Skip to main content

Table 7 Set of the penalty constraints for the SS search

From: Characterized source model of the M7.3 2016 Kumamoto earthquake by the 3D reciprocity GFs inversion with special reference to the velocity pulse at KMMH16

Param

Penalties for the WM value

Tp

\(- 1.0 \times \mathop \sum \limits_{i = 1}^{3} {\text{ln}}\left( {Tp\left( i \right)/0.5} \right)\)

Vra

\(+ 3.0 \times \mathop \sum \limits_{i = 1}^{3} \left| {{\text{ln}}\left( {Vra\left( i \right)/2.52} \right)} \right|\)

Vrb

\(+ 1.0 \times \mathop \sum \limits_{i = 1}^{3} \left| {{\text{ln}}\left( {Vrb\left( i \right)/2.52} \right)} \right|\)

Lcent

\(+ 10\, \times \sum\limits_{i - 1}^{3} {\left( {Lcent\left( i \right)\left\langle {\frac{La\left( i \right)}{2} \cup \,Lcent\left( i \right)} \right\rangle L_{0} \left( i \right) - \,\frac{La\left( i \right)}{2}} \right)}\)

Hcent

\(+ 10\, \times \sum\limits_{i = 1}^{3} {\left( {Hcert\left( i \right)\left\langle {\frac{Ha\left( i \right)}{2} \cup \,Hcert\left( i \right)} \right\rangle H_{0} \left( i \right) - \,\frac{Ha\left( i \right)}{2}} \right)}\)

Lhypo

\(+ 10 \times \mathop \sum \limits_{i = 1}^{3} \left( {Lhypo\left( i \right)\left\langle {\frac{Lcent\left( i \right)}{2} \cup Lhypo\left( i \right)} \right\rangle H_{0} \left( i \right) - \frac{Lcent\left( i \right)}{2}} \right)\)

Hhypo

\(+ 10 \times \mathop \sum \limits_{i = 1}^{3} \left( {Hhypo\left( i \right)\left\langle {\frac{Hhypo\left( i \right)}{2} \cup Hhypo\left( i \right)} \right\rangle H_{0} \left( i \right) - \frac{Hhypo\left( i \right)}{2}} \right)\)

lgMo

\(+ 1.0 \times \mathop \sum \limits_{i = 1}^{3} \left| {{\text{lg}}Mo\left( i \right) - {\text{lg}}Mo0\left( i \right)} \right|\)

  1. *Here: L0 = {8, 12, 12}, H0 = {18, 18, 18}, La = {7.2, 7.2, 10}, Ha = {7.2, 7.2, 10}, \(\mathrm{lg}Mo0\) is the GS result