment tensor, Knopoff and Randall (1970) proposed decomposing the moment tensors into three elementary parts: the isotropic (ISO), double-couple (DC) and compensated linear vector dipole (CLVD) components. Although the moment tensor decomposition is not unique and many other decompositions have been proposed, the decomposition of Knopoff and Randall (1970) proved to be useful for physical interpretations and became widely accepted.…”

“…An explosion is an obvious example of a non-DC source, but non-DC components can also be produced by the collapse of a cavity in mines (Rudajev and Šílený 1985;Šílený and Milev 2008), by shear faulting on a nonplanar (curved or irregular) fault (Sipkin 1986), by tensile faulting induced by fluid injection in geothermal or volcanic areas (Ross et al 1996;Julian et al 1997) when the slip vector is inclined from the fault and causes its opening (Vavryčuk 2001(Vavryčuk , 2011 Roessler et al 2004Roessler et al , 2007. Complications also arise if the source is situated at a material interface (Vavryčuk 2013).In order to identify which type of seismic source is physically represented by the retrieved moment tensor, Knopoff and Randall (1970) proposed decomposing the moment tensors into three elementary parts: the isotropic (ISO), double-couple (DC) and compensated linear vector dipole (CLVD) components. Although the moment tensor decomposition is not unique and many other decompositions have been proposed, the decomposition of Knopoff and Randall (1970) proved to be useful for physical interpretations and became widely accepted.…”

Are deep focus earthquakes caused by a martensitic transformation?

“…One way out of this difficulty was mentioned in Knopoff and Randall (1970): As far as a state-of-the-art seismological analysis is concerned, it is impossible to distinguish between an earthquake whose source mechanism is slip on a fault plane, and one generated by a bulk phase transition which is dominated by simple shear. In this paper we present the conjecture that deep events are generated by means of a well-studied phase transition known as the martensitic transformation, which takes one supercooled solid phase to another having the same chemical composition with a different lattice structure.…”

“…An alternative class of models for the generation of large events assumes that the origin of deep earthquakes is a phase transition between two solid phases (for example, see Vaisnis and Pilbeam, 1976;Sung and Burns, 1976). Such source mechanisms may generally be distinguished from the more usual faulting mechanism by means of an analysis of the resulting seismograms since the moment tensor of a fault-type source has the form of a double couple while a phase transition is expected to be dominated by large monopole and linear vector dipole components (Knopoff and Randall, 1970;Randall and Knopoff, 1970). The empirical analysis of a number of deep events has shown that the double-couple mechanism is dominant in this regime (Knopoff and Randall, 1970;Randall and Knopoff, 1970;Giardini and Woodhouse, 1984;Giardini, 1984;Doornbos, 1985;Stimpson and Pearce, 1987), with the resulting paradox that the source mechanism appears to be just the one which is forbidden by the previous arguments.…”