Deploy to GitHub pages

.buildinfo

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+# Sphinx build info version 1
+# This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done.
+config: 6f51335818d187508385da20397d2891
+tags: 645f666f9bcd5a90fca523b33c5a78b7

CNAME

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+em.geosci.xyz

_downloads/16cd09a07d48eeea36e78d708acd6083/index-1.py

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+L = 1.
+R = 2000.
+alpha = np.logspace(-3, 3, 100)
+Q = (alpha ** 2 + 1j * alpha) / (1 + alpha ** 2)
+fig = plt.figure(figsize=(5, 3))
+ax1 = plt.subplot(111)
+ax1.semilogx(alpha, Q.real, 'k', lw=3)
+ax1.semilogx(alpha, Q.imag, 'r', lw=3)
+ax1.grid(True)
+ax1.legend(("Real","Imaginary"), loc=2)
+ax1.set_xlabel("Induction number ($\\alpha$)")
+ax1.set_ylabel("Response function (Q)")
+plt.tight_layout()
+plt.show()

_downloads/4734b95e928389bbe7dbd1ec84b09bdb/electrostatic_sphere-2.py

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+from matplotlib import patches
+from geoana.em.static import ElectrostaticSphere
+
+sig0 = 10.**-3.         # conductivity of the whole-space in S/m
+sig1 = 10.**-1.         # conductivity of the sphere in S/m
+R    = 50.          # radius of the sphere in m
+E0   = 1.           # inducing field strength in V/m
+
+sphere = ElectrostaticSphere(R, sig1, sig0, E0) # create the sphere object
+
+n = 50             #level of discretization
+xr = np.linspace(-2.*R, 2.*R, n) # X-axis discretization
+yr = xr.copy()      # Y-axis discretization
+X, Y = np.meshgrid(xr, yr)
+Z = np.zeros_like(X)
+
+potentials = sphere.potential((X, Y, Z), field='primary')
+
+fig, ax = plt.subplots(1,1, figsize = (8,6))
+im = ax.pcolor(X, Y, potentials, shading='auto')
+cb = plt.colorbar(im)
+cb.set_label(label='Potential ($V$)')
+ax.add_patch(patches.Circle([0,0], R, fill=False, linestyle='--'))
+
+ax.set_title('Primary Potential')
+ax.set_ylabel('Y coordinate ($m$)')
+ax.set_xlabel('X coordinate ($m$)')
+ax.set_aspect('equal')

_downloads/5900511493c45dc67ef2c2e07f94fcf3/electrostatic_sphere-4.py

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+from matplotlib import patches
+from geoana.em.static import ElectrostaticSphere
+
+sig0 = 10.**-3.          # conductivity of the whole-space in S/m
+sig1 = 10.**-1.         # conductivity of the sphere in S/m
+sig2 = 10.**-5.         # conductivity of the sphere in S/m
+R    = 50.          # radius of the sphere in m
+E0   = 1.           # inducing field strength in V/m
+
+sphere1 = ElectrostaticSphere(R, sig1, sig0, E0) # create the sphere object
+sphere2 = ElectrostaticSphere(R, sig2, sig0, E0) # create the sphere object
+
+n = 50             #level of discretization
+xr = np.linspace(-2.*R, 2.*R, n) # X-axis discretization
+yr = xr.copy()      # Y-axis discretization
+X, Y = np.meshgrid(xr, yr)
+Z = np.zeros_like(X)
+
+Et1, Ep1, Es1 = sphere1.electric_field((X, Y, Z), field='all')
+Et2, Ep2, Es2 = sphere2.electric_field((X, Y, Z), field='all')
+
+fig, axs = plt.subplots(2,2,figsize=(18,12))
+Es = [Et1, Et2, Es1, Es2]
+titles = [
+    'Conductive Sphere: \n Total Electric Field',
+    'Resistive Sphere: \n Total Electric Field',
+    'Conductive Sphere: \n Secondary Electric Field',
+    'Resistive Sphere: \n Secondary Electric Field',
+]
+for ax, E, title in zip(axs.flatten(), Es, titles):
+    E_amp = np.linalg.norm(E, axis=-1)
+    im = ax.pcolor(X, Y, E_amp, shading='auto')
+    cb = plt.colorbar(im, ax=ax)
+    cb.set_label(label= 'Amplitude ($V/m$)')
+    ax.streamplot(X, Y, E[..., 0], E[..., 1], color='gray', linewidth=2., density=0.75)
+    ax.add_patch(patches.Circle([0,0], R, fill=False, linestyle='--'))
+
+    ax.set_ylabel('Y coordinate ($m$)')
+    ax.set_xlabel('X coordinate ($m$)')
+    ax.set_aspect('equal')
+    ax.set_title(title)
+
+plt.tight_layout()
+plt.show()

_downloads/5de421c9f7056bfeb7d3e3d33e26d76f/electrostatic_sphere-5.py

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+from matplotlib import patches
+from geoana.em.static import ElectrostaticSphere
+
+sig0 = 10.**-3.          # conductivity of the whole-space in S/m
+sig1 = 10.**-1.         # conductivity of the sphere in S/m
+sig2 = 10.**-5.         # conductivity of the sphere in S/m
+R    = 50.          # radius of the sphere in m
+E0   = 1.           # inducing field strength in V/m
+
+sphere1 = ElectrostaticSphere(R, sig1, sig0, E0) # create the sphere object
+sphere2 = ElectrostaticSphere(R, sig2, sig0, E0) # create the sphere object
+
+n = 50             #level of discretization
+xr = np.linspace(-2.*R, 2.*R, n) # X-axis discretization
+yr = xr.copy()      # Y-axis discretization
+X, Y = np.meshgrid(xr, yr)
+Z = np.zeros_like(X)
+
+Jt1, Jp1, Js1 = sphere1.current_density((X, Y, Z), field='all')
+Jt2, Jp2, Js2 = sphere2.current_density((X, Y, Z), field='all')
+
+fig, axs = plt.subplots(2,2,figsize=(18,12))
+Js = [Jt1, Jt2, Js1, Js2]
+titles = [
+    'Conductive Sphere: \n Total Current Density',
+    'Resistive Sphere: \n Total Current Density',
+    'Conductive Sphere: \n Secondary Current Density',
+    'Resistive Sphere: \n Secondary Current Density',
+]
+for ax, J, title in zip(axs.flatten(), Js, titles):
+    J_amp = np.linalg.norm(J, axis=-1)
+    im = ax.pcolor(X, Y, J_amp, shading='auto')
+    cb = plt.colorbar(im, ax=ax)
+    cb.set_label(label='Current Density ($A/m^2$)')
+    ax.streamplot(X, Y, J[..., 0], J[..., 1], color='gray', linewidth=2., density=0.75)
+    ax.add_patch(patches.Circle([0,0], R, fill=False, linestyle='--'))
+
+    ax.set_ylabel('Y coordinate ($m$)')
+    ax.set_xlabel('X coordinate ($m$)')
+    ax.set_aspect('equal')
+    ax.set_title(title)
+
+plt.tight_layout()
+plt.show()

_downloads/5faa8585eaa70d059852d013ce157e15/electrostatic_sphere-8.py

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+from matplotlib import patches
+from geoana.em.static import ElectrostaticSphere
+
+sig0 = 10.**-3.          # conductivity of the whole-space in S/m
+sig1 = 10.**-1.         # conductivity of the sphere in S/m
+sig2 = 1.310344828 * 10**-3.
+R0   = 20.          # radius of the sphere in m
+R1   = 40.
+E0   = 1.           # inducing field strength in V/m
+
+sphere1 = ElectrostaticSphere(R0, sig1, sig0, E0) # create the sphere object
+sphere2 = ElectrostaticSphere(R1, sig2, sig0, E0) # create the sphere object
+
+n = 31             #level of discretization
+xr = np.linspace(-100, 100, n) # X-axis dipole midpoints
+yr = xr.copy()      # Y-axis dipole midpoints
+X, Y = np.meshgrid(xr, yr)
+Z = np.zeros_like(X)
+
+Dx = np.linspace(-100, 100, n)
+Dy = np.linspace(-100, 100, n)
+Dz = np.zeros(n)
+electrode_spacing = 10
+
+Mx = Dx - 0.5 * electrode_spacing/np.sqrt(2)
+My = Dy - 0.5 * electrode_spacing/np.sqrt(2)
+Mz = Dz
+Nx = Dx + 0.5 * electrode_spacing/np.sqrt(2)
+Ny = Dy + 0.5 * electrode_spacing/np.sqrt(2)
+Nz = Dz
+
+fig = plt.figure(figsize=(20, 20))
+ax0 = plt.subplot2grid((20, 12), (0, 0), colspan=6, rowspan=6)
+ax1 = plt.subplot2grid((20, 12), (0, 6), colspan=6, rowspan=6)
+ax2 = plt.subplot2grid((20, 12), (8, 0), colspan=6, rowspan=6)
+ax3 = plt.subplot2grid((20, 12), (8, 6), colspan=6, rowspan=6)
+ax4 = plt.subplot2grid((20, 12), (16, 2), colspan=9, rowspan=4)
+
+R = 50
+for ax, color, sig_circ, r in zip([ax0, ax1], [[0.6, 0.1, 0.1], [0.1, 0.1, 0.6]], [sig1, sig2], [R0, R1]):
+    circle = patches.Circle([0,0],radius=r, alpha=0.4, color=color, linewidth=1.5)
+    ax.add_patch(circle)
+    ax.arrow(0., 0., np.sqrt(2.)*r/2., np.sqrt(2.)*r/2., head_width=0., head_length=0.)
+
+    for y in np.linspace(-2 * R, 2 * R, 10):
+        ax.arrow(-2*R, y, 0.3*R, 0.0, head_width=5., head_length=2., color='k')
+
+    ax.text(0, -r/2., f'$\sigma_1$={sig_circ*1000:3.3f} mS/m')
+    ax.text(0, -1.5*r, f'$\sigma_0$={sig0*1000:3.3f} mS/m')
+    ax.text(0.5*np.cos(np.pi/6)*r, 0.5*np.sin(np.pi/6)*r, f'R={r:1.0f} m')
+    ax.text(-1.8*R, 1.3*R, f'$\mathbf{{E_0}} = {E0:1.0f} \mathbf{{\hat{{x}}}}$ V/m')
+
+    ax.set_facecolor([0.4, 0.7, 0.4, 0.3])
+    ax.set_xlim([-2 * R, 2 * R])
+    ax.set_ylim([-2 * R, 2 * R])
+    ax.set_ylabel('Y coordinate ($m$)')
+    ax.set_xlabel('X coordinate ($m$)')
+    ax.set_aspect('equal')
+
+Vt1 = sphere1.potential((X, Y, Z), field='total')
+Vt2 = sphere2.potential((X, Y, Z), field='total')
+titles = [
+        'Conductive Sphere: \n Total Potential',
+        'Resistive Sphere: \n Total Potential',
+    ]
+
+for ax, V, title, r in zip([ax2, ax3], [Vt1, Vt2], titles, [R0, R1]):
+    im = ax.pcolor(X, Y, V, shading='auto')
+    cb = plt.colorbar(im, ax=ax)
+    cb.set_label(label='Potential ($V$)')
+    ax.add_patch(patches.Circle([0,0], r, fill=False, linestyle='--'))
+
+    ax.set_title(title)
+    ax.set_ylabel('Y coordinate ($m$)')
+    ax.set_xlabel('X coordinate ($m$)')
+    ax.set_aspect('equal')
+
+    ax.plot(Dx, Dy, color='gray')
+    ax.scatter(Dx, Dx, color='black', label="Dipole Midpoint")
+    ax.scatter(np.r_[Mx, Nx], np.r_[My, Ny], color='red', label="Electrodes")
+    ax.legend(loc='best')
+
+VM1 = sphere1.potential((Mx, My, Mz), field='total')
+VN1 = sphere1.potential((Nx, Ny, Nz), field='total')
+
+VM2 = sphere2.potential((Mx, My, Mz), field='total')
+VN2 = sphere2.potential((Nx, Ny, Nz), field='total')
+
+#Plot the Data (from Configuration 0)
+ax4.plot(np.sqrt(2)*np.linspace(-100, 100, n), VM1-VN1,
+         marker='o', color='red', linewidth=3., label='Left Model Response' )
+ax4.plot(np.sqrt(2)*np.linspace(-100, 100, n), VM2-VN2,
+         marker='o', color='blue', linewidth=3., label='Right Model Response' )
+ax4.set_xlabel('Profile Distance ($m$)')
+ax4.set_ylabel('Potential Difference ($V$)')
+ax4.legend(loc='best')
+
+plt.show()

_downloads/68ede071af6b09f407fa613a98b8befd/electrostatic_sphere-6.py

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+from matplotlib import patches
+from geoana.em.static import ElectrostaticSphere
+
+sig0 = 10.**-3.          # conductivity of the whole-space in S/m
+sig1 = 10.**-1.         # conductivity of the sphere in S/m
+sig2 = 10.**-5.         # conductivity of the sphere in S/m
+R    = 50.          # radius of the sphere in m
+E0   = 1.           # inducing field strength in V/m
+
+sphere1 = ElectrostaticSphere(R, sig1, sig0, E0) # create the sphere object
+sphere2 = ElectrostaticSphere(R, sig2, sig0, E0) # create the sphere object
+
+n = 50             #level of discretization
+xr = np.linspace(-2.*R, 2.*R, n) # X-axis discretization
+yr = xr.copy()      # Y-axis discretization
+X, Y = np.meshgrid(xr, yr)
+Z = np.zeros_like(X)
+
+q1 = sphere1.charge_density((X, Y, Z), dr=xr[1]-xr[0])
+q2 = sphere2.charge_density((X, Y, Z), dr=xr[1]-xr[0])
+
+fig, axs = plt.subplots(1,2,figsize=(18,6))
+qs = [q1, q2]
+titles = ['Conductive Sphere: \n Charge Accumulation', 'Resistive Sphere: \n Charge Accumulation']
+
+for ax, q, title in zip(axs, qs, titles):
+    im = ax.pcolor(X, Y, q, shading='auto')
+    cb1 = plt.colorbar(im, ax=ax)
+    cb1.set_label(label= 'Charge Density ($C/m^2$)')
+    ax.add_patch(patches.Circle([0,0], R, fill=False, linestyle='--'))
+
+    ax.set_ylabel('Y coordinate ($m$)')
+    ax.set_xlabel('X coordinate ($m$)')
+    ax.set_title(title)
+    ax.set_aspect('equal')
+
+plt.tight_layout()
+plt.show()

_downloads/6fd1b9e961cebbe89c4bb59d036a895a/electrostatic_sphere-7.py

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+from matplotlib import patches
+from geoana.em.static import ElectrostaticSphere
+
+sig0 = 10.**-3.          # conductivity of the whole-space in S/m
+sig1 = 10.**-1.         # conductivity of the sphere in S/m
+sig2 = 10.**-5.         # conductivity of the sphere in S/m
+R    = 50.          # radius of the sphere in m
+E0   = 1.           # inducing field strength in V/m
+
+sphere1 = ElectrostaticSphere(R, sig1, sig0, E0) # create the sphere object
+sphere2 = ElectrostaticSphere(R, sig2, sig0, E0) # create the sphere object
+
+n = 31             #level of discretization
+xr = np.linspace(-100, 100, n) # X-axis dipole midpoints
+yr = xr.copy()      # Y-axis dipole midpoints
+X, Y = np.meshgrid(xr, yr)
+Z = np.zeros_like(X)
+
+Dx = np.linspace(-100, 100, n)
+Dy = np.linspace(-100, 100, n)
+Dz = np.zeros(n)
+electrode_spacing = 10
+
+Mx = Dx - 0.5 * electrode_spacing/np.sqrt(2)
+My = Dy - 0.5 * electrode_spacing/np.sqrt(2)
+Mz = Dz
+Nx = Dx + 0.5 * electrode_spacing/np.sqrt(2)
+Ny = Dy + 0.5 * electrode_spacing/np.sqrt(2)
+Nz = Dz
+
+fig = plt.figure(figsize=(20, 20))
+ax0 = plt.subplot2grid((20, 12), (0, 0), colspan=6, rowspan=6)
+ax1 = plt.subplot2grid((20, 12), (0, 6), colspan=6, rowspan=6)
+ax2 = plt.subplot2grid((20, 12), (8, 0), colspan=6, rowspan=6)
+ax3 = plt.subplot2grid((20, 12), (8, 6), colspan=6, rowspan=6)
+ax4 = plt.subplot2grid((20, 12), (16, 2), colspan=9, rowspan=4)
+
+for ax, color, sig_circ in zip([ax0, ax1], [[0.6, 0.1, 0.1], [0.1, 0.1, 0.6]], [sig1, sig2]):
+    circle = patches.Circle([0,0],radius=R, alpha=0.4, color=color, linewidth=1.5)
+    ax.add_patch(circle)
+    ax.arrow(0., 0., np.sqrt(2.)*R/2., np.sqrt(2.)*R/2., head_width=0., head_length=0.)
+
+    for y in np.linspace(-2 * R, 2 * R, 10):
+        ax.arrow(-2*R, y, 0.3*R, 0.0, head_width=5., head_length=2., color='k')
+
+    ax.text(0, -R/2., f'$\sigma_1$={sig_circ*1000:3.3f} mS/m')
+    ax.text(0, -1.5*R, f'$\sigma_0$={sig0*1000:3.3f} mS/m')
+    ax.text(0.5*np.cos(np.pi/6)*R, 0.5*np.sin(np.pi/6)*R, f'R={R:1.0f} m')
+    ax.text(-1.8*R, 1.3*R, f'$\mathbf{{E_0}} = {E0:1.0f} \mathbf{{\hat{{x}}}}$ V/m')
+
+    ax.set_facecolor([0.4, 0.7, 0.4, 0.3])
+    ax.set_xlim([-2 * R, 2 * R])
+    ax.set_ylim([-2 * R, 2 * R])
+    ax.set_ylabel('Y coordinate ($m$)')
+    ax.set_xlabel('X coordinate ($m$)')
+    ax.set_aspect('equal')
+
+Vt1 = sphere1.potential((X, Y, Z), field='total')
+Vt2 = sphere2.potential((X, Y, Z), field='total')
+titles = [
+        'Conductive Sphere: \n Total Potential',
+        'Resistive Sphere: \n Total Potential',
+    ]
+
+for ax, V, title in zip([ax2, ax3], [Vt1, Vt2], titles):
+    im = ax.pcolor(X, Y, V, shading='auto')
+    cb = plt.colorbar(im, ax=ax)
+    cb.set_label(label='Potential ($V$)')
+    ax.add_patch(patches.Circle([0,0], R, fill=False, linestyle='--'))
+
+    ax.set_title(title)
+    ax.set_ylabel('Y coordinate ($m$)')
+    ax.set_xlabel('X coordinate ($m$)')
+    ax.set_aspect('equal')
+
+    ax.plot(Dx, Dy, color='gray')
+    ax.scatter(Dx, Dx, color='black', label="Dipole Midpoint")
+    ax.scatter(np.r_[Mx, Nx], np.r_[My, Ny], color='red', label="Electrodes")
+    ax.legend(loc='best')
+
+VM1 = sphere1.potential((Mx, My, Mz), field='total')
+VN1 = sphere1.potential((Nx, Ny, Nz), field='total')
+
+VM2 = sphere2.potential((Mx, My, Mz), field='total')
+VN2 = sphere2.potential((Nx, Ny, Nz), field='total')
+
+#Plot the Data (from Configuration 0)
+ax4.plot(np.sqrt(2)*np.linspace(-100, 100, n), VM1-VN1,
+         marker='o', color='red', linewidth=3., label='Left Model Response' )
+ax4.plot(np.sqrt(2)*np.linspace(-100, 100, n), VM2-VN2,
+         marker='o', color='blue', linewidth=3., label='Right Model Response' )
+ax4.set_xlabel('Profile Distance ($m$)')
+ax4.set_ylabel('Potential Difference ($V$)')
+ax4.legend(loc='best')
+
+plt.show()