# Time scales and gaps, Haar fluctuations and multifractal geochronologies

## TL;DR

This paper introduces a new method to analyze geochronology data using Haar fluctuation analysis, revealing how measurement density affects the interpretation of Earth's history.

## Contribution

The paper introduces geochronology measurement densities as a new paleoindicator and uses Haar fluctuation analysis to characterize their scaling properties.

## Key findings

- Measurement density is a new paleoindicator that is typically correlated with primary indicators.
- Haar fluctuation analysis reveals scaling regimes and exponents spanning nine orders of magnitude in time.
- Measurement density characteristics are essential for unbiased statistical interpretations of geochronological data.

## Abstract

Outcrops and cores are primary sources of information about the Earth’s past. Quantitative analyses rely on geochronologies that take into account highly variable sedimentation and erosion rates as well as gaps from missing strata. Using 23 geochronologies from the Holocene, Quaternary, Phanerozoic and Precambrian, we apply Haar fluctuation analysis to statistically characterize the number of measurements per unit time - the measurement densities. The analysis determines the densities’ (multifractal) scaling regimes and exponents; collectively, the analyses span over nine orders of magnitude in time scale. The measurement density is a new paleoindicator that we show is typically correlated with the primary paleoindicator, biasing and complicating its statistical interpretation. We also analyze the distribution of gaps linking the latter’s (probability) scaling with series incompleteness and the length Sadler effect. The density characteristics are needed to unbias spectra and other statistical characterizations.

Geochronology measurement densities (i.e., the number per time) are a new paleo indicator, as statistically characterized using Haar fluctuation analysis, determining the densities’ scaling regimes, exponents and their correlations with the primary paleoindicators.