An Improved Method for Calculating Wave Velocity Fields in Fractured Rock Based on Wave Propagation Probability

Ultrasonic velocity field imaging offers a robust tool for characterizing and analyzing damage and its evolution within fractured rock masses. The combined application of ultrasonic first arrival waves and coda waves can significantly enhance the accuracy and range of velocity field imaging. This manuscript introduces an improved imaging method that integrates the propagation probability distribution of the first arrival and coda waves to calculate the velocity field. The proposed method was applied to the velocity field imaging of a medium with multiple scatterers and varying degrees of fracturing. The overall error and calculation unit error of the proposed method were analyzed, and its improvement in calculation accuracy and applicable scope was verified. Additionally, this method was employed to image the velocity field during the damage process of fractured rock masses. The imaging results were compared against digital speckle patterns to confirm the method’s suitability. Finally, we discussed the impact of measurement errors and sensor missing on the accuracy of the computational outcomes presented in this method. These two situations will affect the calculation results, and the influence of reducing the number of sensors is smaller than that of measuring time shifts with error.