diff --git a/dev/index.html b/dev/index.html index d7a412e..a3032ca 100644 --- a/dev/index.html +++ b/dev/index.html @@ -1,9 +1,9 @@ Home · SeismicQ.jl
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SeismicQ.jl

Tout ce que vous avez toujours voulu savoir sur le Q.

Package Features

  • Compute source functions

Function Documentation: Sources

SeismicQ.Ricker — Function
Ricker(t, t₀, 𝑓₀)

Compute the Ricker function for t, t₀ and 𝑓₀.

\[f = (1.0 - 2.0 (\pi 𝑓₀ (t - t₀))^2) \exp(-π^2 𝑓₀^2 (t - t₀)^2)\]

Examples

julia>  Ricker(0.0, 0.0, 0.0)
-1.0
source
Ricker(x, x₀, t, t₀, 𝑓₀)

Compute the Ricker function with a dirac.

\[f = \delta(x₀) \exp{(-((x-x₀)^2)/2.0/σ₀^2)} (1.0 - 2.0 (\pi 𝑓₀ (t - t₀))^2) \exp(-π^2.0𝑓₀^2.0(t - t₀)^2)\]

Examples

julia> Ricker(2., 2., 0.0, 0.0, 0.0)
-0.1353352832366127
source
Ricker(x, x₀, t, t₀, 𝑓₀, σ₀)

Compute the Ricker function with 1D spatial support.

\[f = \exp{(-((x-x₀)^2)/2.0/σ₀^2)} (1.0 - 2.0 (\pi 𝑓₀ (t - t₀))^2) \exp(-π^2.0𝑓₀^2.0(t - t₀)^2)\]

Examples

julia> Ricker(2., 0., 0.0, 0.0, 0.0, 1)
-0.1353352832366127
source
Ricker(x, x₀, y, y₀, t, t₀, 𝑓₀, σ₀)

Compute the Ricker function with 2D spatial support.

\[f = \exp{(-((x-x₀)^2)/2.0/σ₀^2)} (1.0 - 2.0 (\pi 𝑓₀ (t - t₀))^2) \exp(-π^2.0𝑓₀^2.0(t - t₀)^2)\]

Examples

julia> Ricker(2., 0., 2., 0., 0.0, 0.0, 0.0, 1)
-0.01831563888873418
source

Function Documentation: Rheology

Missing docstring.

Missing docstring for f_bulk. Check Documenter's build log for details.

Function Documentation: Treatment

SeismicQ.Spec — Function
Spec(trace,t0,dt,Nt,tp,ts,\Deltaph)

Returns the amplitude spectrums of the P ans S phases where amplitudes are significant

    trace: the trace recorded at a given virtual station, starting at -t0, with time sampling dt, Nt samples
+1.0
source
Ricker(x, x₀, t, t₀, 𝑓₀)

Compute the Ricker function with a dirac.

\[f = \delta(x₀) \exp{(-((x-x₀)^2)/2.0/σ₀^2)} (1.0 - 2.0 (\pi 𝑓₀ (t - t₀))^2) \exp(-π^2.0𝑓₀^2.0(t - t₀)^2)\]

Examples

julia> Ricker(2., 2., 0.0, 0.0, 0.0)
+0.1353352832366127
source
Ricker(x, x₀, t, t₀, 𝑓₀, σ₀)

Compute the Ricker function with 1D spatial support.

\[f = \exp{(-((x-x₀)^2)/2.0/σ₀^2)} (1.0 - 2.0 (\pi 𝑓₀ (t - t₀))^2) \exp(-π^2.0𝑓₀^2.0(t - t₀)^2)\]

Examples

julia> Ricker(2., 0., 0.0, 0.0, 0.0, 1)
+0.1353352832366127
source
Ricker(x, x₀, y, y₀, t, t₀, 𝑓₀, σ₀)

Compute the Ricker function with 2D spatial support.

\[f = \exp{(-((x-x₀)^2)/2.0/σ₀^2)} (1.0 - 2.0 (\pi 𝑓₀ (t - t₀))^2) \exp(-π^2.0𝑓₀^2.0(t - t₀)^2)\]

Examples

julia> Ricker(2., 0., 2., 0., 0.0, 0.0, 0.0, 1)
+0.01831563888873418
source

Function Documentation: Rheology

For deviatoric rheology, updates take the form of:

\[\tau = \theta_\mathrm{s} \dot\varepsilon + \chi_\mathrm{s} \tau^\mathrm{old}\]

For volumetric rheology, updates take the form of:

\[P = P^\mathrm{old} + \theta_\mathrm{b} \nabla V + \chi_\mathrm{b} \nabla V^\mathrm{old}\]

SeismicQ.θs — Function
θs(G,Δt)

Deviatoric part of the elastic constitutive update: provides the shear modulus G for use in

\[Δτ = 2G Δε\]

source
θs(G,η,Δt)

Deviatoric part of the Maxwell visco-elastic constitutive update: used to compute

\[Δτ = 2 G (DeN / (1+DeN)) Δε + Δτ_{RELAX}\]

with η the shear viscosity, and DeN a numerical Deborah number, equal to

\[DeN = η / (G Δt)\]

source
SeismicQ.χs — Function
χs(G,Δt)

Relaxation part of the deviatoric elastic constitutive update: by definition equal to 1 (no relaxation)

source
χs(G,η,Δt)

Relaxation part of the deviatoric Maxwell visco-elastic constitutive update: for use in the calculation of

\[Δτ = (DeN / (1+DeN)) τ_\mathrm{OLD} + Δτ_\mathrm{CONSTITUTIVE}\]

with DeN a numerical Deborah number, equal to

\[DeN = η / (G Δt)\]

and η the shear viscosity.

source
SeismicQ.θb — Function
θb(K,Δt)

Volumetric part of the elastic constitutive update: provides the bulk modulus K for use in

\[Δp = -K ∇⋅v Δt\]

source

θb(K,ηb,Δt)

compute effective bulk viscosity for a Kelvin visco-elastic constitutive update

source
SeismicQ.χb — Function
χb(K,Δt)

compute effective bulk viscosity linear elastic update: 0.

source
χb(K,ηb,Δt)

compute effective bulk viscosity for a Kelvin visco-elastic constitutive update: here obviously it is for a linear update

source

Function Documentation: Treatment

SeismicQ.Spec — Function
Spec(trace,t0,dt,Nt,tp,ts,\Deltaph)

Returns the amplitude spectrums of the P ans S phases where amplitudes are significant

    trace: the trace recorded at a given virtual station, starting at -t0, with time sampling dt, Nt samples
     tp: picked P-wave phase (s)
     ts: picked S-wave phase (s)
     Δph: width of the phases (s) 
    Vec2dP: modulus of the fft coeffs of P phase where they are larger than max(Vec2dp)/10 
@@ -21,7 +21,7 @@
 phase P is picked at 0.7 s
 phase S is picked at 1.25 s
 phase width is set to 0.35
-+ Figure with 8 subplots
source
SeismicQ.ComputeQgraph — Function
(x,y)=ComputeQgraph(amp1,amp2,freq,index,d1,d2,V)

Returns x and y to plot Q-graph for a given phase using the results of Spec() for two different traces from two stations

    y=V/(π(d2-d1))*ln(amp2(f)/amp1(f)
++ Figure with 8 subplots
source
SeismicQ.ComputeQgraph — Function
(x,y)=ComputeQgraph(amp1,amp2,freq,index,d1,d2,V)

Returns x and y to plot Q-graph for a given phase using the results of Spec() for two different traces from two stations

    y=V/(π(d2-d1))*ln(amp2(f)/amp1(f)
     x=f
 
     Considering two attenuated waves at two different distances from the source (d1<d2), we obtain the following relation:
@@ -31,7 +31,7 @@
     for the developpment of these routines. In an homogeneous Q medium the graph should be linear. In more complex attenuation media,
     the graph could be non-linear?
 
-    Velocity is considered constant: the current code does not account for possible dispersion...

Examples

julia>
source
SeismicQ.Getfreq — Function
Getfreq(dt,Nt)

Returns the frequency vector corresponding to the fft results

    dt is the time sample in s
+    Velocity is considered constant: the current code does not account for possible dispersion...

Examples

julia>
source
SeismicQ.Getfreq — Function
Getfreq(dt,Nt)

Returns the frequency vector corresponding to the fft results

    dt is the time sample in s
     Nt is the number of samples in the trace given to fft()
     The frequency increment is 1/(Nt*dt)
     Vector goes beyond Nyquist Frequency as fft also does. Only the first half of the vectors are useful for us

Examples

julia>  Getfreq(1e-3,2000)
@@ -52,5 +52,6 @@
   998.5
   999.0
   999.5
- 1000.0
source
SeismicQ.GenAttenuatedRicker — Function
time_vec,acc_vec = GenAttenuatedRicker(listₓ,Δt,Nt,Vp,Vs,αp,αs,𝑓₀)  ;

Function that generates a seismic trace (Ricker wavelet) of P and S waves. This wave is attenuated along time and the function creates a matrix of wave amplitude as a function of time and distance to the source. The function takes as inputs: listₓ : vector of geophone distances to the source [m] Δt : time step of the wave signal [s] Nt : number of time steps of the wave signal Vp : P-wave velocity [m/s] Vs : S-wave velocity [m/s] αp : attenuation factor for P-wave αs : attenuation factor for S-wave 𝑓₀ : central frequency of the source [Hz]

and return: timevec : vector containing the time steps of the received wave signal accvec : matrix of wave acceleration at each geophone position

Examples

julia>  time_vec,acc_vec = GenAttenuatedRicker(0:1000:5000,1e-3,2000,7000,4000,2e-4,4e-4,10.0) 
-
source
+ 1000.0source
SeismicQ.GenAttenuatedRicker — Function
time_vec,acc_vec = GenAttenuatedRicker(listₓ,Δt,Nt,Vp,Vs,αp,αs,𝑓₀)  ;

Function that generates a seismic trace (Ricker wavelet) of P and S waves. This wave is attenuated along time and the function creates a matrix of wave amplitude as a function of time and distance to the source. The function takes as inputs: listₓ : vector of geophone distances to the source [m] Δt : time step of the wave signal [s] Nt : number of time steps of the wave signal Vp : P-wave velocity [m/s] Vs : S-wave velocity [m/s] αp : attenuation factor for P-wave αs : attenuation factor for S-wave 𝑓₀ : central frequency of the source [Hz]

and return: timevec : vector containing the time steps of the received wave signal accvec : matrix of wave acceleration at each geophone position

Examples

julia>  time_vec,acc_vec = GenAttenuatedRicker(0:1000:5000,1e-3,2000,7000,4000,2e-4,4e-4,10.0) 
+
source
SeismicQ.PlotReceiverGather — Function
PlotReceiverGather(listₓ,time_vec,acc_vec)

Function that plots a receiver gather The function takes as inputs: listₓ : vector of geophone distances to the source [m] timevec : vector containing the time steps of the wave signal [s] accvec : matrix of wave acceleration at each geophone position

Examples

julia>  PlotReceiverGather(0:1000:5000,time_vec,acc_vec) 
+
source
diff --git a/dev/search/index.html b/dev/search/index.html index ce6e254..1c60377 100644 --- a/dev/search/index.html +++ b/dev/search/index.html @@ -1,2 +1,2 @@ -Search · SeismicQ.jl

Loading search...

    +Search · SeismicQ.jl

    Loading search...

      diff --git a/dev/search_index.js b/dev/search_index.js index 96212d6..0eb2abe 100644 --- a/dev/search_index.js +++ b/dev/search_index.js @@ -1,3 +1,3 @@ var documenterSearchIndex = {"docs": -[{"location":"#SeismicQ.jl","page":"Home","title":"SeismicQ.jl","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"Tout ce que vous avez toujours voulu savoir sur le Q.","category":"page"},{"location":"#Package-Features","page":"Home","title":"Package Features","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"Compute source functions","category":"page"},{"location":"#Function-Documentation:-Sources","page":"Home","title":"Function Documentation: Sources","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"Ricker","category":"page"},{"location":"#SeismicQ.Ricker","page":"Home","title":"SeismicQ.Ricker","text":"Ricker(t, t₀, 𝑓₀)\n\nCompute the Ricker function for t, t₀ and 𝑓₀.\n\nf = (10 - 20 (pi 𝑓₀ (t - t₀))^2) exp(-π^2 𝑓₀^2 (t - t₀)^2)\n\nExamples\n\njulia> Ricker(0.0, 0.0, 0.0)\n1.0\n\n\n\n\n\nRicker(x, x₀, t, t₀, 𝑓₀)\n\nCompute the Ricker function with a dirac.\n\nf = delta(x₀) exp(-((x-x₀)^2)20σ₀^2) (10 - 20 (pi 𝑓₀ (t - t₀))^2) exp(-π^20𝑓₀^20(t - t₀)^2)\n\nExamples\n\njulia> Ricker(2., 2., 0.0, 0.0, 0.0)\n0.1353352832366127\n\n\n\n\n\nRicker(x, x₀, t, t₀, 𝑓₀, σ₀)\n\nCompute the Ricker function with 1D spatial support.\n\nf = exp(-((x-x₀)^2)20σ₀^2) (10 - 20 (pi 𝑓₀ (t - t₀))^2) exp(-π^20𝑓₀^20(t - t₀)^2)\n\nExamples\n\njulia> Ricker(2., 0., 0.0, 0.0, 0.0, 1)\n0.1353352832366127\n\n\n\n\n\nRicker(x, x₀, y, y₀, t, t₀, 𝑓₀, σ₀)\n\nCompute the Ricker function with 2D spatial support.\n\nf = exp(-((x-x₀)^2)20σ₀^2) (10 - 20 (pi 𝑓₀ (t - t₀))^2) exp(-π^20𝑓₀^20(t - t₀)^2)\n\nExamples\n\njulia> Ricker(2., 0., 2., 0., 0.0, 0.0, 0.0, 1)\n0.01831563888873418\n\n\n\n\n\n","category":"function"},{"location":"#Function-Documentation:-Rheology","page":"Home","title":"Function Documentation: Rheology","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"f_bulk","category":"page"},{"location":"#Function-Documentation:-Treatment","page":"Home","title":"Function Documentation: Treatment","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"Spec\nComputeQgraph\nGetfreq\nGenAttenuatedRicker","category":"page"},{"location":"#SeismicQ.Spec","page":"Home","title":"SeismicQ.Spec","text":"Spec(trace,t0,dt,Nt,tp,ts,\\Deltaph)\n\nReturns the amplitude spectrums of the P ans S phases where amplitudes are significant\n\n trace: the trace recorded at a given virtual station, starting at -t0, with time sampling dt, Nt samples\n tp: picked P-wave phase (s)\n ts: picked S-wave phase (s)\n Δph: width of the phases (s) \n\n Vec2dP: modulus of the fft coeffs of P phase where they are larger than max(Vec2dp)/10 \n Vec2dS: modulus of the fft coeffs of S phase where they are larger than max(Vec2dp)/10\n FrequP: corresponding frequency vector to plot P-wave amp. spectrum\n FrequS: corresponding frequency vector to plot S-wave amp. spectrum\n\nExamples\n\njulia> (AmpP,AmpS,fP,fS)=Spec(trace1,0.1,1e-3,2000,0.7,1.25,0.35))\nTrace length is 2.0 s using 2000 samples\nTrace 1 at offset 3000 m is found at index 30\nTrace 2 at offset 5000 m is found at index 50\nTrace 1:\nphase P is picked at 0.4 s\nphase S is picked at 0.75 s\nphase width is set to 0.35\nTrace 2:\nphase P is picked at 0.7 s\nphase S is picked at 1.25 s\nphase width is set to 0.35\n+ Figure with 8 subplots\n\n\n\n\n\n","category":"function"},{"location":"#SeismicQ.ComputeQgraph","page":"Home","title":"SeismicQ.ComputeQgraph","text":"(x,y)=ComputeQgraph(amp1,amp2,freq,index,d1,d2,V)\n\nReturns x and y to plot Q-graph for a given phase using the results of Spec() for two different traces from two stations\n\n y=V/(π(d2-d1))*ln(amp2(f)/amp1(f)\n x=f\n\n Considering two attenuated waves at two different distances from the source (d1 \n\n\n\n\n\n","category":"function"},{"location":"#SeismicQ.Getfreq","page":"Home","title":"SeismicQ.Getfreq","text":"Getfreq(dt,Nt)\n\nReturns the frequency vector corresponding to the fft results\n\n dt is the time sample in s\n Nt is the number of samples in the trace given to fft()\n The frequency increment is 1/(Nt*dt)\n Vector goes beyond Nyquist Frequency as fft also does. Only the first half of the vectors are useful for us\n\nExamples\n\njulia> Getfreq(1e-3,2000)\n2000-element Vector{Float64}:\n 0.5\n 1.0\n 1.5\n 2.0\n 2.5\n 3.0\n 3.5\n 4.0\n ⋮\n 996.5\n 997.0\n 997.5\n 998.0\n 998.5\n 999.0\n 999.5\n 1000.0\n\n\n\n\n\n","category":"function"},{"location":"#SeismicQ.GenAttenuatedRicker","page":"Home","title":"SeismicQ.GenAttenuatedRicker","text":"time_vec,acc_vec = GenAttenuatedRicker(listₓ,Δt,Nt,Vp,Vs,αp,αs,𝑓₀) ;\n\nFunction that generates a seismic trace (Ricker wavelet) of P and S waves. This wave is attenuated along time and the function creates a matrix of wave amplitude as a function of time and distance to the source. The function takes as inputs: listₓ : vector of geophone distances to the source [m] Δt : time step of the wave signal [s] Nt : number of time steps of the wave signal Vp : P-wave velocity [m/s] Vs : S-wave velocity [m/s] αp : attenuation factor for P-wave αs : attenuation factor for S-wave 𝑓₀ : central frequency of the source [Hz] \n\nand return: timevec : vector containing the time steps of the received wave signal accvec : matrix of wave acceleration at each geophone position\n\nExamples\n\njulia> time_vec,acc_vec = GenAttenuatedRicker(0:1000:5000,1e-3,2000,7000,4000,2e-4,4e-4,10.0) \n\n\n\n\n\n\n","category":"function"}] +[{"location":"#SeismicQ.jl","page":"Home","title":"SeismicQ.jl","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"Tout ce que vous avez toujours voulu savoir sur le Q.","category":"page"},{"location":"#Package-Features","page":"Home","title":"Package Features","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"Compute source functions","category":"page"},{"location":"#Function-Documentation:-Sources","page":"Home","title":"Function Documentation: Sources","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"Ricker","category":"page"},{"location":"#SeismicQ.Ricker","page":"Home","title":"SeismicQ.Ricker","text":"Ricker(t, t₀, 𝑓₀)\n\nCompute the Ricker function for t, t₀ and 𝑓₀.\n\nf = (10 - 20 (pi 𝑓₀ (t - t₀))^2) exp(-π^2 𝑓₀^2 (t - t₀)^2)\n\nExamples\n\njulia> Ricker(0.0, 0.0, 0.0)\n1.0\n\n\n\n\n\nRicker(x, x₀, t, t₀, 𝑓₀)\n\nCompute the Ricker function with a dirac.\n\nf = delta(x₀) exp(-((x-x₀)^2)20σ₀^2) (10 - 20 (pi 𝑓₀ (t - t₀))^2) exp(-π^20𝑓₀^20(t - t₀)^2)\n\nExamples\n\njulia> Ricker(2., 2., 0.0, 0.0, 0.0)\n0.1353352832366127\n\n\n\n\n\nRicker(x, x₀, t, t₀, 𝑓₀, σ₀)\n\nCompute the Ricker function with 1D spatial support.\n\nf = exp(-((x-x₀)^2)20σ₀^2) (10 - 20 (pi 𝑓₀ (t - t₀))^2) exp(-π^20𝑓₀^20(t - t₀)^2)\n\nExamples\n\njulia> Ricker(2., 0., 0.0, 0.0, 0.0, 1)\n0.1353352832366127\n\n\n\n\n\nRicker(x, x₀, y, y₀, t, t₀, 𝑓₀, σ₀)\n\nCompute the Ricker function with 2D spatial support.\n\nf = exp(-((x-x₀)^2)20σ₀^2) (10 - 20 (pi 𝑓₀ (t - t₀))^2) exp(-π^20𝑓₀^20(t - t₀)^2)\n\nExamples\n\njulia> Ricker(2., 0., 2., 0., 0.0, 0.0, 0.0, 1)\n0.01831563888873418\n\n\n\n\n\n","category":"function"},{"location":"#Function-Documentation:-Rheology","page":"Home","title":"Function Documentation: Rheology","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"For deviatoric rheology, updates take the form of:","category":"page"},{"location":"","page":"Home","title":"Home","text":"tau = theta_mathrms dotvarepsilon + chi_mathrms tau^mathrmold","category":"page"},{"location":"","page":"Home","title":"Home","text":"For volumetric rheology, updates take the form of:","category":"page"},{"location":"","page":"Home","title":"Home","text":"P = P^mathrmold + theta_mathrmb nabla V + chi_mathrmb nabla V^mathrmold","category":"page"},{"location":"","page":"Home","title":"Home","text":"θs\nχs \nθb\nχb","category":"page"},{"location":"#SeismicQ.θs","page":"Home","title":"SeismicQ.θs","text":"θs(G,Δt)\n\nDeviatoric part of the elastic constitutive update: provides the shear modulus G for use in \n\nΔτ = 2G Δε\n\n\n\n\n\nθs(G,η,Δt)\n\nDeviatoric part of the Maxwell visco-elastic constitutive update: used to compute\n\nΔτ = 2 G (DeN (1+DeN)) Δε + Δτ_RELAX\n\nwith η the shear viscosity, and DeN a numerical Deborah number, equal to \n\nDeN = η (G Δt)\n\n\n\n\n\n","category":"function"},{"location":"#SeismicQ.χs","page":"Home","title":"SeismicQ.χs","text":"χs(G,Δt)\n\nRelaxation part of the deviatoric elastic constitutive update: by definition equal to 1 (no relaxation)\n\n\n\n\n\nχs(G,η,Δt)\n\nRelaxation part of the deviatoric Maxwell visco-elastic constitutive update: for use in the calculation of \n\nΔτ = (DeN (1+DeN)) τ_mathrmOLD + Δτ_mathrmCONSTITUTIVE\n\nwith DeN a numerical Deborah number, equal to \n\nDeN = η (G Δt)\n\nand η the shear viscosity.\n\n\n\n\n\n","category":"function"},{"location":"#SeismicQ.θb","page":"Home","title":"SeismicQ.θb","text":"θb(K,Δt)\n\nVolumetric part of the elastic constitutive update: provides the bulk modulus K for use in \n\nΔp = -K v Δt\n\n\n\n\n\nθb(K,ηb,Δt)\n\ncompute effective bulk viscosity for a Kelvin visco-elastic constitutive update \n\n\n\n\n\n","category":"function"},{"location":"#SeismicQ.χb","page":"Home","title":"SeismicQ.χb","text":"χb(K,Δt)\n\ncompute effective bulk viscosity linear elastic update: 0.\n\n\n\n\n\nχb(K,ηb,Δt)\n\ncompute effective bulk viscosity for a Kelvin visco-elastic constitutive update: here obviously it is for a linear update \n\n\n\n\n\n","category":"function"},{"location":"#Function-Documentation:-Treatment","page":"Home","title":"Function Documentation: Treatment","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"Spec\nComputeQgraph\nGetfreq\nGenAttenuatedRicker\nPlotReceiverGather","category":"page"},{"location":"#SeismicQ.Spec","page":"Home","title":"SeismicQ.Spec","text":"Spec(trace,t0,dt,Nt,tp,ts,\\Deltaph)\n\nReturns the amplitude spectrums of the P ans S phases where amplitudes are significant\n\n trace: the trace recorded at a given virtual station, starting at -t0, with time sampling dt, Nt samples\n tp: picked P-wave phase (s)\n ts: picked S-wave phase (s)\n Δph: width of the phases (s) \n\n Vec2dP: modulus of the fft coeffs of P phase where they are larger than max(Vec2dp)/10 \n Vec2dS: modulus of the fft coeffs of S phase where they are larger than max(Vec2dp)/10\n FrequP: corresponding frequency vector to plot P-wave amp. spectrum\n FrequS: corresponding frequency vector to plot S-wave amp. spectrum\n\nExamples\n\njulia> (AmpP,AmpS,fP,fS)=Spec(trace1,0.1,1e-3,2000,0.7,1.25,0.35))\nTrace length is 2.0 s using 2000 samples\nTrace 1 at offset 3000 m is found at index 30\nTrace 2 at offset 5000 m is found at index 50\nTrace 1:\nphase P is picked at 0.4 s\nphase S is picked at 0.75 s\nphase width is set to 0.35\nTrace 2:\nphase P is picked at 0.7 s\nphase S is picked at 1.25 s\nphase width is set to 0.35\n+ Figure with 8 subplots\n\n\n\n\n\n","category":"function"},{"location":"#SeismicQ.ComputeQgraph","page":"Home","title":"SeismicQ.ComputeQgraph","text":"(x,y)=ComputeQgraph(amp1,amp2,freq,index,d1,d2,V)\n\nReturns x and y to plot Q-graph for a given phase using the results of Spec() for two different traces from two stations\n\n y=V/(π(d2-d1))*ln(amp2(f)/amp1(f)\n x=f\n\n Considering two attenuated waves at two different distances from the source (d1 \n\n\n\n\n\n","category":"function"},{"location":"#SeismicQ.Getfreq","page":"Home","title":"SeismicQ.Getfreq","text":"Getfreq(dt,Nt)\n\nReturns the frequency vector corresponding to the fft results\n\n dt is the time sample in s\n Nt is the number of samples in the trace given to fft()\n The frequency increment is 1/(Nt*dt)\n Vector goes beyond Nyquist Frequency as fft also does. Only the first half of the vectors are useful for us\n\nExamples\n\njulia> Getfreq(1e-3,2000)\n2000-element Vector{Float64}:\n 0.5\n 1.0\n 1.5\n 2.0\n 2.5\n 3.0\n 3.5\n 4.0\n ⋮\n 996.5\n 997.0\n 997.5\n 998.0\n 998.5\n 999.0\n 999.5\n 1000.0\n\n\n\n\n\n","category":"function"},{"location":"#SeismicQ.GenAttenuatedRicker","page":"Home","title":"SeismicQ.GenAttenuatedRicker","text":"time_vec,acc_vec = GenAttenuatedRicker(listₓ,Δt,Nt,Vp,Vs,αp,αs,𝑓₀) ;\n\nFunction that generates a seismic trace (Ricker wavelet) of P and S waves. This wave is attenuated along time and the function creates a matrix of wave amplitude as a function of time and distance to the source. The function takes as inputs: listₓ : vector of geophone distances to the source [m] Δt : time step of the wave signal [s] Nt : number of time steps of the wave signal Vp : P-wave velocity [m/s] Vs : S-wave velocity [m/s] αp : attenuation factor for P-wave αs : attenuation factor for S-wave 𝑓₀ : central frequency of the source [Hz] \n\nand return: timevec : vector containing the time steps of the received wave signal accvec : matrix of wave acceleration at each geophone position\n\nExamples\n\njulia> time_vec,acc_vec = GenAttenuatedRicker(0:1000:5000,1e-3,2000,7000,4000,2e-4,4e-4,10.0) \n\n\n\n\n\n\n","category":"function"},{"location":"#SeismicQ.PlotReceiverGather","page":"Home","title":"SeismicQ.PlotReceiverGather","text":"PlotReceiverGather(listₓ,time_vec,acc_vec)\n\nFunction that plots a receiver gather The function takes as inputs: listₓ : vector of geophone distances to the source [m] timevec : vector containing the time steps of the wave signal [s] accvec : matrix of wave acceleration at each geophone position\n\nExamples\n\njulia> PlotReceiverGather(0:1000:5000,time_vec,acc_vec) \n\n\n\n\n\n\n","category":"function"}] }