Introducing a new statistical theory to quantify the Gaussianity of the continuous seismic signal

The quality of the seismic signal recorded at permanent and temporary stations is sometimes degraded, either abruptly or over time. The most likely cause is a high level of humidity, leading to corrosion of the connectors but environmental changes can also alter recording conditions in various frequency ranges and not necessarily for all three components in the same way. Assuming that the continuous seismic signal can be described by a normal distribution, we present a new approach to quantify the seismogram quality and to point out any time sample that deviates from this Gaussian assumption. To this end the notion of background Gaussian signal (BGS) to statistically describe a set of samples that follows a normal distribution. The discrete function obtained by sorting the samples in ascending order of amplitudes is compared to a modified probit function to retrieve the elements composing the BGS, and its statistical properties, mostly the Gaussian standard deviation, which can then differ from the classical standard deviation. Hence the ratio of both standard deviations directly quantifies the dominant gaussianity of the continuous signal and any variation reflects a statistical modification of the signal quality. We present examples showing daily variations in this ratio for stations known to have been affected by humidity, resulting in signal degradation. The theory developed can be used to detect subtle variations in the Gaussianity of the signal, but also to point out any samples that don't match the Gaussianity assumption, which can then be used for other seismological purposes, such as coda determination.