The TOA BT is a measurement of the radiance of the TIR radiation at 3–5 µm or 8–14 µm from the Earth's surface, atmosphere, and clouds to satellite sensors. It is a direct and fundamental physical quantity expressed by the equivalent blackbody temperature of one channel (e.g., 11.77–12.27 µm band) in Kelvin. In other words, BT is not the normal temperature due to ignoring the emissivity effect. Many satellite sensors obtain TIR measurements, such as the Moderate Resolution Imaging Spectroradiometer (MODIS), Visible Infrared Imaging Radiometer Suite (VIIRS), and Advanced Very High Resolution Radiometer (AVHRR) aboard polar-orbiting satellites and Spinning Enhanced Visible and Infrared Imager (SEVIRI) and Advanced Himawari Imager (AHI) aboard geostationary satellites.

TOA BT data are some of the most-used remote sensing data in thermal anomaly detection because of their easy accessibility and data processing. Several studies indicate that significant BT anomalies existed in seismically active areas about 1 month to 8 days before earthquakes (Lisi et al., 2010, 2015; Pergola et al., 2010). The regions with strong tectonic activities also showed intensive BT anomalies during the preparatory phases of low-magnitude earthquakes (Lisi et al., 2010). After a 10-year retrospective correlation analysis in Greece, TOA BT anomalies are considered to satisfy the qualifications involved in a multi-parametric system for the time-dependent assessment of seismic hazards (Eleftheriou et al., 2016). As shown in Fig. 1, BT anomalies mainly occurred before the earthquake with magnitude greater than 5, but for seismic events with magnitude less than 5 this anomaly indicator became less significant.

Another frequently used precursor at TOA is OLR, which is a critical component of the Earth's energy budget. OLR is the total longwave radiative flux (W m-2) in the TIR wavelength from 4 to 100 µm, which is emitted from the Earth and its atmosphere going to space. More specifically, it is the integrated result of the reflection, absorption, and emission of longwave radiation by the Earth's surface (land and sea), atmosphere, aerosols, and clouds, which finally leaves the Earth system. OLR represents the radiation characteristics of the cloud top when the instantaneous field of view of satellite sensors is covered by clouds and indicates the longwave radiation emitted by the surface and atmosphere under cloudless conditions.

OLR cannot be directly measured but can be derived from measurements of sensors (e.g., AVHRR; Atmospheric Infrared Sounder, AIRS; and Clouds and the Earth's Radiant Energy System, CERES). Among them, the National Oceanic and Atmospheric Administration (NOAA) OLR is the commonly used data product in various studies and is retrieved from the AVHRR TIR bands (10.5–12.5 µm) on a 2.5∘×2.5∘ latitude–longitude grid with daily and monthly mean values from 1981 to the present (Gruber and Krueger, 1984). The latest AIRS OLR product, which is retrieved from hyperspectral TIR data, is AIRS Version 6 Level 3 monthly mean product on a 1∘×1∘ latitude–longitude grid beginning in September 2002 (Aumann et al., 2003). Finally, the CERES OLR dataset is the monthly mean value from 2000 in the CERES Energy Balanced and Filled (EBAF) Edition 4.0 datasets on a 1∘×1∘ latitude–longitude grid (Rose et al., 2013).

Several studies suggest that OLR can be effectively used as a short-term or impending earthquake precursor. OLR appeared as a steadily increasing trend around the epicenter and thus can be used as an indicator of seismic activity (Ouzounov et al., 2007). Figure 2 presents the time series of daily OLR anomaly before the Mw 9.0 Sumatra–Andaman Islands, North Sumatra, earthquake (3.09∘ N, 94.26∘ E) occurred on 26 December 2004. After several small peaks beyond the mean field of OLR, an intense rise showed up shortly following this mega-earthquake. Anomalous OLR occurred 2 months to several days prior to the main shock with at least several thousands of square kilometers. OLR anomaly has a direct significance for earthquakes with magnitude above 5.5 (Eleftheriou et al., 2016). Anomalous OLR variations can reach 30–45 W m-2 around epicentral areas 7–8 days prior to the major earthquake (Rawat et al., 2011). Cumulative elastic energy in the earthquake preparation regions may result in intensive thermal emissions associated with the release of a large amount of energy when an earthquake occurs. Increase in surface temperature, air temperature, water vapor, and other greenhouse gases results in the increase in OLR and TOA BT, especially around the epicenter under clear sky conditions (Tramutoli et al., 2005).

TOA BT and OLR represent longwave radiation variations of the entire surface–atmosphere system and are significantly affected by atmospheric conditions. The height and coverage of clouds have a dominating influence on the total intensity of longwave radiative fluxes received at the TOA (Turner et al., 2015). Therefore, eliminating cloud effects is necessary in applications, which can be difficult when working with low-resolution data. Meanwhile, OLR anomalies may be the result of other atmospheric effects and not of increased surface temperature (Tronin, 2010). In the cases under clear sky conditions, water vapor is another significant factor that has strong absorption and re-emission capabilities on longwave radiation and rapidly changes in the spatiotemporal pattern. These situations are particularly unfavorable for detecting weak pre-seismic anomalies; thus, land surface temperature (LST) and similar data products that are not heavily affected by atmospheric disturbances are preferred (Filizzola et al., 2004; Lisi et al., 2015).

Atmospheric water vapor and temperature are two important physical quantities that describe the status of the atmosphere, especially in the atmospheric boundary layer. They have strongly dependencies and thus can present synchronous responses to the impending earthquakes.

Over 99 % of atmospheric moisture is in the form of water vapor, and it is abundant and highly varies in the atmosphere. Water vapor is the primary greenhouse gas in the Earth's climate system and influences long-term climate changes. The water vapor associated with atmospheric energy drives the development of weather systems and transfer of heat from the tropics to the poles. Atmospheric water vapor content can be referred to as the total column water vapor contained in a vertical column of atmosphere between the Earth's surface and the TOA, which can be retrieved from near-infrared, TIR, or passive microwave data (Chesters et al., 1983; Ferraro et al., 1996; Gao and Kaufman, 2003). For example, the MODIS total precipitable water product (MOD05_L2 and MYD05_L2) has two types of data: one using near-infrared algorithm at the 1 km spatial resolution during the day and the other using infrared algorithm at 5 km resolution during day and night. In general, the accuracy of water vapor products ranges from 5 to 10% (Gao and Kaufman, 2003).

Anomalies of atmospheric water vapor content have been observed prior to several strong earthquakes (Cervone et al., 2004; Dey and Singh, 2003). The 2001 Gujarat earthquake triggered anomalous atmospheric moisture increase of about 15 mm, which were detected using passive microwave data of the Special Sensor Microwave Imager (SSM/I; Dey et al., 2004). The anomalous increase of water vapor level occurred around the epicenter in land regions before the earthquake and in ocean regions after the earthquake. Meanwhile, AIRS data led to the discovery of anomalous changes in relative humidity at different pressure levels reaching 500 hPa, with even larger variations at the lower levels (Singh et al., 2010a). Dey et al. (2004) related this phenomenon to the increase of the surface latent heat flux (SLHF), which is discussed in Sect. 2.5.

Aside from atmospheric moisture, air temperature (or atmospheric temperature) is the most commonly measured weather parameter. It refers to the screen-level air temperature in meteorological terms, which is normally measured at the attitude of 2 m above the ground surface. Air temperature is a more complex parameter than LST and is affected by LST, winds, topography, etc. LST can be estimated based on satellite TIR measurements. However, air temperature cannot be directly derived from LST, and no operational remote sensing data product of air temperature is available at present. The atmospheric profiles provide the air temperature and water vapor amounts at different altitudinal layers in the vertical atmosphere, but this air temperature is different from the screen-level temperature. The atmospheric profiles can be retrieved from TIR multispectral sensors (e.g., MODIS) or infrared sounders (e.g., AIRS) (Aumann et al., 2003; Seemann et al., 2003).

Significant near-surface air temperature anomalies related to earthquakes have been reported in different studies (Panda et al., 2007; Pulinets and Dunajecka, 2007). An approximate increase of air temperature at 2–4 K in a north–south pattern along the Nosrātabād fault zone during 18–20 December was observed prior to the Ms 6.0 Kerman earthquake in Iran on 20 December 2010 (Fig. 3) (Alvan et al., 2013). Anomalous changes of air temperature at different pressure levels from AIRS data were found up to 500 hPa with the variations becoming larger at the lower levels (Singh et al., 2010a). An increase in air temperature along with low air humidity has been observed prior to earthquakes (Pulinets et al., 2006a; Singh et al., 2010a). Ouzounov et al. (2007) and Pulinets and Dunajecka (2007) consider that the anomalies in air temperature and relative humidity prior to strong earthquakes indicated by historical meteorological data are primarily related to the air ionization caused by increased radon emanations from faults in earthquake preparation regions. Anomalous areas are considerably larger than seismic sources, which indicates the difficulty of identifying the epicenter before a main shock.

Atmospheric trace gases make up less than 1 % of the Earth's atmosphere by volume. These gases include CO2, CH4, O3, SO2, and NOx, which are produced from natural geothermal sources, volcanic activity, ecosystem, and anthropogenic sources. Trace gas concentrations are crucial in investigating atmospheric processes. Atmospheric trace gas data, such as CH4, CO2, and CO, can be retrieved from satellite measurements (e.g., AIRS hyperspectral TIR data) (Chahine et al., 2006; Clarisse et al., 2011).

Seismic activities can change atmospheric composition, especially the increment of greenhouse gases prior to strong earthquakes. A 6 % increase in the columnar ozone prior to the 2015 Nepal earthquake was observed (Ganguly, 2016). An increased CO emission at near-surface pressure levels associated with LST over epicenter areas was detected by the Measurements of Pollution in the Troposphere (MOPITT) on board the Terra satellite approximately 1 week before the earthquake (Singh et al., 2010b). Anomalous increases in total column CO and O3 occurred over the epicenter areas 1 to 6 months prior to several strong earthquakes (Cui et al., 2013). Figure 4 indicates that anomalous CO appeared along the San Andreas Fault, while the anomalies of O3 spread over wider areas around the epicenter before and after Ms 7.1 Baja California earthquake on 5 April 2010. However, these phenomena are unstable with only parts of studied earthquakes exhibiting anomalous variations and with persistent time being irregular.

Changes in pressure between rocks due to seismic activity are believed to result in greenhouse gas emissions and local greenhouse effect (Choudhury et al., 2006; Singh et al., 2010a; Zoback and Gorelick, 2012). The experimental results show that gases, such as CH4 and CO2, can obtain energy from the transient electric field and cause a temperature increase. The trace gas anomaly before medium to strong earthquakes was preliminarily believed to exhibit (1) a sudden release of gas and (2) a static electricity of field mutation. Earthquakes may lead to the release of underground carbonaceous gas, which provides a scientific basis for the mechanism of pre-seismic thermal anomalies. In addition, CO2-rich fluids in the deep crust are considered as the possible important carbonaceous gas source in the lithosphere–coversphere–atmosphere coupling (LCAC) process (Chiodini et al., 2011). The anomalies in trace gas concentration can be attributed to gas emissions in the lithosphere and photochemical reactions (Cui et al., 2013). The LST anomalies prior to the 2009 Mw 6.3 L'Aquila earthquake illustrate the strong correlation with the topographic height and were clearly distributed over the mountain tops but not the valleys (Piroddi et al., 2014). The anomalous mechanisms of the activation of electronic charge carriers and emission of greenhouse gases or radon gas are considered to demonstrate a consistent manner because of prominent LST anomalies within the limestone regions in this earthquake case. As a result, LST and air temperature may increase, resulting in changes in SLHF and atmospheric water vapor condensation and propagation to the BT observed by satellite sensors.

Aerosols are the fine solid and liquid particles suspended in the atmosphere that are produced from various sources, such as desert dust, wildfire smoke, sea salt particles, volcanic ash, and urban haze. Aerosols have different optical and microphysical properties depending on their type and size distribution. They have an important influence on cloud formation and are often expressed by the aerosol optical depth (AOD). AOD is a dimensionless physical quantity used to describe quantitatively the extinction degree of the direct solar radiation reaching the ground by the absorption and scattering of aerosols. AOD is defined as the integrated extinction coefficient within a vertical column of unit cross section along the entire atmospheric path, where the planetary boundary layer accounts for most of them. For now, most of multispectral radiometers in the visible, near-infrared, and shortwave-infrared wavelength regions can be used to retrieve AOD. For instance, the MODIS daily Level 2 aerosol product (MOD04), which is produced by the Dark Target and Deep Blue algorithms at a spatial resolution of 10 km at nadir in Collection 6 (Levy et al., 2013), includes many aerosol parameters, such as AOD, aerosol type, angstrom exponent, asymmetry factor, and single scattering albedo.

Aerosols are also used as indicators in many pre-seismic anomaly studies. AOD was observed an increase of 40 % prior to the 2015 Nepal earthquake (Ganguly, 2016). A clear increase in AOD around the epicenter 2 days prior to the 2010 Chile earthquake was found in Fig. 5 using three anomaly detection methods in order to reduce uncertainty of detecting anomaly date (Akhoondzadeh, 2015). An anomalous increase of ground-measured AOD is quasi-synchronous with several abnormal hydrothermal parameters (Wu et al., 2016). Over the sea surface, significant changes in aerosol parameters are considered to be related to the 2001 Gujarat earthquake (Okada et al., 2004). Although aerosols do not directly relate to the TIR radiation, the charged aerosol particles play a role in the water vapor condensation and cloud formation over earthquake fracture areas. A high aerosol concentration causes stronger electric field intensities and increased infrared emissions (Liperovsky et al., 2005). Therefore, indirect effects of aerosols on the pre-seismic anomalies cannot be ignored. Additionally, the air ionization is a possible reason that keeps aerosols suspended in the atmosphere for many days before the earthquake, which could be explained by the p-hole theory (Freund et al., 2009). The predominantly, sometimes exclusively, positive airborne ions generated at the Earth's surface rise through the atmospheric column and attach to aerosol particles; thus the ionized aerosols can suspend in the atmosphere for a longer time. More field measurements, which can validate this theory, still need to be carried out.

SLHF (W m-2) is the flux of the heat absorbed or released by the phase transition (i.e., condensation, evaporation, and melting) of water from the Earth's surface to the atmosphere. SLHF is an important component of Earth's surface energy budget and is mainly affected by the atmospheric relative humidity, wind speed, surface temperature, and season. Traditionally, SLHF is measured through the Bowen ratio technique or by the eddy covariance and can also be obtained from satellite products. MODIS global evapotranspiration product (MOD16) has a spatial resolution of 1 km at 8-day, monthly, and annual intervals (Mu et al., 2011).

Several studies have reported the abnormal increase of SLHF prior to earthquakes. The SLHF increased by approximately 50 W m-2, peaking at 115 W m-2 over 3–23 days before earthquakes in the Middle East (Mansouri Daneshvar et al., 2014). SLHF can also be a possible precursor to coastal earthquakes because anomalous SLHF tends to be more intensive over sea surface than over land surface (Cervone et al., 2004, 2006). The analysis of coastal earthquakes shows that the SLHF increased abnormally a few days before earthquakes, which is the result of the increase in surface temperature in seismically active areas (Pulinets et al., 2006a). SLHF anomaly is significantly weaker on land surface than on sea surface due to obvious differences in air humidity, wind speed, and surface temperature between sea and land surfaces. However, Qin et al. (2014a) found that anomalous SLHF, which is indicated by the dashed circle in Fig. 6, occurred approximately 10 days before the inland Pu'er earthquake (23.8092∘ N, 101.15∘ E) on 2 June 2007. Conversely, the study of Zhang et al. (2013) indicates that no significant anomalous variation of SLHF exists prior to ten studied marine or coastal earthquakes, and that data accuracy and parameter settings have an important effect on quantification of the correlation between SLHF anomaly and earthquake's occurrence.

SLHF anomaly prior to earthquakes is considered to relate to the underground fluid movement and the interaction among the underground, surface, and atmosphere (Alvan et al., 2013). Mansouri Daneshvar et al. (2014) believed that water vapor responses to seismic preparation phases follow a seismic-triggered chain, which undergoes air ionization, SLHF enhancement, water vapor condensation, and increased rainfall. Several studies have proven that SLHF anomalies before earthquakes are linked with soil moisture (Cervone et al., 2004; Dey and Singh, 2003). Meanwhile, air ionization in the lithosphere–atmosphere–ionosphere coupling (LAIC) model may be responsible for soil moisture and SLHF anomalies due to the increase of water condensation on newly formed ions (Pulinets and Ouzounov, 2011).

LST, also known as surface skin temperature, represents a remarkably thin surface layer of medium temperature state, which is affected by solar radiation, surface albedo, vegetation cover, soil moisture, etc. LST affects the energy exchange between the surface and boundary layers and determines the air temperature near the surface. Compared to TOA BT and OLR, LST can indicate the surface warming process better. MODIS LST data are currently the most extensively used products in the 1 km spatial resolution with an inversion accuracy of approximately 1 K (Wan, 2014).

LST is suitable for the analysis of inter-monthly variations, which is beneficial to short-term earthquake monitoring. A 40-day time period is sufficient for anomaly monitoring (Bhardwaj et al., 2017). The LST prior to earthquakes usually increased by at least 3–5 K (Ouzounov et al., 2006; Ouzounov and Freund, 2004; Tronin, 2006). A 1–10 K rise of LST 2 weeks before the main shock of 2011 Tōhoku earthquake was detected around the epicenter (Zoran, 2012). Moreover, the study by Bhardwaj et al. (2017) shows that snow cover levels prior to the 2015 Nepal earthquake noticeably declined and that snow surface temperature is a highly sensitive precursor that presented 3–14 K temperature anomaly in 3–17 days prior to this earthquake. Most studies use nighttime LST data for analysis due to the absence of solar heating, leading to measurements that are predominantly gathered from surface and underground thermal sources. However, LST anomalies can also be significant in the daytime (Blackett et al., 2011; Panda et al., 2007; Saraf et al., 2008).

The pre-seismic anomalies in epicentral areas before strong earthquakes are related to the increase in air temperature, LST, and soil temperature at shallow layers. LST anomaly indicated by MODIS data was consistent with anomalous air temperature variations observed at the meteorological station close to the epicenter (Akhoondzadeh, 2013). The anomalous temperature variations are related to the seismic deformation and follow the fault evolution under seismic stress changes (Ma et al., 2008). Thus, LST is more useful in detecting anomalies than TOA BT or OLR because it is less affected by the atmosphere, which allows it to produce a higher signal-to-noise ratio (SNR) (Aliano et al., 2008; Lisi et al., 2015). Figure 7 shows the spatial and temporal evolution of the sequence of LST anomalies by different colored dashed circles (Lisi et al., 2015). The green dashed circle indicates the possible local warming effect caused by clouds. The LST anomalies which followed the main tectonic lineaments (green lines) in central Italy (black circle), the Balkan region (blue circle), and the Padania plain (purple circle) were possibly associated with the medium–strong earthquakes. Meanwhile, LST, as a thermodynamic parameter of dynamic equilibrium, derived by remote sensing data contains a degree of uncertainty due to the influence of surface types, processes of surface energy balance, and atmospheric turbulence.

Several cases of marine earthquake monitoring using remote sensing TIR data have been successful. Sea surface temperature (SST) anomaly can be related to seismicity (Ouzounov and Freund, 2004), but SST is strongly influenced by weather conditions and currents. Seawater has a large thermal inertia that allows its temperature to change more slowly; therefore, some mechanisms of LST anomalies are not applicable to SST anomalies. The study of the 2000 Blanco earthquake sequence shows that ocean hydrothermal system can be altered by large earthquakes and significant decline of temperature was observed following the main shock (Dziak et al., 2003). Ouzounov et al. (2006) analyzed the decrease of SST before the Ms 6.8 2003 Boumerdès earthquake and implied that this phenomenon was attributed to the upwelling of cold water from the deep ocean caused by crustal deformation. Freund et al. (2009) disagreed with his explanation and offered a physically meaningful mechanism to explain the phenomenon of SST anomalies. The p holes activated by the tectonic stress transfer from the sea floor to the ground-to-water interface and generate the oxidation from H2O to H2O2, which changes the thermal radiation balance of the sea surface.

Visual interpretation method is a type of manual analysis method that interprets the relationship between an earthquake and the relevant parameters through a time series of visible and near-infrared or TIR data before and after the target earthquake. The observed quantity, such as surface temperature, is measured in considerably greater amounts prior to the earthquake around epicenter areas compared to other time period and neighboring regions. The method is simple and effective; thus, it is always used in interpreting preliminary pre-seismic anomalies. Several studies have utilized this method, such as in the aerosol anomaly (Qin et al., 2014b), SLHF anomaly (Dey and Singh, 2003), anomalies of multiple parameters (Pulinets et al., 2006a; Singh et al., 2010a), and BT anomalies of AVHRR and MODIS data (Saraf et al., 2012).

Visual interpretation is mainly based on experience interpretation, which results in strong subjectivity and does not allow current computer technology to deal with massive amounts of satellite data. From Fig. 9, we can distinguish the LST anomalies around the epicenter, but this difference is subtle causing the randomicity during the anomaly recognition. In addition, visually identifying abnormal information can be difficult and calls for further processing, such as the use of pseudo-color synthesis, difference method, and fault profile line method. At the same time, increasingly sophisticated anomaly detection algorithms have been applied to extract signals about pre-seismic anomalies with increases in data source and amount and the quantitative requirement of further research.

The simple image difference method involves identifying the differences in the same region over a series of images captured at different times for qualitative analysis. If the difference exceeds the pre-defined threshold, then the observed precursor value could be regarded as an anomaly that may be associated with an impending earthquake. This method eliminates the influence of background signals and highlights the spatial distribution of pre-seismic anomalies to a certain extent. For example, TIR images captured before and after earthquakes were used to calculate difference values that highlight anomalous variations (Ma et al., 2008; Tronin et al., 2002). The method that uses BT difference has a certain ability to identify cloud pixels but cannot eliminate background influence. Therefore, temperature anomaly is introduced through normalizing the area-averaged LST by subtracting and dividing by multiyear mean LST (Zoran, 2012).

The general anomaly method is to find the difference between current data during an earthquake and the long-term average value (also called a reference value) in order to improve result robustness and eliminate potential bias (Mahmood et al., 2017; Qin et al., 2014a; Wu et al., 2016). This method can be expressed as GAx,y=vx,y,t-μx,y,μx,y=1N∑t=1Nvx,y,t, where v(x,y,t) is the value of a pixel at a spatial location x,y and time t of satellite data required, which can be TOA BT, OLR, or LST. μx,y is the average value at the same position in the same or similar time slot of years using multiyear data. In other words, the anomaly is the difference between what is happening and what is expected over a long-term average trend. General anomaly method is an improvement of the image difference method (Qin et al., 2012).

Given complex influences and possible uncertainties with respect to seasons, local weather, topography, and surface inhomogeneity, the pre-seismic anomaly is a weak signal in the strong background level. Thus, understanding variations of the background field and the variation trend of each influencing factor over time are the key to the anomaly detection. The establishment of a regional reference field based on multiyear data is a basic procedure to identify pre-seismic anomaly, because the reference field can express the trend of physical quantity in the spatiotemporal pattern and relieve random variability due to local meteorological factors. General anomaly method is used to eliminate this tendency change of current observation, thereby highlighting the pre-seismic anomaly. The k times standard deviation (δ) is generally the reference level relative to the long-term normal field. Beyond ± kδ from the mean value of the reference field is regard as the anomaly. A positive anomaly means that the value is higher than the normal trend, whereas a negative anomaly indicates a lower value than the normal value.

The thermal anomaly is a weak signal under strong interference, thus isolating it by simple comparison or threshold is difficult. This may also be an important reason that not all earthquakes exhibit significant pre-seismic anomalies. The eddy field method is used to calculate and add the difference data between adjacent lattice points of the data to obtain the spatial distribution of the vorticity value (Ouzounov et al., 2007). The formula is as follows: EFx,y=4×vx,y-vx-1,y-vx+1,y-vx,y-1-vx,y+1, where EF(x,y) is the eddy value at spatial location x,y, and v is the observation value of a pixel. This method can highlight anomalous changes in the neighborhood and is used for earthquake-related anomaly detection by NOAA OLR data (Ouzounov et al., 2007; Xiong et al., 2010).

Furthermore, normalization by z score (ZS) is as an anomaly index, which hereafter is referred to as the ZS method (Ouzounov et al., 2011). The ZS index is defined as follows: ZS(x,y,t)=vx,y,t-μ(x,y)δ(x,y),δ(x,y)=1N-1∑t=1Nvx,y,t-μx,y2, where δ(x,y) is the standard deviation of this reference field. This method is similar to the robust satellite technique (RST) method, which introduces the concept of SNR. The difference between current and mean values of a reference field represents the signal part, and the standard deviation of a reference field is the noise part. A higher SNR indicates a greater possibility of anomalies prior to an earthquake (Tramutoli et al., 2001).

At present, RST, which is extensively used in the anomaly detection, is a multi-temporal statistical method for analyzing long-term satellite records with similar observation conditions (e.g., same month, same time of day, and same sensor data) (Genzano et al., 2015; Lisi et al., 2010; Pergola et al., 2010; Tramutoli et al., 2005). RST combines the neighborhood difference in the eddy field method and the normalization of the reference field in the ZS method, and it clearly defines the mathematical expression of the pre-seismic anomaly in statistics. This method considers the statistical characteristics of the historical data in seismically active areas to discriminate the possible pre-seismic abnormal behavior of current signals. It is also considered applicable to different atmosphere and surface conditions and different satellite observation geometries and can reduce the probability of occurrence of false anomalies (Filizzola et al., 2004; Pergola et al., 2010).

The robust estimator of TIR anomalies (RETIRA) index is used to express the intensity of anomalies in RST method, as follows: ⊗Δv(x,y,t)=Δvx,y,t-μΔv(x,y)δΔv(x,y),Δvx,y,t=vx,y,t-v‾(t), where v‾(t) is the spatially average value in the homogeneous neighborhood, such that Δv(x,y,t) represents the difference between the value of a pixel in (x, y) and ambient homogeneous pixels; μΔv(x,y) and δΔv(x,y) are, respectively, the mean and standard deviation in (x, y) of the reference field calculated from Δv(x,y,t) in the same or similar time slot from many years, which are referred to Eq. (2) and (5). The RETIRA index is further used to indicate the relationship with future seismic activity. Generally, a value greater than 3 to 4 is used as the threshold for the presence of anomalies that are associated with possible earthquake occurrences (Eleftheriou et al., 2016; Lisi et al., 2010, 2015).

If continuous and large-scale anomalies appear from a time series of images within study areas, then they can be considered as pre-seismic anomalies (Aliano et al., 2008). Therefore, an index of significant sequences of thermal anomalies (SSTAs), which measures the persistence and continuity of thermal anomalies in temporal and spatial patterns, is defined to remove problematic values as far as possible (Genzano et al., 2015; Lisi et al., 2015). SSTAs standards include the following: (1) relative strength, in which the RETIRA index is greater than or equal to 3; (2) spatial persistence, in which the area of thermal anomalous pixels in the region of 1∘×1∘ is larger than 150 km2; and (3) temporal continuity, in which the phenomenon of thermal anomalies occurs at least once within 7 days before or after current time.

The purpose of SSTAs is similar to that of a deviation–time–space–thermal (DTS-T) anomaly recognition method proposed by Wu et al. (2012), which is applied to analyses of several large earthquakes. The DTS-T method defines a normalized quantitative index to express the stability of thermal anomalies considering the significance of numerical differences, synchronization of time, and adjacency of geographical location. Both indices are intended to improve the stability of detected thermal anomalies that are related to impending earthquakes as much as possible. In addition, geostationary satellite data are more advantageous than polar-orbiting satellite data in the anomaly detection (Aliano et al., 2008; Lisi et al., 2015) because they have higher temporal resolution and a fixed observation geometry, and thereby its data have a higher SNR in detecting seismically related anomalies when using RST-based method. The principle of this algorithm is concise; however, the impact of short-term meteorological warming is also difficult to eliminate. Therefore, this method should be combined with other data to identify the interpretation of anomaly detection results.

Wavelet analysis is one of the most popular seismic anomaly detection methods in recent years. Wavelet decomposition, wavelet packet, and power spectrum are used in determining the transformation and decomposition of TIR signals to extract useful feature signals for identifying pre-seismic anomalies. Wavelet transform has the feature of multi-resolution analysis, which can characterize the local characteristics of the signal in time–frequency domain.

The influence factors of surface thermal radiation are complex and varied; therefore, influences of various field sources are difficult to separate. Furthermore, non-tectonic factors, such as landforms, land covers, and meteorology, always have greater effects on thermal radiation than tectonic activities or thermal radiation induced by earthquakes. The weak signal under strong interference is difficult to separate, resulting in unstable results of anomaly detection methods. Continuous TIR radiation data can be considered to include the long-period components (e.g., the basic radiation field of the Earth, the interannual or seasonal radiation field, and terrain induced radiation field), the short-period components (e.g., diurnal radiation field, cloud and cold air flow in several hours to days, and thermal radiation components caused by tectonic movements or earthquakes), and the last residual factors (e.g., high-frequency noise components). Wavelet transform can decompose the time series signal into signals of different frequency bands that correspond to the above different components; thus, studying the energy variation in each frequency band is convenient.

The relative power spectrum (RPS) method performs wavelet transform on time series data to realize bandpass filtering, remove long- and short-period components, and retain certain intermediate frequency band information that may be connected with seismic-related signal changes and is expressed in the form of power spectrum. RPS method was used to analyze BT anomalies of the 2008 Wenchuan earthquake (Zhang et al., 2010). Figure 10 presents the obvious BT anomalies from 25 April to 19 June 2008 over the Longmenshan fault zone and demonstrates the good results of the RPS method. The wavelet transform is initially used to process the multiyear data after cloud filtering and filling in of missing data. For each pixel, the basic temperature field, annual variation temperature field, daily variation temperature field, and other factors can be separated, and remaining information may include earthquake-related information. The RPS is then calculated by Fourier transform with a certain time window and sliding window length. On the basis of TOA BT, the RPS approach was used to analyze pre-seismic anomalies, but non-seismic anomalies always appeared (Xie et al., 2013).

The wavelet transform method is used to eliminate low-frequency annual and seasonal components and high-frequency random components, such as local meteorological conditions and human activities. The local maxima are then extracted from time series of MODIS LST data by a predefined threshold, which is sensitive to peak changes (Saradjian and Akhoondzadeh, 2011). Another wavelet maxima method proposed by Cervone et al. (2004) uses one-dimensional wavelet transform to identify the isolated local maxima. The maxima mostly associated with impending earthquakes are then refined based on the geometrical continuity from spatial and temporal constraints to remove wrong maxima lines due to significant noise in input data. Wavelet maxima method is further utilized to analyze the result of eddy field method (Xiong et al., 2010).

Wavelet transform is based on the communication theory, and thus its mathematical and physical foundation is complete, making it a highly promising method. The time series physical quantities derived from remote sensing are taken as the input information via a series of filtering and other processing, and finally pre-seismic anomalies are extracted. Wavelet transform can decompose the time series data into mutually independent frequency components almost without loss of information. Each component has a different dominant factor, thereby making the physical meaning much clearer than other methods. However, the determination of high- and low-frequency signals in this method requires geography- and geology-related knowledge with a certain arbitrariness. Although this algorithm achieves a high degree of decomposition and analysis of, for example, TIR signals, the mechanism that relates to earthquake preparation must be further improved. Moreover, wavelet transform requires continuous time series of input data, but missing values in TIR data always appear due to cloud cover. Thus, the interpolation of missing data is required, which brings in uncertainties with regard to real values.

Single precursor in pre-seismic monitoring research shows its limitations. Changes in various land, ocean, and atmospheric parameters before and after strong earthquakes can be observed from satellite platforms, along with ground measurements. Comprehensive utilization of multiple precursors provides another promising choice, which can raise the reliability and credibility of the relationship between different anomalies and imminent seismic events (Eleftheriou et al., 2016; Singh et al., 2010a). The preliminary step is to identify which precursors present anomalous variations prior to strong earthquakes around the epicenter. OLR, air temperature, and relative humidity were used in the seismic anomaly analysis for the 2005 Mw 7.6 Kashmir and 2013 Mw 7.7 Awaran earthquakes (Mahmood et al., 2017). Singh et al. (2007) analyzed changes in SLHF, atmospheric water vapor, SST, wind, cloud liquid water, precipitation rate, and chlorophyll concentrations prior to and after the 2004 Sumatra earthquake. In short, many geophysical parameters show abnormal variations prior to earthquakes to some extent.

Anomalous variations of parameters in the surface, atmosphere, and ionosphere prior to earthquakes present interrelations with one another and show the existence of strong coupling effects (Singh et al., 2007). Multiparametric analysis of the 2008 Wenchuan earthquake by Jing et al. (2013) indicates different response times for different parameters. Anomalous OLR occurred first, followed by air temperature, relative humidity, and air pressure presented abnormal variations. Finally, SLHF anomaly occurred the day before the main shock. Wu et al. (2016) used multiple parameters from reanalysis datasets and ground measurements to interpret the potential LCAC process. In Fig. 11, the precursor parameters of soil moisture, soil temperature, total column water vapor, and screen-level air temperature present quasi-synchronous anomalies in the time window between 29 March and 1 April 2009 preceding the Mw 6.3 L'Aquila earthquake. Anomalous multiple parameters also indicate that the process of energy transfer is caused by tectonic activities, which is from the deep of crust to the land surface and then to the atmosphere. Multiparametric analysis helps in better understanding the sequence of processes that occurs in the lithosphere, hydrosphere, and atmosphere (Mansouri Daneshvar and Freund, 2017).

The night thermal gradient (NTG) method calculates the linear trend of the nighttime surface temperature using geostationary satellite LST data with high temporal resolution (Piroddi and Ranieri, 2012; Piroddi et al., 2014). In general, the surface temperature at night gradually decreases and reaches the minimum in the early morning, and thus an NTG value greater than 0 is regarded as an abnormal temperature increase. Furthermore, the most intensive anomalies of soil and air temperature are spatially coincident with TIR anomaly detected by NTG method (Wu et al., 2016). This approach is highly suitable for the geostationary satellite data that have continuous time series observations.

The interquartile method is used to establish upper and lower boundaries of temperature changes. The values that exceed boundaries are considered anomalous values that are associated with possible near-future earthquakes (Akhoondzadeh, 2013; Saradjian and Akhoondzadeh, 2011). This method is only sensitive to the highest intensity anomaly, and its formula is as follows: M-k⋅IQR<V<M-k⋅IQR, where M is the median value, k is a threshold value, IQR is the interquartile range between 75th and 25th percentiles, and V is the observed value. This equation can be reformed as V-MIQR<k. The interquartile method is analogous to the ZS method, in which the average value and standard deviation are substituted by the medium value and interquartile range, respectively.

A variety of machine learning methods have been used in the anomaly detection, which show great advantages in various fields in recent years and may have a considerable potential in this field. Autoregressive integrated moving average, artificial neural network (ANN), support vector machine, and adaptive network-based fuzzy inference system (ANFIS) have been compared for detecting thermal and total electron content anomalies (Akhoondzadeh, 2013). ANN model can handle well the noise in input data. ANFIS that integrates both ANN and fuzzy inference systems is more effective at modeling nonlinear time series predictions than other methods. However, machine learning methods are always required to set certain empirical parameters, and appropriate selection of these parameters is a challenging task in phases of model training and prediction. The Kalman filter method is an iterative optimization system with high predictive power and is also used for detecting surface temperature anomalies (Saradjian and Akhoondzadeh, 2011). This approach takes advantage of predicting nonlinear times series data with non-normal distribution, such as the occurrence of LST anomalies. These methods are more complex and have not been widely used in the anomaly detection as other abovementioned methods. The comparison among these methods with different independent properties should be conducted based on more earthquake cases in order to screen out more effective approaches.