Analytically Modelling Dst Arrival Time Databases With High Order Polynomials For Optimal High Resolution Imaging

Downhole Seismic Testing (DST) is an extensively utilized geotechnical tool for site characterization. DST provides low strain (<10-5) in-situ interval shear and compression wave velocity estimates. These velocities are determined by obtaining relative arrival times of source waves as they travel through the stratigraphy and are recorded by one or more vertically offset seismic sensors. The DST arrival times have associated measurements errors and resolution limitations, which become more pronounced as the depth interval of analysis is reduced. Baziw Consulting Engineers (BCE) has developed a new DST analysis technique, the so-called DSTPolyKF algorithm, whereby the arrival times of DST data set are used to define a high order polynomial. The main advantages of this new technique are four-fold: 1) the ability to utilize all arrival time estimates irrespective of measurement errors. 2) the ability to analyze the data with user specified and even small (≤ 0.5m) depth intervals. 3) the ability to apply sophisticated data fusion for significantly more accurate DST interval velocity estimation. 4) the use of polynomial regression accuracy parameters to quantify how well the “best fit” polynomial fits the acquired arrival time data sets. This paper outlines the mathematical details of the best fit polynomial where a Kalman filter formulation is implemented. The performance of the DSTPolyKF algorithm is demonstrated by processing real DST data sets.