Principles of vectorial tomography - The effects of model parametrization and regularization in tomographic imaging of seismic anisotropy

Abstract

Imaging seismic anisotropy is equivalent to determining the spatial variations of an anisotropy vector. This anisotropy vector can be described by its projection on the axes of a geographical reference frame or by a length and two angles that define the orientation of this vector with respect to the reference axes. Classical tomographic approaches use the former description, which leads to a linear inverse problem. When anisotropy varies spatially over scales smaller than the Fresnel zone, damping and smoothing produce strong artefacts in the solution, in particular for the amplitude of anisotropy. Regularization constraints favour models in which anisotropy is weak where fabrics are disoriented. These shortcomings can be overcome by the latter choice of parametrization, which leads to a non-linear inverse problem. The direct resolution of this strongly non-linear problem by a Gauss-Newton algorithm is difficult. It converges only if the starting model is sufficiently close to the global minimum of the misfit function. However, a robust and stable solution can be obtained following a 3-step algorithm, which consists in (1) inverting the fast directions, the amplitudes of anisotropy being fixed to an arbitrary (but small) constant value, (2) finding the average amplitude of anisotropy inside the model and (3) inverting the fluctuations of anisotropy with respect to this average value. © 2009 The Authors Journal compilation © 2009 RAS.