A least squares method based on quaternions to derive absolute orientation of geophones with AHRS

In this paper, we developed a least squares method based on quaternions to get the relative rotation between geophone pairs, and combined with an attitude and heading reference system (AHRS) we can derive the orientation of all geophones in geographical coordinates. This method can be used in vertical seismic profile (VSP), or the free-fall ocean-bottom seismometer (OBS), or deep-tow acoustics and geophysics system (DTAGS). Compared with the traditional geophone reorientation method, this method can be applied in cases where seismic source location is unknown or a priori information is missing. An AHRS is installed in a geophone as the reference, and used a least squares method we can obtain the relative rotation between the reference and other geophones. Therefore, the orientation of all geophones in geographical coordinates can be derived with minimal additional hardware. In addition to apply the method in data processing, we developed a geophone reorientation scheme and estimated the uncertainties of the relative rotation between geophone pairs. We modified the borehole acquisition system to include the AHRS, and tested it in Daqing oilfield, China. Comparing the orientation determined by the method proposed in this paper with the orientation measured by the AHRS, the deviation is less than 1.2° which is acceptable and can satisfy the requirement of data processing . The results demonstrated the validity of the modified system and with the least hardware device. The method proposed in this paper provides a much easier and more convenient way to get the orientation of all geophones in geographical coordinates.

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