SEISMIC FORWARD MODELING AND INVERSION FOR GAS H...
In order to identify BSR reasonably and understand amounts of gas hydrates above the BSR and distribution of free gas beneath the BSR，seismic velocity structures of hydrated sediments have been studied in the 1990s.Numerous studies involving forward modeling and inversion of seismic reflection have been carried out［4～9］.These studies used BSR reflection coefficients，reflection waveform modeling，and amplitude-versus-offset（AVO）characteristics to constrain seismic velocity variation above the BSR and the presence of low velocity associated with free gas in the sediment pore space beneath it.
Ecker et al.obtained one gas hydrate and free gas saturation profile in the Blake Ridge from interval velocity using stacking velocity analysis based on the rock physics model（see Fig 2）［5］.The AVO Study of Lee et al.indicated that continuous-looking BSRs in seismic profiles were highly segmented in detail and that gas-filled sediments underneath the hydrates sediments have variable thickness［6］.The different appearances of the BSRs are mainly caused by variations of gas-filled sediments underneath hydrated sediments rather than the lateral heterogeneity of hydrated sediments（see Fig 3）.The weak BSR is the reflection from a thin gas zone（less than 2m thickness）or from the interface between hydrated sediments and water-saturated sediments.Mallick et al.analyzed a marine multichannel seismic data from an ocean basin，offshore India［7］.They obtained intercept section，gradient section by the AVO analysis and inverted acoustic impedance section and Poisson ratio section by poststack inversions.
Fig.2 Stacked section after migration（left panel）and gas hydrate saturation（right panel）from interval velocity section［5］
Fig.3 A conceptual model for the hydrated sediments and their associated features indeep sea marine sediments.Elastic parameters，expected reflection and geometrical relations for various BSRs are shown.a=P-wave velocity in km/s，β=S-wave velocity in km/s，andρis density in 103kg/m3［6］(https://www.daowen.com)
Singh，et al.used waveform inversion technique first to estimate the long wavelengths of velocity variation using random search and then to estimate the short wavelengths of velocity and density variation using nonlinear local search［8］.Holbrook et al.obtained seismic velocities measured in three drill holes through a gas hydrate deposit on the Blake Ridge，offshore South Carolina from vertical seismic profile（VSP）data［4］.It is indicated that substantial free gas exists to at least 250meters beneath the BSR and the average methane hydrate saturation above the BSR is relatively low（5%～7%of porosity）.
Korenaga，et al.analyzed coincident single-channel seismic and wide-angle ocean bottom seismic data acquired in the Blake Ridge and the Carolina Rise［9］.Joint inversion of vertical-incidence and wide-angle travel times was performed to model two-dimensional velocity structure using an iterative，damped least-squares inversion.Full waveform inversion of wide angle reflection data was then applied for nearly one-dimensional experiments to derive fine-scale velocity structure and determine the seismic origin of the BSRs using the generalized reflection transmission matrix method in the frequency-slowness domain（figure 4）.The hydrates seem to be concentrated near the base of the hydrate stability zone，and the maximum hydrate concentration is estimated as about 20%at the Blake Ridge and about 7%at the Carolina Rise.They are too high to be explained by in situ biogenic activity only and require some secondary accumulation mechanism.
Fig.4 Carolina Rise data in theτ-p domain（thick line），plotted with best fitseismogram（thin line）.Inset is enlargement of a portion of BSR phase，showing extremely good waveform agreement.Corresponding velocity model is shown to the right；light line is starting long-wavelength model［9］
Therefore，these studies are calculation of interval velocities from stacking velocities，travel time inversion，poststack acoustic impedance inversion，the AVO analysis and one-dimensional single parameter full waveform inversion of wide-angle reflection data.
