We developed a new approach to model seismic velocity and attenuation dispersion caused by mesoscopic wave-induced fluid flow due to sub-log-scale heterogeneity (patchy saturation). The proposed procedure does not require a-priori information on spatial scale of heterogeneity, but utilizes existing velocity measurements, like the Gassmann equation (Gassmann, 1951) in standard fluid substitution problems. One of the practical benefits of the Gassmann equation is that it does not require detailed information about the solid grain geometry. Starting with the bulk modulus of a rock saturated with one fluid, which can be measured at field in-situ conditions, the Gassmann equation allows us to predict the bulk modulus of a rock saturated with another fluid. Proposed procedure also starts from one measured velocity and predicts velocity and attenuation (inverse quality factor) at another frequency without knowing the spatial heterogeneity scale explicitly in advance. Furthermore, this approach can allow us to model both velocity and attenuation from only a velocity measurement at one frequency. Application to laboratory velocity and attenuation measurements confirms the validity of the method. This new approach will become a first step in forward attenuation modeling for quantitative interpretation of seismic attenuation attributes.


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