2.1 Weighted Time-average and Wood's Equation Mode...
Simple formulae of time-average equation for gas hydrate-bearing sediments can be expressed as［1］
where VP is the velocity of gas hydrate-bearing sediment，Vw，Vh，Vmare the velocities of pore water，pure gas hydrate，and sediment matrix respectively，φis the porosity，and S is the concentration of gas hydrate.The velocity of gas hydrate-bearing sediment can be calculated by the combination of the velocities of sediment matrix，pure gas hydrate and pore water.
Wood's equation for gas hydrate-bearing sediments corresponding to the time-average equation can be defined as［3］
(https://www.daowen.com)
whereρis bulk density of sediment，ρw is density of the fluid，ρhis density of pure gas hydrate andρm is density of sediment matrix.
The velocities of solids are described in the time-average equation and the velocities of particles in suspension are described in Wood's equation.The time-average equation overestimates and the Wood's equation underestimates velocity-porosity relationship in unconsolidated high-porosity marine sediments.A weighted equation is proposed by Lee et al.［3］as
where VP1is P wave velocity by the Wood's equation，VP2is P wave velocity by the time-average equation，W is a weighted factor and n is a constant simulating the rate of lithification with gas hydrate concentration.Lee et al.［3］assumed that S wave velocity increase with the concentration as P wave velocity.Elastic parameters of sediments based on weighted time-average and Wood equation［3］are shown in table 1.
