Introduction to the Vertical Derivatives of Horizontal Stress (VDoHS) Rates
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We explain the structure of the force balance equations at the Earth’s surface for flat Earth and spherical Earth cases. A key assumption is that at the surface of the Earth, where GPS observations are made, the inter-seismic behavior is purely elastic; that is, the rocks are cold and the rheology is much less complicated than at mid- and lower-crustal depths. Whereas at depth velocities are related to total stresses because ductility comes into play, at the surface inter-seismic displacements are related only to incremental stresses and surface velocities are related only to rates of change of stress. A simple consequence is that the horizontal-component manifestations at the surface of any subsurface deformation source, in the form of the vertical derivatives of horizontal stress (VDoHS) rates, can be deduced from surface observations of horizontal velocity using elasticity theory alone.
KeywordsForce balance equations Earth’s surface Flat Earth Spherical Earth Elastic inter-seismic behavior Surface velocities Stress rates Strain rates VDoHS rates Green’s functions
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