2:30 PM - 2:45 PM
[SSS11-21] Reassessment of the Relationship between MJMA and Seismic Moment for Inland Earthquakes and Subsequent Scaling Laws
Keywords:Seismic moment, Scaling law, JMA magnitude, Global fault parameters
It is extremely important for quantitative strong-motion prediction to set source parameters as accurately as possible based on the fault information from geological and geomorphological surveys. The scaling laws for macroscopic and microscopic fault parameters are compiled into the so-called “strong-motion prediction recipe.” The observed data is essential for improving the scaling laws’ accuracy. In this report, we first summarize the relationship between the JMA magnitude Mjma and the seismic moment M0 of the F-net CMT solution of NIED, or its equivalent moment magnitude Mw, for earthquakes that occurred in Japan between January 1989 and January 2024. The relationships for both plate boundary and intraplate earthquakes are identical, whereas there is a significant difference for inland crustal earthquakes. If we include earthquakes with smaller Mjma, we obtain a coefficient slightly smaller than that of the standard Mw-M0 relationship, 1.5. However, if we limit the Mjma to 5.5 or larger, we get the following simple equations:
Mjma = Mw+0.356 or log (M0) = 1.5 Mjma + 8.566 (Eq.1)
These regression formulas show a constant difference between Mjma and Mw or between the Mjma-M0 and Mw-M0 relationships. These relationships differ significantly from the conventional Mjma-M0 relationship proposed by Takemura (1990) (the Takemura formula) with a different coefficient, 1.2.
The strong-motion prediction recipe by the Headquarters of the Earthquake Research Promotion includes one route based on the fault area S (the S-method) and the other route based on the fault length L (the L-method). In the current L-method, we combine the Takemura formula and the Mjma-L relationship proposed by Matsuda (1975) (the Matsuda formula), and we get:
log (L) = 0.513 log (M0) - 8.397 (Eq.2)
This relationship is a single-stage model that applies to a range of Mjma>7 and L≦80 km, which is inconsistent with the S-method that uses a three-stage model for a wide range of magnitudes. Therefore, we extend the scaling laws in the L-method to a wide range of M0 by assuming an appropriate fault width W at each stage. The resultant M0-L relationships for the three-stage L-model are:
log (L) = 0.333 log (M0) - 4.993 (M0≦7.5×1018 N m)
log (L) = 0.500 log (M0) - 8.128 (7.5×1018 N m0≦1.8×1020 N m) (Eq.3)
log (L) = 1.000 log (M0) - 18.255 (1.8×1020 N m< M0)
We found that the scaling law of the second stage is almost identical to the scaling law of the current L-method (Eq.2). This means that even if the Mjma-M0 relationship is inconsistent with the observed data, the resultant M0-L relationship becomes consistent. The left panel in the figure shows the model of the three-stage L-method (red dotted lines) proposed here. They are consistent with recently observed data plotted as symbols. The green dashed line is the Takemura-Matsuda relation (Eq.2). The figure also shows the two-stage model proposed by Takemura (1998) as two solid black lines, but the second stage is apparently inconsistent with the data.
Next, the new Mjma-M0 equation obtained earlier was substituted into the L-method with three stages to obtain equations for the relationships between Mjma and L. We get:
log (L) = 0.50 Mjma - 2.137
log (L) = 0.75 Mjma - 3.845 (Eq.4)
log (L) = 1.50 Mjma - 9.689
These scaling laws for Mjma and L are plotted in the right panel as red lines, together with the observed data by symbols. The green dotted line shows the Matsuda formula. The panel shows that the new scaling laws agree with the observed data. At the same time, the Matsuda formula has a slope intermediate between the first and second stages. Still, its level is generally smaller than the data, indicating that L is underestimated by 60%. The current scaling of the L-method obtained by the Takemura + Matsuda formulas (Eq.2) was almost identical to the scaling of the second stage of the new L-method (Eq.3). It turned out that the agreement was achieved because the deviations in the Mjma-M0 and Mjma-L relationships were just mutually canceled out.
Mjma = Mw+0.356 or log (M0) = 1.5 Mjma + 8.566 (Eq.1)
These regression formulas show a constant difference between Mjma and Mw or between the Mjma-M0 and Mw-M0 relationships. These relationships differ significantly from the conventional Mjma-M0 relationship proposed by Takemura (1990) (the Takemura formula) with a different coefficient, 1.2.
The strong-motion prediction recipe by the Headquarters of the Earthquake Research Promotion includes one route based on the fault area S (the S-method) and the other route based on the fault length L (the L-method). In the current L-method, we combine the Takemura formula and the Mjma-L relationship proposed by Matsuda (1975) (the Matsuda formula), and we get:
log (L) = 0.513 log (M0) - 8.397 (Eq.2)
This relationship is a single-stage model that applies to a range of Mjma>7 and L≦80 km, which is inconsistent with the S-method that uses a three-stage model for a wide range of magnitudes. Therefore, we extend the scaling laws in the L-method to a wide range of M0 by assuming an appropriate fault width W at each stage. The resultant M0-L relationships for the three-stage L-model are:
log (L) = 0.333 log (M0) - 4.993 (M0≦7.5×1018 N m)
log (L) = 0.500 log (M0) - 8.128 (7.5×1018 N m0≦1.8×1020 N m) (Eq.3)
log (L) = 1.000 log (M0) - 18.255 (1.8×1020 N m< M0)
We found that the scaling law of the second stage is almost identical to the scaling law of the current L-method (Eq.2). This means that even if the Mjma-M0 relationship is inconsistent with the observed data, the resultant M0-L relationship becomes consistent. The left panel in the figure shows the model of the three-stage L-method (red dotted lines) proposed here. They are consistent with recently observed data plotted as symbols. The green dashed line is the Takemura-Matsuda relation (Eq.2). The figure also shows the two-stage model proposed by Takemura (1998) as two solid black lines, but the second stage is apparently inconsistent with the data.
Next, the new Mjma-M0 equation obtained earlier was substituted into the L-method with three stages to obtain equations for the relationships between Mjma and L. We get:
log (L) = 0.50 Mjma - 2.137
log (L) = 0.75 Mjma - 3.845 (Eq.4)
log (L) = 1.50 Mjma - 9.689
These scaling laws for Mjma and L are plotted in the right panel as red lines, together with the observed data by symbols. The green dotted line shows the Matsuda formula. The panel shows that the new scaling laws agree with the observed data. At the same time, the Matsuda formula has a slope intermediate between the first and second stages. Still, its level is generally smaller than the data, indicating that L is underestimated by 60%. The current scaling of the L-method obtained by the Takemura + Matsuda formulas (Eq.2) was almost identical to the scaling of the second stage of the new L-method (Eq.3). It turned out that the agreement was achieved because the deviations in the Mjma-M0 and Mjma-L relationships were just mutually canceled out.