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P- and S-wave seismic velocities have been used to investigate geologic structure and characterize physical properties, but seismic velocities consist of three unknown parameters, namely the density and two types of elastic constants (e.g., bulk and shear modulus). Separation of the components allows us to estimate the geomechanical properties of the formation and the degree of gas saturation in pore space, which have been difficult to evaluate so far. One of the separation methods is combining seismic exploration and muography, which is a non-destructive method that can be used to estimate the density distribution inside an object based on observations of muons produced by reactions between cosmic rays and nuclei in the Earth’s atmosphere. Furthermore, there are some petrophysical relationships between the density and elastic wave velocity, so integrated analysis of muon and seismic data sets using the relationships can provide more accurate reconstruction of the density, elastic wave velocity, and elastic constants. There has been limited consideration given to joint inversion methods for muon and elastic wave data, especially for P- and S-waves. We conducted a preliminary test by comparing independently and jointly recovered models for the synthetic subsurface model and demonstrated the potential of the joint inversion method.