A computer-implemented method for determining elastic properties for a heterogeneous anisotropic geological formation is described herein. The method includes grouping sonic velocity data from a borehole section (or borehole sections) into a number of clusters (e.g., one or more clusters). The sonic velocity data is grouped into clusters using petrophysical log data from the borehole section. The method also includes inverting the sonic velocity data for the clusters to determine elastic properties for each cluster. In some cases, the elastic properties for the clusters are combined to determine a relationship between the elastic properties and formation heterogeneity.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A computer-implemented method for determining a plurality of elastic properties for an heterogeneous anisotropic geological formation, the method comprising: grouping sonic velocity data from at least one borehole section into at least one cluster, wherein the sonic velocity data is grouped using petrophysical log data from the at least one borehole section; and inverting the sonic velocity data for at least one cluster to determine a plurality of elastic properties for each cluster. 2. The method of claim 1, further comprising: combining the elastic properties for a plurality of the clusters to determine a relationship between the elastic properties and formation heterogeneity. 3. The method of claim 1, further comprising: determining uncertainty parameters for each of the elastic properties. 4. The method of claim 1, wherein the anisotropic formation is transversely isotropic. 5. The method of claim 4, wherein the plurality of elastic properties comprises five elastic properties. 6. The method of claim 5, wherein the five elastic properties comprise three Thomsen parameters and two velocities. 7. The method of claim 1, wherein the elastic properties are independent of each other. 8. The method of claim 1, wherein at least some of the elastic properties are dependent on each other. 9. The method of claim 1, wherein the plurality of elastic properties comprises components of elastic stiffness tensors. 10. The method of claim 1, wherein the plurality of elastic properties comprises components of elastic compliance tensors. 11. The method of claim 1, wherein the plurality of elastic properties comprises elastic Young's moduli and Poisson's ratios. 12. The method of claim 1, wherein at least some of the elastic properties are density normalized. 13. The method of claim 1, wherein the sonic velocity data is inverted using a misfit-norm-based iterative process. 14. The method of claim 3, wherein the uncertainty parameters are determined using a Bayesian probability method 15. The method of claim 3, wherein the uncertainty parameters comprise posterior probability distribution functions for each of the elastic properties. 16. The method of claim 3, wherein the uncertainty parameters comprise posterior probability distribution functions for combinations of elastic properties. 17. The method of claim 1, wherein the petrophysical log data comprise data selected from the group consisting of: gamma ray measurements, density measurements, clay volume measurements, porosity measurements, resistivity measurements, mineralogical measurements, and a combination thereof. 18. The method of claim 1, further comprising: acquiring sonic log data for the borehole section; analyzing the sonic log data to determine the sonic velocity data for the borehole section. 19. The method of claim 4, further comprising: determining a dip azimuth and a dip angle of a transverse isotropic plane for the transversely isotropic formation. 20. The method of claim 19, wherein the dip azimuth and dip angle are determined from borehole image logs for the borehole section. 21. The method of claim 19, further comprising: determining borehole azimuth and borehole deviation for the borehole section. 22. The method of claims 21, further comprising: determining a relative dip angle between an axis of the borehole section and the transverse isotropic plane. 23. The method of claim 1, wherein the at least one borehole section comprises a plurality of borehole sections from at least two different wells. 24. A non-transitory computer readable medium encoded with instructions, which, when loaded on a computer, establish processes for determining a plurality of elastic properties for a heterogeneous anisotropic geological formation, the processes comprising: grouping sonic velocity data from at least one borehole section into at least one cluster, wherein the sonic velocity data is grouped using petrophysical log data from the at least one borehole section; and inverting the sonic velocity data for at least one cluster to determine a plurality of elastic properties for each cluster. 25. The non-transitory computer readable medium according to claim 24, wherein the processes further comprise: combining the elastic properties for a plurality of the clusters to determine a relationship between the elastic properties and formation heterogeneity. 26. The non-transitory computer readable medium according to claim 24, wherein the processes further comprise: determining uncertainty parameters for each of the elastic properties. 27. The non-transitory computer readable medium according to claim 24, wherein the anisotropic formation is transversely isotropic. 28. The non-transitory computer readable medium according to claim 27, wherein the plurality of elastic properties comprises five elastic properties. 29. A system for determining a plurality of elastic properties for a heterogeneous anisotropic geological formation, the system comprising: a processor; and a memory storing instructions executable by the processor to perform processes that include: grouping sonic velocity data from at least one borehole section into at least one cluster, wherein the sonic velocity data is grouped using petrophysical log data from the at least one borehole section; and inverting the sonic velocity data for at least one cluster to determine a plurality of elastic properties for each cluster. 30. The system according to claim 29, wherein the processes further comprise: combining the elastic properties for a plurality of the clusters to determine a relationship between the elastic properties and formation heterogeneity. 31. The system according to claim 29, wherein the processes further comprise: determining uncertainty parameters for each of the elastic properties. 32. The system according to claim 29, wherein the anisotropic formation is transversely isotropic.