Fourier Source Spectrum

The source spectrum can be computed through interaction with the SourceParameters type, or the higher level FourierParameters type that holds a SourceParameters instance as a property.

The source spectrum $E(f; \bm{\theta}E)$ is most commonly written in terms of:

\[ E(f; \bm{\theta}_E) = \mathcal{C} M_0 E_s(f; \bm{\theta}_E)\]

where $\mathcal{C}$ is a constant term, to be defined shortly, $M_0$ is the seismic moment, and $E_s(f; \bm{\theta}_E)$ is the source spectral shape.

The most commonly adopted source spectral shape is the $\omega^2$ model that has the form:

\[ E_s(f) = \frac{1}{1 + \left(\frac{f}{f_c}\right)^2}\]

Functionality

StochasticGroundMotionSimulation.fourier_constant — Function

fourier_constant(src::SourceParameters)

Define the constant source term for the Fourier Amplitude Spectrum. Constant set to permit distances to be passed in km, densities in t/m^3, and velocities in km/s The reference distance is set to 1.0 km (and interpreted to be a rupture distance).

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StochasticGroundMotionSimulation.fourier_source_shape — Function

fourier_source_shape(f::T, m::S, src::SourceParameters) where {S<:Real,T<:Float64}

Source shape of the Fourier Amplitude Spectrum of displacement, without the constant term or seismic moment. This simply includes the source spectral shape.

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fourier_source_shape(f, m, fas::FourierParameters)

Source shape of the Fourier amplitude spectrum of displacement, without the constant term or seismic moment. Defined using a FourierParameters instance for the source model.

See also: fourier_source_shape

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fourier_source_shape(f::Float64, fa::T, fb::T, ε::T, model::Symbol) where T<:Real

Fourier amplitude spectral shape for displacement defined by corner frequencies.

See also: fourier_source_shape

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StochasticGroundMotionSimulation.fourier_source — Function

fourier_source(f::T, m::S, src::SourceParameters) where {S<:Real,T<:Float64}

Source Fourier Amplitude Spectrum of displacement, without the constant term. This simply includes the seismic moment and the source spectral shape.

See also: fourier_source_shape

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fourier_source(f, m, fas::FourierParameters)

Source Fourier Amplitude Spectrum of displacement, without the constant term. This simply includes the seismic moment and the source spectral shape. Defined using a FourierParameters instance for the source model.

See also: fourier_source_shape

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StochasticGroundMotionSimulation.corner_frequency — Function

corner_frequency(m::U, src::SourceParameters{S,T}) where {S<:Float64, T<:Real, U<:Real}

Computes a 3-tuple of corner frequency components, depending upon source spectrum type. By default the single-corner Brune spectrum is considered, but if src.model equals :Atkinson_Silva_2000 then the components of the double-corner spectrum are returned. If some other symbol is passed then the Brune model is returned.

Examples

    m = 6.0
    Δσ = 100.0
    κ0 = 0.035
    fas = FASParams(Δσ, κ0)
    # compute single corner frequency
	src.model = :Brune
    fc, tmp1, tmp2 = corner_frequency(m, src)
    # compute double corner frequencies
	src.model = :Atkinson_Silva_2000
    fa, fb, ε = corner_frequency(m, src)

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StochasticGroundMotionSimulation.magnitude_to_moment — Function

magnitude_to_moment(m::T) where T<:Real

Converts moment magnitude to seismic moment (in dyne-cm).

# Examples

	m = 6.0
	M0 = magnitude_to_moment(m)

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