An Effective Algorithm to Correct the Orientation Error and Time Shift of Downhole Seismograms


Estimating the orientation error of a downhole seismometer, in general, is a two-parameter optimization problem. It requires determining both the time shift and orientation error at same time. Although this estimation involves a tedious computation, the resolution of this optimization is still limited by the grid size selected for global searching. To improve the computing efficiency and resolution, we derive an analytic formulation for calculating the maximum cross-correlation function between synthetic and rotated seismograms and apply it to an orientation-error-correction method developed by Chiu and Huang (2003). This modified method is capable of giving an accurate and efficient estimation of the orientation error in one step for a given time shift. This algorithm consists of two stages: (1) computing the synthetic seismograms at the downhole station, and (2) searching a time shift that yields a maximum cross-correlation between the rotated seismograms (observations) and the synthetic seismograms at the downhole station. Results show that this modified algorithm allows for a more flexible selection of data for analysis, and gives a fast, stable and accurate estimation of the orientation error.

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