Table 1 Mutually dimensionless indicator equations.

1

Fault signal ratio

\({X_{SFR}} = \frac{{[\int {_\Re |y{|^l}p(y)dz{]^{1/l}}} }}{{[\int {_\Re |s{|^m}p(s)dz{]^{1/m}}} }} =\frac{{\root l \of {{E(|y{|^l})}}}}{{\root m \of {{E(|s{|^m})}}}}\)

2

When \(l = 2,m = 1\) , the mutual waveform indicator:

\({S_{SFR}} = \frac{{[\int {_\Re |y{|^\mathrm{{2}}}p(y)dz{]^{1/2}}} }}{{[\int {_\Re |s{|^{}}p(s)dz{]^{}}} }}\) \(=\frac{{\root \of {{E(|y{|^2})}}}}{{E(|s|)}}\)

3

When \(l \rightarrow \infty ,m = 1\) , the mutual pulse indicator:

\({I_{SFR}} = \mathop {\lim }\nolimits _{l \rightarrow \infty } \frac{{[\int {_\Re |y{|^l}p(y)dy{]^{1/l}}} }}{{[\int {_\Re |s{|^{}}p(s)ds{]^{}}} }}\) \(=\frac{{\mathop {\lim }\nolimits _{l \rightarrow \infty } \root l \of {{E(|y{|^l})}}}}{{E|s|}}\)

4

When \(l \rightarrow \infty ,m = 1/2\) , the mutual margin indicator:

\(C{L_{SFR}} = \mathop {\lim }\nolimits _{l \rightarrow \infty } \frac{{[\int {_\Re |y{|^l}p(y)dy{]^{1/l}}} }}{{[\int {_\Re |s{|^{1/2}}p(s)ds{]^2}} }}\) \(=\frac{{\mathop {\lim }\nolimits _{l \rightarrow \infty } \root l \of {{E(|y{|^l})}}}}{{{{[E(\sqrt{|s|} )]}^2}}}\)

5

When \(l \rightarrow \infty ,m = 2\) , the mutual peak indicator:

\({C_{SFR}} = \mathop {\lim }\nolimits _{l \rightarrow \infty } \frac{{[\int {_\Re |y{|^l}p(y)dy{]^{1/l}}} }}{{[\int {_\Re |s{|^2}p(s)ds{]^{{1/ 2}}}} }}\) \(=\frac{{\mathop {\lim }\nolimits _{l \rightarrow \infty } \root l \of {{E(|y{|^l})}}}}{{\sqrt{E(|s{|^2}} )}}\)

6

Directly define the mutual kurtosis indicator:

\({K_{SFR}} = \frac{{\int {_\Re {y^4}p(y)dy} }}{{[\int {_\Re |s{|^2}p(s)ds{]^2}} }}\) \(=\frac{{E(|y{|^4})}}{{{{[E(|s{|^2})]}^2}}}\)

7

Directly define the mutual skewness indicator:

\(S{K_{SFR}} = \frac{{\int _\Re {{y^3}p(y)dy} }}{{{{\left[ {\int _\Re {{\mathrm{{s}}^2}p(s)ds} } \right] }^{3/2}}}}\) \(=\frac{{E({{\left| y \right| }^3})}}{{{{\left[ {E({{\left| s \right| }^2})} \right] }^{3/2}}}}\)