Analytically Modelling DST Arrival Time Databases with High Order Polynomials For Optimal High Resolution Imaging-Paper 2

Paper 2

Pdf Summary

The paper presents DSTPolyKF, a method for estimating depth-dependent seismic velocities from Downhole Seismic Testing (DST) arrival times. Conventional estimates can be affected by noisy measurements, limited sensor resolution, and small depth intervals, making velocity profiles less reliable.<br /><br />DSTPolyKF fits a polynomial to arrival times as a function of depth using a Kalman filter. The filter processes measurements sequentially, accommodates different measurement uncertainties, and supports data fusion from multiple seismic traces. Polynomial degrees 2–7 are assessed using error and goodness-of-fit measures, including RMSE, MAPE, and the coefficient of determination; the lowest degree with strong accuracy measures is selected. The fitted arrival-time curve can then be used with forward raypath modelling to derive interval velocities at user-selected depth increments.<br /><br />The authors demonstrate the approach on real onshore and offshore data. In both cases, sixth- and seventh-degree polynomials generally provide the strongest fits. Onshore results show substantial differences between left- and right-side arrival estimates and between velocity estimates near the bottom of the fitted range; one unstable estimate is recommended for exclusion. Offshore estimates from the two polynomial orders are mostly consistent, with larger discrepancies near the deepest data.<br /><br />The method offers a way to use all available arrival-time estimates and generate higher-resolution velocity profiles, including at intervals smaller than the original measurement spacing. The authors characterize it as promising, but note that the minimum number of data points needed for a reliable profile remains an open question requiring further investigation and validation.

Keywords

DSTPolyKF

Downhole Seismic Testing

seismic velocity estimation

arrival-time fitting

Kalman filter

polynomial regression

depth-dependent velocities

interval velocity

raypath modelling

goodness-of-fit metrics