The complex pore structure of carbonate aquifers presents a challenge to interpreters analyzing geophysical logs and geologic data. A significant task is to develop physical rock models to determine the microstructure that provides information about flow-zone paths within the aquifer. In an attempt to achieve this task, an algorithm is devised to predict the secondary porosity formed by stiff macropores, compliant micropores, touching vugs, and pore aspect ratios from sonic logs. The pore aspect ratios are classified in intervals that delineate permeable and low permeability zones of aquifers. This provides information about the presence of isolated vugs, which do not contribute to the flow and connect or touch vugs that are part of the flow zones. The inversion results determined that permeable channels have pore aspect ratios 0.01–0.2. Alternatively, vugs with aspect ratios 0.5–1 are not forming permeable paths because they are isolated and are not contributing to flow zones. The inversion of P- and S-wave velocity logs using density and total porosity logs obtains the secondary porosity and pore aspect ratios. It found optimum correlation coefficients of 0.9975 for S-wave and 0.9405 for P-wave velocities by constraining the solution with the natural relation of the total porosity versus primary plus secondary porosities. The Port Mayaca aquifer includes Stoneley-wave permeability, formation microimager logs, and microresistivity logs, which together with pore aspect ratio and secondary porosity logs delineate and characterize the flow zones. In addition, data integration demonstrates that the vug porosity log detects fractures in resistive, permeable, and dense cemented zones. This new finding creates vug signatures, with their maximums resembling the shapes of the corresponding resistivity heights in the microresistivity log. In conclusion, it is shown that the anomaly zones correspond to water production regions, and their presence is confirmed with flow meter logs.