EarthRef.org Reference Database (ERR) -- Alexandrescu et al. 1995

Wavelet analysis is applied to detect and characterize singular events, or singularities, or jerks, in the time series made of the last century monthly mean values of the east component of the geomagnetic field from European observatories. After choosing a well-adapted wavelet function, the analysis is first performed on synthetic series including an ''internal,'' or ''main,'' signal made of smooth variation intervals separated by singular events with different ''regularities,'' a white noise and an ''external'' signal made of the sum of a few harmonics of a long-period variation (11 years). The signatures of the main, noise, and harmonic signals are studied and compared, and the conditions in which the singular events can be clearly isolated in the composite signal are elucidated. Then we apply the method systematically to the real geomagnetic series (monthly means of Y from European observatories) and show that five and only five remarkable events are found in 1901, 1913, 1925, 1969, and 1978. The characteristics of these singularities (in particular, homogeneity of some derived functions of the wavelet transform over a large range of timescales) demonstrate that these events have a single source (of course, internal). Also the events are more singular than was previously supposed (their ''regularity'' is closer to 1.5 than to 2., indicating that noninteger powers of time should be used in representing the time series between the jerks). ¿ American Geophysical Union 1995 Wavelet analysis is applied to detect and characterize singular events, or singularities, or jerks, in the time series made of the last century monthly mean values of the east component of the geomagnetic field from European observatories. After choosing a well-adapted wavelet function, the analysis is first performed on synthetic series including an ''internal,'' or ''main,'' signal made of smooth variation intervals separated by singular events with different ''regularities,'' a white noise and an ''external'' signal made of the sum of a few harmonics of a long-period variation (11 years). The signatures of the main, noise, and harmonic signals are studied and compared, and the conditions in which the singular events can be clearly isolated in the composite signal are elucidated. Then we apply the method systematically to the real geomagnetic series (monthly means of Y from European observatories) and show that five and only five remarkable events are found in 1901, 1913, 1925, 1969, and 1978. The characteristics of these singularities (in particular, homogeneity of some derived functions of the wavelet transform over a large range of timescales) demonstrate that these events have a single source (of course, internal). Also the events are more singular than was previously supposed (their ''regularity'' is closer to 1.5 than to 2., indicating that noninteger powers of time shoul