Modification of IPI Method for Extraction of Short-Term and Imminent OLR Anomalies and Case Study of Two Large Earthquakes

Abstract

The Pattern Informatics Method (PI) was initially developed for medium-to-long-term earthquake prediction by analyzing changes in seismic activity. It has since been refined and extended to identify ionospheric anomalies associated with earthquakes. Notable advancements include the development of modified and improved methods, which have demonstrated their capability to detect significant short-term and ionospheric anomalies preceding earthquake events. In this study, the IPI method was applied to infrared satellite observation data for the first time, and a new algorithm for extracting short-term and imminent anomalies from infrared earthquakes was explored based on the IPI method, from which we obtained the MIPI (Modified Improved Pattern Informatics Method). Using 1° × 1° nighttime Outgoing Longwave Radiation (OLR) data from NOAA_18 satellites of the National Oceanic and Atmospheric Administration’s Climate Prediction Center (NOAA-CPC) of the United States, the evolution of OLR anomalies before the Ridgecrest Ms 6.9 earthquake in the United States on 6 July 2019 as recorded by the China Earthquake Networks Center (CENC) and the Maduo Ms 7.4 earthquake in China on 21 May 2021 as recorded by the China Earthquake Networks Center (CENC) were studied. In order to make the IPI method suitable for the calculation of OLR data, two modifications were made to the IPI algorithm: (1) the quartile method was applied for automatically determining the abnormal changes in the OLR observation data and they were used as the input data instead of ionospheric data; (2) the standard deviation of the multi-year OLR residual data of each grid was used instead of the maximum anomaly index used in the original method to re-assign and obtain the relative anomaly index, and finally the anomaly evolution time series diagram was drawn. The results show the following: (1) The MIPI method can effectively extract short-term and imminent OLR anomalies prior to earthquakes. (2) Short-term and imminent OLR anomalies appeared about two weeks before each earthquake and lasted until the earthquake occurrence, disappearing after the earthquake. During this process, the anomalies exhibited a certain evolutionary trend. (3) The short-term and imminent OLR anomalies prior to each earthquake were distributed near the epicenter or near the seismogenic fault, about 200 KM away from the epicenters. The above results are similar to the spatiotemporal evolution characteristics of seismic infrared short-term anomalies previously studied, which indicates that the MIPI method can effectively extract seismic infrared anomalies and might provide a practical method for the extraction of seismic infrared short-term and imminent anomalies.

1. Introduction

The occurrence of major earthquakes causes serious disasters in human societies, such as the 1960 Mw 9.5 earthquake in Chile, the 2008 Wenchuan Mw 7.9 earthquake in China, and the 2023 Mw 7.8 earthquake in Turkey. Therefore, earthquake prediction, especially short-term and medium-term prediction, is crucial for reducing casualties and property loss. However, earthquake fault systems are nonlinear and complex systems. Facing the complexity of these fault systems, Rundle introduced a nonlinear threshold system used in meteorology for analyzing ocean–atmosphere interactions and the El Niño-Southern Oscillation (ENSO) to the study of seismicity changes. They subsequently proposed the Pattern Informatics (PI) method [1,2,3,4]. This method assesses whether seismicity in a given region has significantly deviated from its historical average state over a period, categorizing the area as being in a state of “seismic quiescence” or “seismic activation”. The locations identified are called “Hot Spots”, which are considered areas with a high seismic hazard in the future. The PI method has achieved good results in medium-to-long-term earthquake prediction [1,2,3,5,6,7,8,9,10,11]. Wu adapted the PI method to make it suitable for extracting ionospheric parameter anomalies from the DEMETER satellite, resulting in the Modified Pattern Informatics (MPI) method, which is applicable for short-term and imminent earthquake prediction on a monthly scale. They extracted ionospheric electron density anomalies before the 2008 Wenchuan earthquake and found anomalies around 20 days before the earthquake near the epicenter [12]. Later, Maimaitusun, N. (2012), Xia, C. (2015), and Song, C. (2017) applied the MPI method to study DEMETER satellite ionospheric anomalies and summarized their characteristics. They discovered that ionospheric anomalies often occur about one month before an earthquake, with an overall evolution pattern of “appearance–enhancement–weakening–disappearance–reappearance–disappearance again (a few days before the earthquake)” prior to the earthquake, returning to normal after the earthquake [13,14,15]. Tian improved the MPI method and developed the Improved Pattern Informatics (IPI) method, suitable for extracting ionospheric parameter anomalies from the China Seismo-electromagnetic Satellite (CSES). They conducted a retrospective study of the 2021 Maduo Mw 7.3 earthquake and found that ionospheric electron density anomalies appeared about one month before the earthquake, following an evolution pattern of “appearance–persistence–disappearance–reappearance–disappearance”. This indicated that the IPI method performed well in retrospective studies and is suitable for short-term and imminent earthquake prediction [16]. The above studies demonstrate that image-based methods have been applied to anomaly extraction and earthquake prediction using seismicity and ionospheric data, which are suitable for medium-to-long-term, short-term, and imminent earthquake predictions, respectively. As effective methods for earthquake prediction, the PI method and its modified methods have had strong effects, but they have not been applied to infrared data for earthquake anomaly extraction and prediction. This study aims to use an image-based method to extract short-term and imminent infrared anomalies related to earthquakes and explore new techniques for extracting earthquake-related infrared anomalies.

Existed studies have indicated that thermal anomalies before strong earthquakes are significant precursory phenomena. Gorny et al. (1988) found that pre-seismic thermal anomalies might be related to fault activity [17]. Subsequently, scholars proposed three mechanisms for earthquake-related infrared anomalies: gas emissions from the Earth, “exothermic” reactions due to stress changes, and infrared radiation excited by electric fields [18,19,20,21]. Based on these theoretical foundations, researchers conducted numerous case studies and found that pre-seismic infrared anomalies exhibit certain regularities. Statistical analyses have revealed that earthquake infrared anomalies are characterized by a temporal and spatial evolution process with the temporal persistence of the anomaly distribution location near the epicenter or the seismogenic fault of the future earthquake [19,22,23,24,25,26,27,28,29,30,31,32]. Currently, there are six types of research data in the field of infrared anomalies, including brightness temperature, Outgoing Longwave Radiation (OLR), latent heat flux, temperature data from the reanalysis of the National Centers for Environmental Prediction (NCEP), surface temperature, and trace gasses in the atmosphere [33]. Outgoing longwave radiation (OLR) has been observed to exhibit anomalous behavior preceding significant seismic events, potentially due to stress-induced thermal changes in the Earth’s crust; its global coverage and continuous monitoring make it a valuable parameter for earthquake-related anomaly detection [33]. In recent years, more studies on extracting OLR anomalies have been able to extract anomaly features prior to earthquakes, such as temporal lasting, near their epicenters or fault zones, or at least within their active fault areas, with consistency [34,35,36,37,38,39,40,41,42,43,44,45]. All these features help identify anomalies prior to earthquakes. Due to the advantages for which OLR data have been used in the study of earthquake-related infrared anomalies over larger spatial and temporal scales, OLR data were selected for analysis in this paper so that the results of OLR anomalies could be compared between different methods.

To make the image-based method applicable for extracting short-term and imminent anomalies related to earthquakes from infrared observational data, this study modified the IPI algorithm, resulting in (what we call) the MIPI method. Utilizing the NOAA-18 satellite’s 1° × 1° nighttime Outgoing Longwave Radiation (OLR) data [46], this study extracts short-term and imminent OLR anomalies for two typical earthquakes: the Ridgecrest Ms 6.9 earthquake in the United States on 6 July 2019, and the Maduo Ms 7.4 earthquake in China on 21 May 2021. These two earthquakes were recorded by the China Earthquake Networks Center (CENC). Additionally, the spatial and temporal characteristics of the short-term and imminent OLR anomalies for these two earthquakes are analyzed to explore whether the image-based method is suitable for extracting short-term and imminent anomalies from infrared data.

2. Data Sources and Preprocessing in This Study

The infrared data used in this study are the NOAA-CPC’s NOAA_18 satellite 1° × 1° nighttime OLR product-level data. This dataset includes time, latitude and longitude, and outgoing longwave radiation values at each sampling point. The times are recorded in Coordinated Universal Time (UTC), and the spatial grid covers latitudes from 90° S to 90° N and longitudes from 0° (the prime meridian) to 180° E and then back to 0°. The outgoing longwave radiation values are recorded in units of W/m² [46]. To reduce interference from solar radiation, this study follows previous research by selecting nighttime data for anomaly extraction [47].

The IPI method requires gridding the study area and each grid cell needs input data. In this study, the residuals between the observed OLR values and the multi-year average values were taken as input data. However, because the NOAA_18 satellite’s 1° × 1° OLR product combines both daytime and nighttime data and some grid points have missing data, four steps of preprocessing of the OLR data were necessary: (1) firstly, filter out the global nighttime OLR data; (2) secondly, perform kriging interpolation on the global nighttime OLR data to fill in the missing grid data; (3) thirdly, after numbering the grids, perform cubic spline interpolation to ensure the temporal continuity of the nighttime OLR data; (4) finally, calculate the multi-year average nighttime OLR for each grid, and subtract this average to obtain the “nighttime OLR residual sequence” for all global grids, which is then used as the input data for the IPI method. The preprocessing workflow is illustrated in Figure 1.

3. Methods

The research method in this study is based on the IPI method, which is suitable for extracting anomalies from electromagnetic satellite ionospheric data [16] and has been improved to develop an algorithm applicable to OLR data. The specific process is as follows:

(1) Define the study area and grid it. This study adopts the method of defining the study area used by Tian, which refers to Dobrovolsky’s empirical formula for the radius of the preparation zone [48] to obtain the preparation radius. The research area is defined as the inscribed square of the “preparation circle” centered at the epicenter. The formula and a schematic diagram are as follows:

R = 10^0.43M
 R_IPI = √2 R

(1)

where M is the earthquake magnitude, R is the radius of the seismogenic zone, and R_IPI is the length of the sides of the study area, showing in Figure 2.

For grid division, Tian divided the operational range of the CSES (−180° to 180° E, −70° to 70° N) into grids of 5° × 2°, while the OLR data product records data in a grid format of 1° × 1°. Therefore, this study divides the research area into smaller grids of 1° × 1°.

(2) Set the threshold. For the IPI method, it is necessary to calculate the cumulative anomaly frequency of ionospheric electron density for each grid over a specified time period, with anomalies being determined based on a threshold. Tian manually confirmed the threshold based on the distribution range of electron concentration values within the research area for each earthquake case during the study period. In this study, we employed the interquartile method with a threshold set at 1.5 times the interquartile range to automatically define the threshold interval for screening OLR data, facilitating the calculation of anomaly frequency. The formula is as follows:

IQR = Q3 − Q1
 RNC_low = Q1 − 1.5·IQR
 RNC_up = Q3 + 1.5·IQR

(2)

where Q₁ is the first quartile of the input data (nighttime OLR residual value data), Q₃ is the third quartile of the input data, IQR is the interquartile range, NC_low is the lower threshold limit, and NC_up is the upper threshold limit.

(3) Study window setting. In the IPI method used by Tian, five time points are defined: t₀, t_b, t₁, t₂, and an arbitrary time t. The time point t_b slides between t₀ and t₁, and based on these time points, two time-windows are defined—the background window and the learning window—along with the sliding interval for t_b. For each calculation, the lengths of the background window and the learning window need to be set as parameters. As t_b slides, calculations are performed for each model for the day t₂, and by sliding t₀, t₁, and t₂, the required time series of the results is obtained. Similarly, this study defines five time points (with the same meaning), but since the OLR data in the study area exhibit annual variability, the interval between t_b and t₁ is set to 12 months. The length of the learning window will be explained in the case studies. According to previous studies, infrared anomaly evolution maps generally use a 3-month time series [24,25,26,28,49], so the sliding lengths of t₀, t₁, and t₂ are all set to 3 months. The time window settings are illustrated in Figure 3.

(4) Calculation of anomaly intensity for each grid. Tian filtered out anomalies based on the set threshold and used a Boolean (0/1) distribution to quantify the electron density anomalies as frequencies. They then calculated the average anomaly frequency for each grid from t_b to t, which was used as the anomaly intensity of the electron density for that grid during the time period. This study adopts the same method, where based on the threshold interval set in Equation (2), residual values within the threshold interval are considered non-anomalous (denoted as value 0), and those exceeding the threshold are considered anomalous (denoted as value 1). The average anomaly frequency for each grid from t_b to t is calculated as the OLR anomaly intensity for that grid during the time period. The formula is as follows:

$$I_i\left(t_b,t\right)={\displaystyle \frac{1}{t-t_b}}\sum _{t^{\prime }=t_b}^t{N}_i\left(t^{\prime }\right)$$

(3)

where N_i(t′) is the anomaly frequency of the i-th grid at time t.

(5) Normalization. To facilitate comparison across the entire study area, Tian normalized the electron density anomaly intensity for each grid. In this study, the same normalization method is applied to the OLR anomaly intensity. The formula is as follows:

$$\widehat{I_i}\left(t_b,t\right)={\displaystyle \frac{I_i\left(t_b,t\right)-〈I_i\left(t_b,t\right)〉}{\sigma \left(t_b,t\right)}}$$

(4)

where ⟨I_i(t_b,t)⟩ is the average OLR anomaly intensity for the entire study area at time t, and σ(t_b,t) is the standard deviation of the OLR anomaly intensity for the entire study area at time t.

(6) Calculation of changes in each grid during the learning period relative to the background period. This step in the study is the same as in the IPI method, with the only change being the replacement of electron density data with OLR data. The formula is as follows:

$$\mathit{\Delta }\widehat{I_i}\left(t_b,t_1,t_2\right)=\widehat{I_i}\left(t_b,t_2\right)-\widehat{I_i}\left(t_b,t_1\right)$$

(5)

(7) Calculation of the average change in anomaly intensity for each grid during the sliding of t_b. As t_b slides from t₀ to t_m, many $\mathit{\Delta }\widehat{I_i}\left(t_b,t_1,t_2\right)$ values are generated. To better represent the degree of change for each grid during the learning window relative to the set background window, the average change is calculated. This step in the study is the same as in the IPI method, with the only change being the replacement of electron density data with OLR data. The formula is as follows:

$$\overline{\mathit{\Delta }\widehat{I_i}\left(t_0,t_1,t_2\right)}={\displaystyle \frac{1}{t_m-t_0}}{\sum }_{t_b=t_0}^{t_{\mathrm{m}}}\mathit{\Delta }\widehat{I_i}\left(t_b,t_1,t_2\right)$$

(6)

(8) Definition of anomaly information for each grid. By taking the absolute value of the average change obtained from Equation (6) and then amplifying it, the anomaly information $P_i\left(t_0,t_1,t_2\right)$ for each grid is obtained. This step does not differ from the IPI method, with the only change being the replacement of electron density data with OLR data. The formula is as follows:

$$P_i\left(t_0,t_1,t_2\right)=e^{|\overline{\mathit{\Delta }\widehat{I_i}\left(t_0,t_1,t_2\right)}|}$$

(7)

(9) Definition of anomaly index as the gain of anomaly information relative to the entire area. To highlight the more pronounced anomalies within the entire study area, the anomaly information calculated from Equation (7) is subtracted from the background anomaly information. This step does not differ from the IPI method, with the only change being the replacement of electron density data with OLR data. The formula is as follows:

$$\mathit{\Delta }{P}_i\left(t_0,t_1,t_2\right)=P_i\left(t_0,t_1,t_2\right)-⟨P_i\left(t_0,t_1,t_2\right)⟩$$

(8)

where $⟨P_i\left(t_0,t_1,t_2\right)⟩$ is the average anomaly information for the entire study area.

(10) Reassigning values to obtain the relative anomaly index. Once a set of time points is determined, the calculations described above will yield a data file containing the anomaly index for all grids in the study area on day t₂. By synchronously sliding the time points t₀, t₁, and t₂ forward by 3 months, a data file containing a 3-month time series will be generated. Before plotting the anomaly time evolution graph, each grid must undergo the following processing: ${IPI}_i\left(t_0,t_1,t_2\right)$= $\mathit{\Delta }{P}_i\left(t_0,t_1,t_2\right)$/σ_i, where σ_i represents the standard deviation of the OLR residual values for the i-th grid over the data time span. This will ultimately yield the relative anomaly values for all grids over the 3-month time series, allowing for the plotting of the anomaly time evolution graph. In this step, Tian used the maximum anomaly index value (${\mathit{\Delta }{P}_i\left(t_0,t_1,t_2\right)}_{max}$) from all grids in the study area during the study period as the denominator for reassignment. To reduce the interference from extreme anomaly values, this study improves upon previous research by using σ_i as the denominator for reassignment [33].

Compared to the IPI method by Tian, the ionospheric electron density data were replaced with OLR data as the input data in this study. Additionally, except for improvements made in steps (2) and (10), all other steps follow the processing of the IPI method, only substituting OLR data for the ionospheric electron density data. The improvements made include the following: (1) employing the quartile method to automatically determine the threshold range in step (2) when setting the threshold; and (2) using σ_i instead of ${\mathit{\Delta }{P}_i\left(t_0,t_1,t_2\right)}_{max}$ as the denominator in the calculation formula when reassessing the relative anomaly index in step (10). The modified IPI method is named the MIPI method in this study.

4. Earthquake Case Studies

We selected two case studies: the Ridgecrest earthquake in the United States on 6 July 2019 and the Maduo earthquake on 21 May 2021. We used the MIPI method for the extraction of OLR anomalies, with detailed earthquake parameters listed in

Table 1. Earthquake information table of earthquake cases.

Earthquake Event	Earthquake Types	Magnitude (CENC/USGS)	Longitude/E° (CENC/USGS)	Latitude/N° (CENC/USGS)
Ridgecrest earthquake, in the United States, on 6 July 2019	Land–shallow-intraplate earthquake	Ms 6.9/Mw 7.1	−117.58/−117.59	35.75/35.77
Maduo earthquake, in China, on 21 May 2021	Land–shallow-intraplate earthquake	Ms 7.4/Mw 7.3	98.34/98.25	34.59/34.59

CENC—China Earthquake Networks Center (https://news.ceic.ac.cn/history.html) (accessed on 28 August 2024). USGS—United States Geological Survey (https://earthquake.usgs.gov/earthquakes/search/) (accessed on 28 August 2024).

. Since the OLR data is recorded in UTC, the occurrence times of these two earthquakes are also uniformly expressed in Coordinated Universal Time. For both earthquakes, this study utilized data from 2018 to 2022, using the residual values after removing the background field of each grid over the 5-year period as the input data for the IPI algorithm to perform anomaly extraction.

4.1. 2019-07-06 Ridgecrest Ms 6.9 Earthquake, USA

Based on measurements from the China Earthquake Networks Center (CENC), a Ms 6.9 earthquake occurred on 6 July 2019 (UTC + 8) in Ridgecrest, Kern County, Southern California, at the location of (−117.58° E, 35.75° N) with a depth of 10 km. This event is one of the strongest events in California in the past 20 years, resulting in thousands of aftershocks and forming a significant seismic sequence. Two days before, on 4 July 2019 (UTC + 8), a Ms 6.4 earthquake occurred in the Mojave Desert region of Eastern California, considered a foreshock to the main event, with the two epicenters being about 10 km apart. This earthquake took place within a complex fault system in California, involving interactions between multiple fault systems, including the Eastern California Shear Zone and the Garlock Fault. The Eastern California Shear Zone is one of the main strike-slip fault systems in the region, located east of the San Andreas Fault, and is a major area of seismic activity in Southern California; the Garlock Fault is one of the few major faults with an east–west orientation in California, closely related to the activity of the Ridgecrest earthquake. The interactions between these faults triggered this seismic event [50,51].

4.1.1. Study Area and Calculation Parameters

Based on the empirical formula for the seismogenic area, a 12° × 12° study area centered on the earthquake’s epicenter was defined, covering the range from −123.6° E to −111.6° E and 29.8° N to 41.8° N. The details of the study area are shown in Figure 4.

Based on previous research, the short-term and imminent OLR anomaly characteristics include the following: (1) Temporally, anomalies usually appear from one month before the earthquake on to the day of the earthquake, and sometimes persist after the event, mostly occurring close to the earthquake time, typically lasting for at least about a week. (2) Spatially, they are generally distributed near the epicenter or the fault zone, at least within the active fault area, with continuity before and after the event. (3) Morphologically, they should maintain a consistent appearance once they emerge [34,35,36,37,38,39,40,41,42,43,44,45]. These three characteristics will be used as reference criteria for identifying short-term and imminent OLR anomalies in this study.

To select an appropriate background window length, this study plotted the 5-year annual variation trend of the sum of OLR residuals across all grids in the Ridgecrest earthquake study area, as shown in Figure 5. It was observed that the total OLR residuals in the study area exhibited a clear annual variation trend. Therefore, the background window length was fixed at 12 months (1 year). According to Figure 3, the learning window was varied from 10 days to 180 days, with an interval of 10 days. It was observed that for learning windows of 100 and 110 days, sustained OLR anomalies appeared near the epicenter, consistent with the identified OLR anomaly characteristics mentioned earlier. To further refine the analysis and obtain the most persistent anomaly closest to the epicenter, the learning window was adjusted by increments of 1 day, ranging from 101 to 109 days. It was eventually found that a 106-day learning window yielded the best results; other models either failed to successfully extract short-term and imminent OLR anomalies that met the above anomaly identification criteria, or the extracted short-term and imminent OLR anomalies did not exhibit the three characteristic features as well as the model with the 106-day learning window parameter. All this resulted in a total of 27 learning window parameters and 27 corresponding models, as listed in

Table 2. Parameter settings for the Ridgecrest earthquake model.

Model Number	Size of Study Area	Background Window Length (Months)	Learning Window Length (Days)
1	12° × 12°	12	10
2	12° × 12°	12	20
3	12° × 12°	12	30
4	12° × 12°	12	40
5	12° × 12°	12	50
6	12° × 12°	12	60
7	12° × 12°	12	70
8	12° × 12°	12	80
9	12° × 12°	12	90
10	12° × 12°	12	100
11	12° × 12°	12	110
12	12° × 12°	12	120
13	12° × 12°	12	130
14	12° × 12°	12	140
15	12° × 12°	12	150
16	12° × 12°	12	160
17	12° × 12°	12	170
18	12° × 12°	12	180
19	12° × 12°	12	101
20	12° × 12°	12	102
21	12° × 12°	12	103
22	12° × 12°	12	104
23	12° × 12°	12	105
24	12° × 12°	12	106
25	12° × 12°	12	107
26	12° × 12°	12	108
27	12° × 12°	12	109

.

4.1.2. Results

The evolution of short-term and imminent OLR anomalies is shown in Figure 6 and

Table 3. Statistical table of short-term and imminent anomaly evolution for Ridgecrest earthquake. The ‘√’ means occurring in this day.

Anomaly Grouping	Distance from Epicenter (KM) (Approximate)	June											July						Lasting Time of Consistant Anomaly
		20	21	22	23	24	25	26	27	28	29	30	1	2	3	4	5	6
1	580				√	√						√	√	√	√	√	√	√	7
2	600				√	√	√	√	√	√	√	√	√	√	√	√			12
3	670				√	√	√	√	√	√	√	√	√	√	√	√	√	√	14
4	200						√	√	√	√	√	√	√	√	√	√	√	√	12

. No OLR anomalies were detected in the study area between 20 June and 22 June, so only 20 June is displayed; starting from 23 June, anomalies began to appear in the study area until 25 June, when OLR anomalies near the epicenter began to show characteristics consistent with the reference features; hence, all are displayed. From 25 June to 6 July, OLR anomalies continued to appear near the epicenter; thus, one OLR anomaly map is shown every three days, with 6 July displayed separately; anomalies disappeared after 7 July, so only 7 July is displayed. For better visual presentation, this study only displays the top 70% of the anomalies, and any relative anomaly values exceeding one are set to one. The statistical table is presented in Table 3.

The anomaly evolution diagram shown in Figure 6 begins on 20 June 2019 (15 days before the earthquake) and ends on 7 July 2019 (1 day after the earthquake). The anomalies in the figure are grouped based on the order of their appearance, with anomalies occurring in the same location sharing the same group, while those lasting within 5 days of each other are not grouped together. For the four main groups of OLR anomalies observed before the earthquake, a group of anomalies (Group 4) appeared near the epicenter on the southwest side starting from 25 June 2019 (10 days before the earthquake), approximately 200 km from the epicenter. This group was located near the Garlock Fault (see Figure 7) and persisted until 6 July 2019 (the day of the earthquake), gradually intensifying as the time of the earthquake approached and disappeared afterward. In comparison, Groups 1, 2, and 3 were located further from the epicenter (all over 500 km away, thus not advantageous for indicating the epicenter’s position). Based on the aforementioned reference features, we suggest that the persistent anomalies appearing near the Garlock Fault on the southwest side of the epicenter may indicate short-term and imminent infrared anomalies associated with this earthquake. The reason for the other anomalies in the study area, which did not correspond to any earthquakes, will be discussed in the Section 5.

4.2. 2021-05-21 Maduo Ms 7.4 Earthquake, China

According to the China Earthquake Networks Center (CENC), on 22 May 2021 (UTC + 8), an Ms 7.4 earthquake struck the Maduo area of Qinghai Province, China. The epicenter was located at the point of (98.34° E, 34.59° N), with a focal depth of 17 km. This earthquake was a typical intraplate event occurring in the eastern section of the Qinghai–Tibet Plateau, where the complex interaction between the Indian Plate and the Eurasian Plate results in significant tectonic stress. The cause was attributed to activity along the Maduo–Gande Fault, part of the Kunlun fault system, which is a left-lateral strike-slip fault. Following the main event, a series of Ms 3.0~5.0 aftershocks occurred near the epicenter. This region is part of the northern boundary of the Bayan Har Block, known for its intense tectonic activity. The area frequently experiences moderate to strong earthquakes, with significant fault ruptures and horizontal displacement, reflecting the ongoing crustal deformation and stress redistribution within the plateau [52,53,54].

4.2.1. Study Area and Calculation Parameters

According to the empirical formula for the seismogenic area range, a research area of 20° × 20° (ranging from 88° E to 108° E, and from 24° N to 44° N) was defined with the epicenter at its center. The research area is shown in Figure 8.

Since the total OLR residual value in the research area for the Maduo earthquake also shows an annual variation trend, the background window length was similarly fixed at 12 months. According to Figure 3, the learning window was varied from 10 days to 180 days, with an interval of 10 days. It was observed that for learning windows of 80 and 90 days, sustained OLR anomalies appeared near the epicenter, consistent with the identified OLR anomaly characteristics mentioned earlier. To further refine the analysis and obtain the most persistent anomaly closest to the epicenter, the learning window was adjusted by increments of 1 day, ranging from 81 to 89 days. It was eventually found that an 88-day learning window yielded the best results; other models either failed to successfully extract short-term and imminent OLR anomalies that met the above anomaly identification criteria, or the extracted short-term and imminent OLR anomalies did not exhibit the three characteristic features as well as the model with the 88-day learning window parameter. This resulted in a total of 27 learning window parameters and 27 corresponding models, as listed in

Table 4. Parameter settings for the Maduo earthquake model.

Model Number	Size of Study Area	Background Window Length (Months)	Learning Window Length (Days)
1	20° × 20°	12	10
2	20° × 20°	12	20
3	20° × 20°	12	30
4	20° × 20°	12	40
5	20° × 20°	12	50
6	20° × 20°	12	60
7	20° × 20°	12	70
8	20° × 20°	12	80
9	20° × 20°	12	90
10	20° × 20°	12	100
11	20° × 20°	12	110
12	20° × 20°	12	120
13	20° × 20°	12	130
14	20° × 20°	12	140
15	20° × 20°	12	150
16	20° × 20°	12	160
17	20° × 20°	12	170
18	20° × 20°	12	180
19	20° × 20°	12	81
20	20° × 20°	12	82
21	20° × 20°	12	83
22	20° × 20°	12	84
23	20° × 20°	12	85
24	20° × 20°	12	86
25	20° × 20°	12	87
26	20° × 20°	12	88
27	20° × 20°	12	89

.

4.2.2. Results

A short-term and imminent OLR anomaly evolution diagram is shown in Figure 9 and

Table 5. Statistical table of short-term and imminent anomaly evolution for Maduo earthquake. The ‘√’ means occurring in this day.

Anomaly Grouping	Distance from Epicenter (KM) (Approximate)	May										Lasting Time of Consistent Anomaly
							12	13	14	15	16	17	18	19	20	21
1	200	√	√	√	√	√	√	√	√	√	√	10
2	700	√	√	√	√	√	√	√	√	√		9
3	850	√	√	√	√	√	√	√	√	√	√	10
4	800	√	√	√	√	√	√	√	√	√	√	10

. No characteristic OLR anomalies appeared near the epicenter between 10 May 2021 and 11 May 2021, so only one image is shown for this period. From 12 May 2021 to 16 May 2021, OLR anomalies continued to appear near the epicenter; only two images are shown. After that, the anomalies near the epicenter exhibit a weakening trend; we thus show the anomaly images day by day. After 22 May 2021, the anomalies disappeared, so only the image of 21 May 2021 is shown. For better visual presentation, this study only displays the top 70% of the anomalies, and any relative anomaly values exceeding one are set to one. The statistical table is provided in Table 3.

The main spatiotemporal evolution of OLR anomalies (Group 1) displayed in Figure 9 spans from 12 May 2021 (10 days before the earthquake) to 22 May 2021 (1 day after the earthquake). The anomalies in the diagram are grouped according to their order of appearance, with those occurring in the same location grouped together, while anomalies lasting less than 5 days are not grouped together. Among the major OLR anomalies before the earthquake, one group of anomalies appeared on 3 May 2021 (10 days before the earthquake), located about 200 km northeast of the epicenter and near the earthquake-generating fault, which was the Maduo–Gande Fault (Figure 10). This anomaly persisted until the day of the earthquake (21 May 2021) and exhibited a certain evolutionary trend as the earthquake approached, disappearing afterward. During this period, other anomalies appeared (Groups 2, 3, and 4) far from the epicenter. Based on the aforementioned characteristic features, we consider this group of anomalies a possible short-term and imminent precursor of the earthquake. The reason for the other anomalies in the study area, which did not correspond to any earthquakes, will be discussed in the Section 5.

5. Conclusions and Discussion

This study modified the IPI method (Tian) for extracting short-term and imminent OLR anomalies prior to earthquakes by utilizing 1° × 1° nighttime OLR data from the NOAA_18 satellite. We examined the OLR anomaly evolution processes for the Ridgecrest earthquake in California on 6 July 2019 and the Maduo earthquake in China on 21 May 2021. The results obtained are presented in

Table 6. Statistical table of seismic anomaly extraction results.

Earthquake	Earthquake Types	Magnitude (Ms)	Model Parameters	Pre-Earthquake Anomaly Characteristics	Anomalies Begin to Appear
Ridgecrest earthquake, United States, 6 July 2019	Land–shallow-intraplate earthquake	6.9	12-Month Background Window Length, 106-Day Learning Window Length	The anomaly lasted for 12 days until the day of the earthquake, disappearing afterward; spatially, it was located southwest of the epicenter near the fault, approximately 200 KM from the epicenter; morphologically, it exhibited consistency before and after, exhibiting a certain evolutionary trend.	12 days before earthquake
Maduo earthquake, China, 21 May 2021	Land–shallow-intraplate earthquake	7.4	12-Month Background Window Length, 88-Day Learning Window Length	The anomaly lasted for 10 days until the day of the earthquake, disappearing afterward; spatially, it was located southwest of the epicenter near the fault, approximately 200 KM from the epicenter; morphologically, it exhibited consistency before and after, exhibiting a certain evolutionary trend.	10 days before earthquake

.

The extracted results for short-term and imminent OLR anomalies show the following characteristics in terms of time, space, and morphology:

1. Regarding time, these short-term and imminent OLR anomalies appeared approximately two weeks before the earthquake and continued until the day of the event, disappearing afterward.

2. For space, the short-term and imminent OLR anomalies were distributed near the epicenter or close to the fault zone, approximately 200 KM from the epicenter.

3. For morphology, the anomalies exhibited consistency over time, exhibiting a certain evolutionary trend.

These characteristics are similar to the pre-earthquake OLR anomaly phenomena extracted in existing studies, indicating that the MIPI method can effectively extract short-term and imminent OLR anomalies, demonstrating good extraction results. Combining earlier studies on the mechanisms and characteristics of earthquake infrared anomalies, we analyzed the possible mechanisms behind the extracted short-term and imminent OLR anomalies: The activity of seismic faults or the subduction of tectonic plates prior to an earthquake causes stress and fracturing in the rocks. This process leads to thermal anomalies in localized areas near the fractured rocks. Such thermal anomalies propagate through the underground medium to the surface, reaching the atmosphere as emitted radiation, which is then captured by satellites. The IPI method extracts these signals, ultimately presenting them as OLR anomalies. The locations of these anomalies are distributed near the fault or within the active fault zone, often directly around the epicenter. The stress accumulation caused by fault activity has a temporal continuity; so, in the absence of strong non-seismic disturbances, short-term and imminent OLR anomalies should persist over time, exhibit consistency in morphology, and gradually increase in intensity as the earthquake approaches, disappearing after the stress is released. If subjected to significant interference from meteorological and other factors, the evolution of infrared anomalies can be affected, potentially disrupting their inherent process [55]. In the period of weakening anomalies prior to the Maduo earthquake, we point out the relevance of meteorological events, which might explain the weakening observed in the anomaly evolution prior to the Maduo earthquake [56].

In this study, the pre-earthquake OLR anomaly evolution map for the Ridgecrest earthquake displayed other anomalies that were temporally persistent, morphologically consistent, and located at a certain distance from the epicenter; however, no earthquakes occurred nearby. Based on the “red swelling theory” proposed by Fu et al. (1971) and the multi-point (stress) model suggested by Ma et al. (1980) [57,58], we suggest that the absence of earthquakes at these anomaly locations may be caused by the ceased seismogenic process due to stress shadowing affected by the occurrence of large earthquakes nearby. In other words, the occurrence of a significant earthquake in one area can alter the stress state across the region, thereby affecting seismic activity in other areas.

Previous studies have shown that the selection of study area size, background window length, and learning window length can all affect the final extraction results [13,14,15,16,59,60,61,62,63]. In this study, we determined the study area size and background window length parameters based on empirical formulas for the earthquake-prone area and the annual variation trend of total OLR residual values. We focused solely on the learning window length parameter and did not explore other parameters, especially the selection of the study area. Therefore, future research should conduct an in-depth analysis of how the choice of study area impacts extraction results.

In addition, we will include more earthquake cases in future research to verify whether the MIPI method is a universal approach for extracting infrared short-term and imminent anomalies. We aim to conduct a more in-depth mechanistic analysis of the correlation between anomalies and earthquakes, obtaining a more comprehensive and practical understanding of short-term and imminent OLR anomaly characteristics. This will enable a shift from retrospective studies of earthquake cases to research focused on earthquake prediction. Furthermore, the MIPI method can serve as an additional layer of analysis within existing seismic monitoring frameworks. By integrating this method with ground-based and satellite-based observations, it is possible to enhance the reliability and spatial coverage of early warning earthquake systems. Future work could focus on automating the anomaly detection process for near-real-time applications, as well as exploring its applicability to other natural hazard studies, such as volcanic eruptions and landslides.