The seismic velocity of rock material is sensitively affected by the pore geometry, and pore geometry is a key parameter related to the hydraulic properties of the rock. In this study, we propose a grid-search inversion method to estimate pore geometry and grain elastic moduli from observed velocity-porosity relationships. In our inversion, we compare laboratory-derived velocity-porosity relationships with the theoretical relationship calculated via the differential effective medium (DEM) model, assuming rock samples of the same lithology have the same crack aspect ratio. Compared with existing approaches to estimate elastic moduli and pore geometry, our approach is easy to apply because it can be applied to physical properties measured at atmospheric pressure without changing pressure. We tested our proposed inversion method using synthetic data, and successfully estimated the grain elastic moduli and crack aspect ratio. We also applied our inversion method to P-wave velocity and porosity measured in the laboratory on various rock samples acquired at the hydrothermal field and plate spreading centre, and found that the velocity-porosity relationship derived from DEM theory for the inverted model parameters agreed with the laboratory data. Using our proposed method, we estimate the average pore aspect ratio and grain bulk moduli for basaltic and hydrothermal ore deposit samples. Furthermore, the root mean square error (RMSE) distribution obtained in the grid-search inversion enables us to evaluate the uncertainty of the estimated values.
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