Elastic moduli and the aspect ratio spectrum of rock using simulated annealing

We propose a new method for estimating pore volume concentrations associated with inclusions with different aspect ratios and also the rock matrix and pore fluid moduli using very fast simulated annealing. We use the Kuster and Toksöz effective modulus formulations as a forward model that takes the pore shapes into consideration. In order to provide this method, we first estimated the model parameters, then calculated the P‐ and S‐wave velocities as a function of pressure in dry and saturated conditions and finally compared the calculated velocities with the measured ultrasonic velocities of sandstone, limestone and granite. The calculated velocity fitted well with the measured velocity. Furthermore, we verified the calculated bulk modulus and shear modulus of the rock matrix. As these moduli were consistent with the results from other experiments and were almost the same as those by the inversion method, we believe that this method can satisfactorily calculate the moduli. Next, we conducted optimization under several cases of moduli setting. We obtained the best results using the independent shear modulus under saturated conditions. The result indicates that the shear modulus varies according to the fluid in the pores in sandstone. Finally, we optimized the average aspect ratio of rock and found that the average aspect ratio may depend on the type of rock. The velocity calculated by the single aspect ratio is similar to the velocity calculated by using a spectrum of aspect ratios for the same rock.