Add 1D -> receiver gather example

examples/Wave2D_Day3.jl

@@ -156,7 +156,7 @@ function MainSource()
                                     *((τ.i.xy[2:end,2:end-1]-τ.i.xy[1:end-1,2:end-1])/Δ.x
                                     + (τ.j.yy[2:end-1,2:end]-τ.j.yy[2:end-1,1:end-1])/Δ.y 
                                     - (P.j[2:end-1,2:end]-P.j[2:end-1,1:end-1])/Δ.y 
-                                    - 0.0*Xf_ext.c[2:end-1,2:end-1]))   
+                                    - 0.0*f_ext.c[2:end-1,2:end-1]))   
 
 
     #     # Absorbing boundary Cerjean et al. (1985)

examples/Wave_Day2_anais.jl

@@ -0,0 +1,143 @@
+using SeismicQ, Plots
+
+function MainSource()
+
+    # Spatial extent
+    Lx  = 25.0      # (en m)
+
+    # Mechanical parameters
+
+    ρ₀ = 1100.0      # (kg.m-3)
+    K₀ = 1.0e9       # (Pa)
+    G₀ = 1.0e8       # (Pa)
+
+
+
+    # Discretization
+    Ncx = 10
+    Δx  = Lx/Ncx
+
+    # Central frequency of the source [Hz]
+    𝑓₀  = 10.
+    t₀  = 1.2/𝑓₀
+
+    # Time domain
+    Δt  = 1e-3
+    Nt  = 1000
+    t   = -t₀
+    v   = 0.0
+
+    # Storage
+
+    szv  = (Ncx+1,)
+    szc  = (Ncx+2,)
+    K    = ones(Ncx+2)*K₀
+    G    = ones(Ncx+2)*G₀
+    ρ    = ones(Ncx+1)*ρ₀
+    Vx   = zeros(Ncx+1)
+    ε̇    = (xx = zeros(szc), yy = zeros(szc) , zz = zeros(szc)  )
+    τ    = ( xx = zeros(szc), yy = zeros(szc) , zz = zeros(szc) )
+    P    = zeros(Ncx+2) 
+    ∇V   = zeros(Ncx+2)
+
+ #    time_src = zeros(Nt)
+ #    acc_src  = zeros(Nt)
+ #    vel_src  = zeros(Nt)
+ #    v_src    = 0.
+
+
+    @show ε̇.xx[1]
+
+    # Time loop
+    for it=1:Nt
+
+        V0 = V 
+
+        # Compute Ricker function
+        t += Δt
+        a  = Ricker(t, t₀, 𝑓₀)
+        v += a*Δt
+
+        # BC 
+        V.x[1]  = v
+
+        # gard V components
+
+        ∂Vx∂x   = (V.x[2:end] - V.x[1:end-1]) / Δx
+        ∂Vy∂y   = (V.y[2:end] - V.y[1:end-1]) / Δy
+        ∂Vz∂z   = (V.z[2:end] - V.z[1:end-1]) / Δz
+
+        ∂Vx∂y   = (V.y[2:end] - V.y[1:end-1]) / Δy
+        ∂Vx∂z   = (V.y[2:end] - V.y[1:end-1]) / Δy
+
+        ∂Vy∂z   = (V.y[2:end] - V.y[1:end-1]) / Δz
+        ∂Vz∂y   = (V.z[2:end] - V.z[1:end-1]) / Δy
+
+
+        # divergence 
+        ∇V      = ∂Vx∂x +  ∂Vx∂y + ∂Vx∂z
+
+        # Deviatoric strain rate 
+
+         ε̇.xx[2:end-1] = ∂Vx∂x - 1/3 * ∇V[2:end-1]
+         ε̇.yy[2:end-1] = ∂Vy∂y - 1/3 * ∇V[2:end-1]
+         ε̇.zz[2:end-1] = ∂Vz∂z - 1/3 * ∇V[2:end-1] 
+         ε̇.xy[2:end-1] = 0.5 * (∂Vx∂y + ∂Vy∂x)
+         ε̇.xz[2:end-1] = 0.5 * (∂Vx∂z + ∂Vz∂x)
+         ε̇.yz[2:end-1] = 0.5 * (∂Vy∂z + ∂Vz∂y)
+
+        # Stress update 
+       τ.xx = f_shear(G) * Δt * (ε̇.xx) + f_relax(G) * τ.xx
+       τ.yy = f_shear(G) * Δt * (ε̇.yy) + f_relax(G) * τ.yy
+       τ.zz = f_shear(G) * Δt * (ε̇.zz) + f_relax(G) * τ.zz
+       τ.xy = f_shear(G) * Δt * (ε̇.xy) + f_relax(G) * τ.xy
+       τ.xz = f_shear(G) * Δt * (ε̇.xz) + f_relax(G) * τ.xz
+       τ.yz = f_shear(G) * Δt * (ε̇.yz) + f_relax(G) * τ.yz
+
+
+        # Pressure update
+        P   = P0 + Δt * f_bulk(K) * ∇V
+        dvdt * rho = div τ - grad P 
+        V.x = V0.x + Δt / ρ * ( (τ.xx[2:end]-τ.xx[1:end-1]) / Δx
+                               +(τ.xy[2:end]-τ.xy[1:end-1]) / Δy
+                               +(τ.xy[2:end]-τ.x[1:end-1]) / Δz
+                               - P[2;end]/Δx
+
+        V.y = V0.y + Δt / ρ * ( (τ.yy[2:end]-τ.yy[1:end-1]) / Δx
+                               +(τ.xy[2:end]-τ.xy[1:end-1]) / Δy
+                               +(τ.xy[2:end]-τ.x[1:end-1]) / Δz
+                               - P[2;end]/Δx
+        V.z = V0.z + Δt / ρ * ( (τ.xx[2:end]-τ.xx[1:end-1]) / Δx
+                               +(τ.xy[2:end]-τ.xy[1:end-1]) / Δy
+                               +(τ.xy[2:end]-τ.x[1:end-1]) / Δz
+                               - P[2;end]/Δx
+
+
+
+        # For visualisation purpose
+ #       time[it] = t
+ #       acc[it]  = a
+ #       vel[it]  = v
+    end
+
+    # Visualisation
+ #   p1 = plot(time, acc, xlabel="t", ylabel="a")
+ #   p2 = plot(time, vel, xlabel="t", ylabel="v")
+ #   plot(p1, p2, layout=(2,1))
+
+end
+
+function f_bulk(K)
+    return Ṗ = -K
+end
+
+function f_shear(G)
+    return 2*G 
+end
+
+function f_relax(G)
+    return 1.
+end
+
+
+MainSource()