Stress ratio determinations from striated faults: a spherical plot for cases of near-vertical principal stress

Abstract

For stress regimes with one principal axis, z, vertical, the stress ratio is best represented by an angular function F′ = arctan[ Γ3( σ z - ( σ x1 + σ x2 + σ z )/3)/( σ x1 - σ x2 ], or if the larger of the horizontal principal stresses ( σ x1 and σ x2 ) is designated σ y , by F = arctan[ Γ3( σ z - ( σ x + σ y + σ z )/3)/( σ y - σ x )]. Traditional palaeostress regimes (normal, wrench, reverse) represent equal-angular sectors of F′ or F, and may be subdivided. On a spherical projection of F against 2 y (where y is the bearing of maximum horizontal stress), the locus of all combinations of stress orientation and stress ratio capable of generating one datum (known slip direction on a known fault plane) is a great circle, since tan F = - cos(2 y - (2 s + b))/ Γ3 cos b, where tan b = tan ω/cos d, and s, d and ω are the fault strike, dip and striation pitch, respectively. Stereographic construction is simple using pencil and paper, and gives a visual appreciation of the definition of palaeostress states which could have generated the fault motions. It facilitates better than previous methods (1) the identification of radially symmetrical stress states; (2) recognition of suspect or incompatible data; and (3) delimiting the palaeostress state according to sense of shear, where this is known. Great circle and pole representations are suited to different purposes and data types, for which examples are given.