Table 1 List of physical parameters used in modeling.

ρ

Density

2650 kg/m³

λ_r

Thermal conductivity of rock

1.5 W/m/K

λ_m

Thermal conductivity of magma

1.2 W/m/K

C_p

Specific heat capacity

1350 J/K/kg

L_*

Latent heat of melting/crystallization

3.5 × 10⁵ J/K/kg

T_m

Magma intrusion temperature

950 °C

T_top

Temperature at depth z = 0 km

100 °C

ΔT

Temperature geothermal gradient

20 °C/km

ν

Poisson’s ratio of rock

0.3

E

Young’s modulus of rock

15.6 GPa

Q_in

Intrusion rate

1.2 km³/1000 year

[z_min, z_max]

Dike center depth

3–24 km

W

Width of dike intrusion region (focusing)

5(3) km

[zs_min, zs_max]

Depth range of sills formation

3–4 km

θ

Dike rotation angles

85°–95°

a

Dike half length

100–1500 m

b

Dike half thickness

10–20 m

h

Dike transverse width

5 km

δ_cr

Critical melt fraction

90%