oa Optimal correction of data from misoriented multi-component geophysical sensors

Incorrectly oriented geophysical sensors affect data analysis procedures, which can lead to errors in results and interpretations. These problems generally occur in applications, in which the orientation of the sensor cannot be actively controlled and is not known a priori. Common examples are sensors deployed in borehole installations or on the seafloor. We introduce two methods to optimally correct data sets from misaligned two- and three-component sensors. Firstly, we demonstrate how a set of multiple two-component sensors can be re-oriented in a single step calculation. In the second part, we introduce a quaternion-based analytical method for the calculation of the optimal re-orientation of three-component sensors. A common approach to the re-orientation of three-component data is to assume that the vertical axis does not have to be corrected during the processing. We show, that this approximation can lead to significant deviations between re-oriented data and original data. Therefore, the estimation of not only an optimal rotation angle, but also the rotation axis can help to mitigate a systematic source of error in the processing of geophysical data.