A method for the near‐source anisotropy by the pair‐event inversion of Rayleigh‐wave radiation patterns

Summary. A novel method is proposed for retrieving the 3‐D orientation of axes of symmetry of near‐source anisotropy by a non‐linear inversion of observed radiation patterns of seismic displacement spectra of Rayleigh waves. If faulting is generated within an anisotropic source region, body force equivalents for the faulting are in general not a double couple but the sum of three orthogonal dipole forces (Kosevich; Kawasaki & Tanimoto). As a result of the third dipole force, radiation patterns of Rayleigh waves are deformed, the deformation amounting to several per cent of those for an isotropic source medium. The non‐linear inversion is carried out to find the optimum fault plane solutions giving the minimum square residual between observed and theoretical radiation patterns in some period range. In order to remove effects of heterogeneity along propagation paths, a pair‐event scheme is involved in the inversion, which denotes taking spectral amplitude ratios and differential phases of the seismic displacement spectra of the pair‐events having close hypocentres and different fault plane solutions. The uniqueness of the fault plane solutions of the non‐linear inversion is afforded a proof by the Monte‐Carlo experiment. The non‐linear inversion is repeated for some possible types of symmetry of the near‐source orthotropic anisotropy due to the preferred orientation of olivine crystals as mantle materials. Square residuals thus obtained are compared with each other to see which orientation gives the minimum. The method is applied to pair‐events which occurred in the anomalous mantle beneath the Mid‐Atlantic Ridge. This leads to a discovery that one type of symmetry of the preferred orientations with a ‐, b ‐ and c‐axes aligned vertical, parallel to and perpendicular to the trend (N11E) of the ridge axis, respectively, is most likely existing in the anomalous mantle.