Scaling relations for outer-rise earthquakes and their applications to tsunami forecasts

Abstract Outer-rise earthquakes can generate destructive tsunamis, yet their scaling relations remain poorly constrained, limiting forecast accuracy. This study introduces new scaling relations between seismic moment $${M}_{0}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>M</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> (Nm) and fault area $$S$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>S</mml:mi> </mml:math> (km 2 ) for outer-rise earthquakes based on 24 datasets from 14 earthquakes ( $${M}_{\text{w}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>M</mml:mi> <mml:mtext>w</mml:mtext> </mml:msub> </mml:math> 7.0–8.4). We derived linear and bilinear scaling relations and compared them to an existing scaling relation while assessing the effects of data approaches on scaling estimates. To evaluate practical implications, we applied both linear and bilinear scaling relations to tsunami forecasts. For hypothetical $${M}_{\text{w}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>M</mml:mi> <mml:mtext>w</mml:mtext> </mml:msub> </mml:math> 8.7 scenarios off Sanriku, Japan, coastal tsunami heights predicted by the bilinear scaling relation were 11% larger, on average, than those from the linear scaling relation. These findings demonstrate that tsunami forecasts are highly sensitive to the choice of the scaling relation. Therefore, careful application of scaling relations is essential for reliable tsunami forecasting. Graphical Abstract