Normative expression and accurate understanding of focal mechanism parameters

Abstract

This paper aims at the understanding of the relationship between the upper and lower hemisphere projection maps of the focal sphere, the correct reading of the focal mechanism parameters on the projection diagram, and to investigate if there is uncertainty about whether the slip angle has a unique solution when there are only two nodal strikes and dip angles. Based on the principle of stereographic projection, the following four expressions and understanding skills about focal mechanism parameters are refined: (1) according to the principle of stereographic projection, we analyzed the difference of the presentation of focal mechanism parameters on different projection maps. There is a 180° rotation relationship between the upper and the lower hemisphere projection map. (2) The method of determining the nodal strike on the upper and lower hemisphere projections: for the former, the observer faces the convex direction of the nodal arc, and the direction to the right of the nodal plane is the stike of the fault. The angle turned clockwise in the north direction is the strike angle of the nodal plane; For the latter, the observer faces the convex direction of the arc of the nodal plane, and the point corresponding to the point on the right side of the nodal plane plus 180° is the strike of the fault. (3) The relationship between the azimuth angles of the P, T and N-axis on upper and lower hemisphere projections: the azimuth angles of the P, T, and N-axis on the upper hemisphere projection map = the azimuth angles of the P, T, and N-axis on the lower hemisphere projection map + 180°. (4) Only the strike and dip angles of two nodal planes are used to derive the rake: according to the slip angle formula, two groups of rake solution can be calculated, indicating that the solution are not unique. The actual slip angle can be determined by combining the hanging wall and footwall and strike of fault, or by combining the actual P-axis and T-axis data, or the first motion of P-waves. Aims to aid accurate understanding and long-term memory of focal mechanism parameters with consistent and simple rules.