Predictable and unpredictable aspects of earthquakes from P-wave onsets of acceleration seismograms

Abstract It is widely acknowledged that predicting the final size of an earthquake from the P-wave onset in seismograms is nearly impossible. We confirm this fact by measuring the slope (parameter $$B$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>B</mml:mi> </mml:math> ) of the acceleration record shortly after onset assuming a constant rupture speed. Since 2007, $$B$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>B</mml:mi> </mml:math> has been used in the Japanese earthquake early warning system as an indicator of epicentral distance, yet it may also provide deeper insights into earthquake dynamics and wave propagation. Utilizing high-sensitivity seismograms from approximately 800 borehole stations in Hi-net and combining manually picked P-wave arrival times and focal mechanisms for about 1800 earthquakes, we estimate $$B$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>B</mml:mi> </mml:math> for each station and earthquake pair within a 0.1 s window. We confirm that $$B$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>B</mml:mi> </mml:math> decreases from the square to the fourth power of the P-wave travel time, a phenomenon not explainable by simple geometric decay or intrinsic attenuation alone. Residuals between observed values and travel time dependencies are further decomposed into event and site terms, alongside radiation pattern dependency, which is close to a power of 0.5—possibly reflecting complex rupture processes that begin at a minute scale. The event term primarily represents the initial stress drop, showing minimal dependency on final size and a clear dependency on event depth, mirroring observations of average stress drop. This term also shows a statistically significant negative trend with the moment-normalized duration estimated independently using S-waves, suggesting limited predictability of the rupture process. The site terms, which correlate with tectonic structure, help reduce errors in estimating arrival times, especially for nearby earthquakes, thus offering practical benefits for early warning systems. Graphical abstract