where Sh is the hydrate saturation of the pore space. The bulk and shear moduli of the solid phase are now a mixture of the sediment solid and the hydrate and can be calculated from the Hill average:
where Ks and Gs are the bulk and shear moduli of the sediment without hydrate and fh is the volume fraction of hydrate in the solid phase. It can be calculated as follows:
The dry and saturated moduli can then be determined using equations 3, 4, 5 and 6.