Seismic Moment Tensor Components Calculator

A moment tensor is the compact way of describing what an earthquake source does to the surrounding rock without modelling the rupture in detail. It is a symmetric 3 by 3 matrix with six independent components, representing the system of force couples that would produce, in a perfectly elastic Earth, the same radiated field as the real fault slip. Its value is that far-field displacement is linear in those components, so recorded waveforms can be inverted for them directly. For pure shear faulting the tensor is a double couple and its trace Mxx + Myy + Mzz is zero, since slip on a plane changes no volume. A non-zero trace signals an isotropic component, large and positive for explosions and often present in volcanic and mining-induced events. The components computed here follow the Aki and Richards formulation, which maps fault geometry onto the tensor: strike measured clockwise from north with the fault dipping to the right, dip from horizontal between 0 and 90 degrees, and rake within the fault plane from -180 to 180, where 0 or 180 is strike-slip, 90 pure thrust and -90 pure normal. The scalar moment M0 = mu x A x D uses a crustal rigidity usually taken as about 30 GPa. Two limitations are intrinsic. Every moment tensor has two nodal planes that fit the data equally well, so the actual fault plane cannot be chosen without aftershock or field evidence, and for very shallow sources the vertical dip-slip components are poorly resolved because they trade off against depth.

Focal mechanisms began with first motions. From the 1920s Perry Byerly and others plotted whether the initial P arrival at each station pushed up or down, and found the pattern divided the focal sphere into four quadrants, the signature of a double couple. Whether that force system was physically correct remained disputed for decades, until theoretical work in the late 1950s and early 1960s established the equivalence between a dislocation on a fault and a distribution of body forces, notably by Alexandra Vvedenskaya, Takuo Maruyama, and Robert Burridge and Leon Knopoff in 1964. Freeman Gilbert introduced the moment tensor itself in 1971 as the natural way to express how a source excites the free oscillations of the Earth, since normal mode amplitudes depend linearly on it. With Adam Dziewonski he developed inversion schemes through the 1970s, and in 1981 Dziewonski, T.-A. Chou and John Woodhouse published the centroid moment tensor method, which solves simultaneously for the tensor and for the position and time of the equivalent point source. The resulting Harvard catalogue, now the Global CMT Project, has produced solutions continuously since 1976 and holds tens of thousands of events, making the moment tensor the standard published description of an earthquake source. The 1989 review by Malte Jost and Robert Herrmann remains the usual entry point for the decompositions.