• Anisotropy;
  • Tomography;
  • Inverse problem;
  • Electromagnetics;
  • Seismics


In geological materials, anisotropy may arise due to different mechanisms and can be found at different scales. Neglecting anisotropy in traveltime tomographic reconstruction leads to artefacts that can obscure important subsurface features. In this paper, a geostatistical tomography algorithm to invert cross-hole traveltime data in elliptically anisotropic media is presented. The advantages of geostatistical tomography are that the solution is regularized by the covariance of the model parameters, that known model parameters can be used as constraints and fitted exactly or within a prescribed variance and that stochastic simulations can be performed to appraise the variability of the solution space. The benefits of the algorithm to image anisotropic media are illustrated by two examples using synthetic georadar data and real seismic data. The first example confirms suspected electromagnetic anisotropy in the vadose zone caused by relatively rapid water content variations with respect to wavelength at georadar frequencies. The second presents how sonic log data can be used to constrain the inversion of cross-well seismic data and how geostatistical simulations can be used to infer parameter uncertainty. Results of both examples show that considering anisotropy yields a better fit to the data at high ray angles and reduces reconstruction artefacts.