Applying Backus averaging for deriving seismic anisotropy of a long-wavelength equivalent medium from well-log data

Abstract

Backus averaging is often applied to well logs in order to estimate the elastic properties of a stack of thin layers at a longer wavelength to be used in seismic data analysis. Schoenberg and Muir extended Backus's method to layers with arbitrary anisotropy, but simple analytical equations are available for isotropic and transversely isotropic layers only. There is growing exploration interest in shale reservoirs, which exhibit lower symmetry seismic anisotropy if the reservoir is fractured. Here, simple analytical equations for Backus averaging are presented for symmetries up to monoclinic, of which averaging equations for orthorhombic and monoclinic layers are new. After Backus averaging, a stack of isotropic layers results in a vertical transverse isotropy (VTI), a stack of VTI layers results in a VTI, a stack of horizontal transverse isotropy layers results in an orthorhombic, a stack of orthorhombic layers results in an orthorhombic and a stack of monoclinic layers results in a monoclinic. Workflows for Backus averaging are presented along with numerical examples using well-log data from the Haynesville shale play in East Texas, USA.