Study of inversion for third order elastic constants and in situ stress by multifrequency dispersion of cross dipole sonic logging

Based on acoustoelastic theory, the method of inversion for third order elastic constants (TOECs) and in situ stress from the multi-frequency phase velocity of cross dipole sonic logging data and the effect of different signal to noise ratio (SNR) on the inversion result is studied. Qualitative and quantitative analysis shows that the contribution of the terms in acoustoelastic velocity-stress model not containing TOECs to the total velocity variation can be neglected, when compared to the contribution of the terms containing TOECs. This means that the inversion of TOECs and in situ stress is a severely ill-posed problem or an indeterminate one when only using the data at one time. The inversion stability is simulated for every accurate and approximate inversion model at different level SNR. Numerical result shows that the result inverted from the cross logging data at one borehole pressure using accurate model is affected heavily by noise. Both accurate model and approximate one in the inversion of data gotten at two different borehole pressures have the same accuracy. Thus, the latter can take place of the former to improve the computation speed and to simplify the model. The result also shows that the two-step method can give a better estimation of TOECs and in situ stress.