Earthquake Spatio-Temporal Patterns Around Precursory Thermal Infrared (TIR) Anomalies

In this work, we analyze outgoing longwave radiation (OLR) data from the National Oceanic and Atmospheric Administration (NOAA) to extract thermal infrared (TIR) anomalies over mainland China from 2007 to 2019. These anomalies are statistically significantly correlated with earthquakes of magnitude <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\geq 4.5$ </tex-math></inline-formula>, 5.0 and 5.5. We then calculate the distance (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$d/^{\circ } $ </tex-math></inline-formula>) and time lag <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(t/\text {days})$ </tex-math></inline-formula> between each TIR anomaly and the corresponding earthquake. By examining the distribution of earthquakes in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$t \times d$ </tex-math></inline-formula> space, our results show that the normalized frequency of earthquakes as a function of distance and time follows a power-law distribution: <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$f(d,t,M)=\phi (M) *t^{-d_{t}(M)}*d^{-d_{d}(M)}$ </tex-math></inline-formula>, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$f(d,t,M)$ </tex-math></inline-formula> represents the frequency of earthquakes with magnitude <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\geq }M$ </tex-math></inline-formula> occurring within the time-space unit <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(t, d)$ </tex-math></inline-formula> around TIR anomalies. The coefficient <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\phi (M)$ </tex-math></inline-formula> is negatively correlated with magnitude <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$[\phi (4.5)=0.31,\phi (5.0)=0.30,\phi (5.5)=0.28]$ </tex-math></inline-formula>, while <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$d_{d}(M)$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$d_{t}(M)$ </tex-math></inline-formula> are two positive coefficients <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$[d_{t}(4.5)=1.59,d_{t}(5.0)=1.58,d_{t}(5.5)=1.50;d_{d}(4.5)=2.76,d_{d}(5.0)=2.66,d_{d}(5.5)=2.59]$ </tex-math></inline-formula>. A larger <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\phi $ </tex-math></inline-formula> suggests that earthquakes are more spatially and temporally concentrated around TIR anomalies, while <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$d_{d}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$d_{t}$ </tex-math></inline-formula> represent the decay rates of frequency with distance and time, respectively. These findings imply that earthquakes are more likely to occur near TIR anomalies, and the model <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$f(d,t,M)$ </tex-math></inline-formula> could potentially be used to construct a probabilistic earthquake forecasting system based on TIR anomalies.