Volcanic-Deformation

McTigue (1987) finite-sphere model for volcanic surface deformation. Extends the Mogi (1958) point-source model by incorporating higher-order correction terms that account for the finite radius of a spherical deformation source. The correction depends on ε = a/d and improves accuracy for larger ε: within 5% of FE models for ε < 0.59, vs ε < 0.37 for Mogi. Three purely-algebraic equations: R = sqrt(x²+d²) (source-to-surface distance), Ur = (Mogi_Ur) × C (Eq. 3, radial displacement), Uz = (Mogi_Uz) × C (Eq. 4, vertical displacement), where C = 1 + (a/d)³ × [(1+ν)/(2(−7+5ν)) + 15d²(−2+ν)/(4R²(−7+5ν))] is the McTigue finite-sphere correction factor. Migrated from Geodynamics.jl@d680af419676cc576d60b16af0d3dd40c0b23eea src/mogi_mctigue.jl:107 (`McTigueModel` @component).

Mogi (1958) point-source model for volcanic surface deformation. Computes horizontal-radial (Ur) and vertical (Uz) surface displacements due to a pressurized spherical cavity in an elastic half-space, using the small-sphere (point-source) approximation (ε = a/d ≪ 1). Three purely-algebraic equations: R = sqrt(x²+d²) (source-to-surface distance), Ur = a³ΔP(1−ν)x / (G·R³) (Eq. 1, radial displacement), Uz = a³ΔP(1−ν)d / (G·R³) (Eq. 2, vertical displacement). Migrated from Geodynamics.jl@d680af419676cc576d60b16af0d3dd40c0b23eea src/mogi_mctigue.jl:48 (`MogiModel` @component).