Earthquake forecasting is arguably one of the most challenging tasks in Earth sciences owing to the high complexity of the earthquake process. Over the past 40 years, there has been a plethora of work on finding credible, consistent and accurate earthquake precursors. This paper is a cumulative survey on earthquake precursor research, arranged into two broad categories: electromagnetic precursors and radon precursors. In the first category, methods related to measuring electromagnetic radiation in a wide frequency range, i.e., from a few Hz to several MHz, are presented. Precursors based on optical and radar imaging acquired by spaceborne sensors are also considered, in the broad sense, as electromagnetic. In the second category, concentration measurements of radon gas found in soil and air, or even in ground water after being dissolved, form the basis of radon activity precursors. Well-established mathematical techniques for analysing data derived from electromagnetic radiation and radon concentration measurements are also described with an emphasis on fractal methods. Finally, physical models of earthquake generation and propagation aiming at interpreting the foundation of the aforementioned seismic precursors, are investigated.

This work examines if chaos and long memory exist in PM₁₀ concentrations recorded in Athens, Greece. The algorithms of Katz, Higuchi, and Sevcik were employed for the calculation of fractal dimensions and Rescaled Range (R/S) analysis for the calculation of the Hurst exponent. Windows of approximately two months’ duration were employed, sliding one sample forward until the end of each utilized signal. Analysis was applied to three long PM₁₀ time series recorded by three different stations located around Athens. Analysis identified numerous dynamical complex fractal time-series segments with patterns of long memory. All these windows exhibited Hurst exponents above 0.8 and fractal dimensions below 1.5 for the Katz and Higuchi algorithms, and 1.2 for the Sevcik algorithm. The paper discusses the importance of threshold values for the postanalysis of the discrimination of fractal and long-memory windows. After setting thresholds, computational calculations were performed on all possible combinations of two or more techniques for the data of all or two stations under study. When all techniques were combined, several common dates were found for the data of the two combinations of two stations. When the three techniques were combined, more common dates were found if the Katz algorithm was not included in the meta-analysis. Excluding Katz’s algorithm, 12 common dates were found for the data from all stations. This is the first time that the results from sliding-window chaos and long-memory techniques in PM₁₀ time series were combined in this manner.

Earthquake forecasting is arguably one of the most challenging tasks in Earth sciences owing to the high complexity of the earthquake process. Over the past 40 years, there has been a plethora of work on finding credible, consistent and accurate earthquake precursors. This paper is a cumulative survey on earthquake precursor research, arranged into two broad categories: electromagnetic precursors and radon precursors. In the first category, methods related to measuring electromagnetic radiation in a wide frequency range, i.e. from a few hz to several MHz, are presented. Precursors based on optical and radar imaging acquired by space borne sensors are also considered, in the broad sense, as electromagnetic. In the second category, concentration measurements of radon gas found in soil and air, or even in ground water after being dissolved, form the basis of radon activity precursors. Well-established mathematical techniques for analysing data derived from electromagnetic radiation and radon concentration measurements are also described with an emphasis on fractal methods. Finally, physical models of earthquake generation and propagation aiming at interpreting the foundation of the aforementioned seismic precursors, are investigated

The overall seismicity of Pakistan from 1820 to 2020 is analysed in terms of its multifractal behaviour. Seismic events of magnitude M_L = 3.0 and above are spatially clustered into four distinct groups, each one corresponding to a different region of high seismic activity. The Multifractal Detrended Fluctuation Analysis (MFDA) method applied on each cluster reveals pronounced inter-cluster heterogeneity in terms of the resulting generalised Hurst exponent and fractality spectrum, possibly due to the particular tectonic characteristics of the regions under investigation. Additional results on the variability of the Gutenberg–Richter b-value across the defined clusters further corroborate the uniqueness of the seismic profile of each region.

This paper reports kHz EM observations recorded by the Kardamas station in Ilia, Greece a few days before four near-field earthquakes occurred within a 24 km radius, with epicentral depths below 29 km. This work investigated the fractal features hidden in the EM observations via power-law analysis. All EM signals exhibited characteristic fractal epochs with organisation in space and time. A significant number of accurate fractal segments were delineated in the majority of the EM observations. A significant number of fractal areas corresponded to predictable Class I fBm category with 1 ≤ b ≤ 3 (0 ≤ H ≤ 1). Numerous persistent key-periods are reported with 2 < b ≤ 3 (0.5 ≤ H ≤ 1) which are deemed as signs of impeding earthquakes according to the literature. Numerous segments were found with strong persistent b-values in the range (2.3 ≤ b ≤ 3) (0.65 ≤ H ≤ 1) and b-values corresponding to switching between antipersistency and persistency with (1.7 ≤ b < 2.3) (0.35 ≤ H < 0.65). These are deemed as the most significant precursory signs. Interpretations are given via the asperity model.

This paper reports the multifractal characteristics of lengthy PM₁₀ time series from five stations in the Greater Athens Area (GAA), Greece. A novel methodology based on the multifractal detrended fluctuation analysis (MFDFA) is applied to raw and shuffled series in 74 segments in 11 date-periods, previously located, with very strong self-organised critical (SOC) and fractal properties. The MFDFA identified multifractality in all segments. Generalised and classical Hurst exponents are in the range 0.8–1.5 and 9–4.5 for the raw and shuffled series, while the multifractal $f\left(a\right)-a$ is within 0.5–1.2 and 0.1–2, respectively. The $f\left(a\right)-a$ data are fitted to polynomials to calculate the multifractal parameters W, $FWHM$ and $f_{max}$. While these are bimodal, a new parameter, $FWHM/f_{max}$, is normally distributed, and due to this, it is employed to locate the important multifractal behaviour via the $FWHM/f_{max}$ outliers. Five date-periods are found. The date-period 8 January 2015 has extraordinary multifractality for raw and shuffled series for both the AGP and LYK stations. This date-period is one of the three reported in the most recent combination study. Finally, sliding window MFDFA evolution plots of all the series are given. The results provide very strong evidence of the multifractality of the PM₁₀ time series.