New procedures to decompose geomagnetic field variations and application to volcanic activitiy

SUMMARY We report the development of numerical procedures for extracting long‐term geomagnetic field variations caused by volcanic activity from an observed geomagnetic field by using statistical methods. The newly developed procedures are to estimate the trend from the observed data, as well as variations of non‐volcanic origin such as periodic components, components related to external geomagnetic variations and observational noise. We also aim at referring to data obtained at a remote standard geomagnetic observatory rather than using a temporarily installed reference site for reasons of data quality. Two different approaches—a Bayesian statistical method and a Kalman filter method—are applied to decompose the geomagnetic field data into four components for comparison. The number of filter coefficients and the degree of condition realizations are optimized on the basis of minimization of the information criteria. The two procedures were evaluated by using a synthetic data set. Generally, the results of both methods are equally sufficient. Subtle differences are seen at the first, several data points due to arbitrarily selected initial values in the case of the Kalman filter method and at the smaller residual for the Bayesian statistical method. The largest differences are in computation time and memory size. The Kalman filter method runs a thousand times faster on a testing workstation and requires less memory than the Bayesian method. The Kalman filter method was applied to the total intensity data at Kuchi‐erabu‐jima volcano. The result suggests that the procedure works reasonably well.