AVO analysis of BSR to assess free gas within fine-grained sediments in the Shenhu area, South China Sea

Abstract

Gas hydrates have been identified from two-dimensional (2D) seismic data and logging data above bottom simulating reflector (BSR) during China’s first gas hydrate drilling expedition in 2007. The multichannel reflection seismic data were processed to be preserved amplitudes for quantitatively analyzing amplitude variation with offset (AVO) at BSRs. Low P-wave velocity anomaly below BSR, coinciding with high amplitude reflections in 2D seismic data, indicates the presence of free gas. The absolute values of reflection coefficient versus incidence angles for BSR range from 0 to 0.12 at different CMPs near Site SH2. According to logging data and gas hydrate saturations estimated from resistivity of Site SH2, P-wave velocities calculated from effective media theory (EMT) fit the measured sonic velocities well and we choose EMT to calculate elastic velocities for AVO. The rock-physics modeling and AVO analysis were combined to quantitatively assess free gas saturations and distribution by the reflection coefficients variation of the BSRs in Shenhu area, South China Sea. AVO estimation indicates that free gas saturations immediately beneath BSRs may be about 0.2 % (uniform distribution) and up to about 10 % (patchy distribution) at Site SH2.

Appendices

Appendix 1: Theory of elastic velocities calculation

Time-average weighted equation (modified after Lee et al. 1996)

Pearson et al. (1983) used the three-phase, time-average equation with concentration of hydrate in the pore space (as a fraction) for the velocity. Here we use saturation instead of concentration, and change the equation into

$$ \frac{1}{{V_{p} }} = \frac{\phi - S}{{V_{w} }} + \frac{S}{{V_{h} }} + \frac{1 - \phi }{{V_{m} }}, $$

(1)

where V _p , V _h , V _w , and V _m are compressional velocity of the hydrated sediment, the pure hydrate, the fluid, and the matrix, respectively. ϕ is porosity (as a fraction). S is saturation of hydrate.

Three-phase Wood equation (modified after Lee et al. 1996)

Like the Pearson et al. (1983) three-phase time-average equation, the three-phase Wood equation for hydrated is

$$ \frac{1}{{\rho V_{p}^{2} }} = \frac{\phi - S}{{\rho_{w} V_{w}^{2} }} + \frac{S}{{\rho_{h} V_{h}^{2} }} + \frac{1 - \phi }{{\rho_{m} V_{m}^{2} }}, $$

(2)

where ρ _h , ρ _w , and ρ _m are the pure hydrate, the fluid, and the matrix, respectively. ρ, equal to (1-ϕ) ρ _m  + (ϕ-S) ρ _w + Sρ _h , is the bulk density of the sediment.

Three-phase weighted equation (modified after Lee et al. 1996)

Lee et al. (1996) proposed that three-phase weighted equation mean of Eqs. (1) and (2) can be written as

$$ \frac{1}{{V_{p} }} = \frac{{W\phi (1 - {S \mathord{\left/ {\vphantom {S \phi }} \right. \kern-0pt} \phi })^{n} }}{{V_{p1} }} + \frac{{1 - W\phi (1 - {S \mathord{\left/ {\vphantom {S \phi }} \right. \kern-0pt} \phi })^{n} }}{{V_{p2} }} , $$

(3)

where V _p1 is P-wave velocity by the Wood equation, V _p2 is P-wave velocity by the time-average equation, W is a weighted factor, and n is a constant simulating the rate of lithification with hydrate concentration.

Effective media theory (Ecker et al. 1998, 2000)

Ecker et al. (1998, 2000) used three rock-physics models (A, B, and C) to estimate elastic velocities of gas hydrate on the sediment. The performance of calculation includes two parts, sediments without and with gas hydrate.

Sediments without gas hydrate

The bulk and shear elastic moduli of the dry frame of sediment without gas hydrate (K _dry and G _dry , respectively) can be calculated by

$$ K_{dry} = \left[ {\frac{{{\phi \mathord{\left/ {\vphantom {\phi {\phi_{c} }}} \right. \kern-0pt} {\phi_{c} }}}}{{K_{HM} + \tfrac{4}{3}G_{HM} }} + \frac{{1 - {\phi \mathord{\left/ {\vphantom {\phi {\phi_{c} }}} \right. \kern-0pt} {\phi_{c} }}}}{{K + \tfrac{4}{3}G_{HM} }}} \right]^{ - 1} - \frac{4}{3}G_{HM} , $$

(4a)

$$ G_{dry} = \left[ {\frac{{{\phi \mathord{\left/ {\vphantom {\phi {\phi_{c} }}} \right. \kern-0pt} {\phi_{c} }}}}{{G_{HM} + Z}} + \frac{{1 - {\phi \mathord{\left/ {\vphantom {\phi {\phi_{c} }}} \right. \kern-0pt} {\phi_{c} }}}}{G + Z}} \right]^{ - 1} - Z ; $$

(4b)

$$ Z = \frac{{G_{HM} }}{6}\left[ {\frac{{9K_{HM} + 8G_{HM} }}{{K_{HM} + 2G_{HM} }}} \right];\phi < \phi_{c} ; $$

(5)

$$ K_{dry} = \left[ {\frac{{(1 - {{\phi )} \mathord{\left/ {\vphantom {{\phi )} {(1 - \phi_{c} )}}} \right. \kern-0pt} {(1 - \phi_{c} )}}}}{{K_{HM} + \tfrac{4}{3}G_{HM} }} + \frac{{({{\phi - \phi_{c} )} \mathord{\left/ {\vphantom {{\phi - \phi_{c} )} {(1 - \phi_{c} )}}} \right. \kern-0pt} {(1 - \phi_{c} )}}}}{{\tfrac{4}{3}G_{HM} }}} \right]^{ - 1} - \frac{4}{3}G_{HM} , $$

(6a)

$$ G_{dry} = \left[ {\frac{{(1 - \phi )/(1 - \phi_{c} )}}{{G_{HM} + Z}} + \frac{{(\phi - \phi_{c} )/(1 - \phi_{c} )}}{Z}} \right]^{ - 1} - Z;\,\phi \ge \phi_{c} ; $$

(6b)

where ϕ is porosity; ϕ _c is the porosity of a dense random sphere pack (about 36 %); K and G are the bulk and shear moduli of the mineral phase, respectively. They can be calculated from the moduli of m mineral constituents (K _i and G _i ) using Hill’s average:

$$ K = \frac{1}{2}\left[ {\sum\limits_{i = 1}^{m} {f_{i} K_{i} + \left( {\sum\limits_{i = 1}^{m} {\frac{{f_{i} }}{{K_{i} }}} } \right)^{ - 1} } } \right] , $$

(7a)

$$ G = \frac{1}{2}\left[ {\sum\limits_{i = 1}^{m} {f_{i} G_{i} + \left( {\sum\limits_{i = 1}^{m} {\frac{{f_{i} }}{{G_{i} }}} } \right)^{ - 1} } } \right] ; $$

(7b)

where f _i is the volumetric fraction of the ith component in the solid phase. K _HM and G _HM are calculated from the Hertz-Mindlin theory as

$$ K_{HM} = \left[ {\frac{{G^{2} n^{2} \left( {1 - \phi_{c} } \right)^{2} }}{{18\pi^{2} \left( {1 - \nu } \right)^{2} }}P} \right]^{\frac{1}{3}} , $$

(8a)

$$ G_{HM} = \frac{5 - 4\nu }{5(2 - \nu )}\left[ {\frac{{3G^{2} n^{2} \left( {1 - \phi_{c} } \right)^{2} }}{{2\pi^{2} \left( {1 - \nu } \right)^{2} }}P} \right]^{\frac{1}{3}} ; $$

(8b)

where ν is the Poisson’s ratio of the mineral phase calculated from K and G; n is the average number of contacts per grain taken as 8.5; P is the effective pressure

$$ P = (1 - \phi )(\rho_{s} - \rho_{f} )gh , $$

(9)

where ρ _s and ρ _f are the densities of the solid and fluid phase, respectively; g is gravity acceleration; and h is depth below seafloor.

The subsequent saturation sediment bulk and shear moduli (K _sat and G _sat , respectively) are calculated using the Gassmann equation:

$$ K_{sat} = K\frac{{\phi K_{dry} - {{(1 + \phi )K_{f} K_{dry} } \mathord{\left/ {\vphantom {{(1 + \phi )K_{f} K_{dry} } K}} \right. \kern-0pt} K} + K_{f} }}{{(1 - \phi )K_{f} + \phi K - {{K_{f} K_{dry} } \mathord{\left/ {\vphantom {{K_{f} K_{dry} } K}} \right. \kern-0pt} K}}} , $$

(10a)

$$ G_{sat} = G_{dry} ; $$

(10b)

where K _f is the bulk modulus of the pore fluid which, at saturation S _w , is the isostress average of those of water (K _w ) and gas (K _g ):

$$ K_{f} = \left[ {\frac{{S_{w} }}{{K_{w} }} + \frac{{(1 - S_{w} )}}{{K_{g} }}} \right]^{ - 1} . $$

(11)

Sediments with gas hydrate

Model A: Hydrate is part of pore fluid

In this case, the bulk modulus of the fluid is isostress average of those of water and hydrate (K _h ):

$$ K_{f} = \left[ {\frac{{S_{w} }}{{K_{w} }} + \frac{{(1 - S_{w} )}}{{K_{h} }}} \right]^{ - 1} . $$

(12)

Model B: Hydrate is part of the dry sediment frame

In this case, gas hydrate acts to (a) reduce the porosity and (b) alter the elastic properties of the solid phase. The reduced porosity ϕ _r is

$$ \phi_{\text{r}} = \phi Sw = \phi \left( { 1- S_{h} } \right), $$

(13)

where S _h is gas hydrate saturation, and the elastic moduli of the altered solid phase are calculated using Hill’s average as

$$ K = \frac{1}{2}\left( {f_{h} K_{h} + (1 - f_{h} )K_{s} + \left[ {\frac{{f_{h} }}{{K_{h} }} + \frac{{(1 - f_{h} )}}{{K_{s} }}} \right]^{ - 1} } \right) , $$

(14a)

$$ G = \frac{1}{2}\left( {f_{h} G_{h} + (1 - f_{h} )G_{s} + \left[ {\frac{{f_{h} }}{{G_{h} }} + \frac{{(1 - f_{h} )}}{{G_{s} }}} \right]^{ - 1} } \right) ; $$

(14b)

$$ f_{h} = \frac{{\phi (1 - S_{w} )}}{{1 - \phi S_{w} }} ; $$

(14c)

where K _s and G _s are the solid bulk and shear moduli of the original sediment’s solid phase, respectively, and K _h and G _h are those of pure gas hydrate. Those altered porosity and elastic moduli are used as input to the above model for the moduli of the dry frame.

Finally, the elastic wave velocities are calculated from the elastic moduli and bulk density ρ _B as

$$ V_{p} = \sqrt {{{\left( {K_{sat} + \frac{4}{3}G_{sat} } \right)} \mathord{\left/ {\vphantom {{\left( {K_{sat} + \frac{4}{3}G_{sat} } \right)} {\rho_{B} }}} \right. \kern-0pt} {\rho_{B} }}} , $$

(15a)

$$ V_{s} = \sqrt {{{G_{sat} } \mathord{\left/ {\vphantom {{G_{sat} } {\rho_{B} }}} \right. \kern-0pt} {\rho_{B} }}} . $$

(15b)

For patchy saturation, the effective bulk modulus K _sat of the volume is

$$ \left( {K_{sat} + {{4G} \mathord{\left/ {\vphantom {{4G} 3}} \right. \kern-0pt} 3}} \right)^{ - 1} = S_{w} \left( {K_{1} + {{4G} \mathord{\left/ {\vphantom {{4G} 3}} \right. \kern-0pt} 3}} \right)^{ - 1} + \left( {1 - S_{w} } \right)\left( {K_{0} + {{4G} \mathord{\left/ {\vphantom {{4G} 3}} \right. \kern-0pt} 3}} \right)^{ - 1} $$

(16)

where K₁ and K₀ are the bulk moduli of the rock at Sw = 1 and Sw = 0, respectively (Dvorkin et al. 1999).

Model C is not used because it is not consistent with the gas hydrate state in Shenhu area, northern South China Sea.

Empirical relationship between P-wave and S-wave velocity

$$ V_{s} = V_{p} \left[ {\alpha (1 - \phi ) + \beta S} \right] $$

(17)

with α = V _s /V _p |_matrix, β = V _s /V _p |_hydrate.

Appendix 2: Exact Zoeppritz equations for P–P reflection coefficients

Exact Zeoppritz’s equation (Aki and Richards 2002)

The exact formulate for P–P reflection coefficients can be expressed as (Aki and Richards 2002)

$$ R_{pp} (\theta ) = {{\left[ {\left( {b\frac{{\cos i_{1} }}{{\alpha_{1} }} - c\frac{{\cos i_{2} }}{{\alpha_{2} }}} \right)F - \left( {a + d\frac{{\cos i_{1} }}{{\alpha_{1} }}\frac{{\cos j_{2} }}{{\beta_{2} }}} \right)Hp^{2} } \right]} \mathord{\left/ {\vphantom {{\left[ {\left( {b\frac{{\cos i_{1} }}{{\alpha_{1} }} - c\frac{{\cos i_{2} }}{{\alpha_{2} }}} \right)F - \left( {a + d\frac{{\cos i_{1} }}{{\alpha_{1} }}\frac{{\cos j_{2} }}{{\beta_{2} }}} \right)Hp^{2} } \right]} D}} \right. \kern-0pt} D}, $$

(18)

$$ \begin{aligned} a & = \rho_{2} (1 - 2\beta_{2}^{2} p^{2} ) - \rho_{1} (1 - 2\beta_{1}^{2} p^{2} ),\quad b = \rho_{2} (1 - 2\beta_{2}^{2} p^{2} ) + 2\rho_{1} \beta_{1}^{2} p^{2} , \\ c & = \rho_{1} (1 - 2\beta_{1}^{2} p^{2} ) + 2\rho_{2} \beta_{2}^{2} p^{2} ,\quad d = 2(\rho_{2} \beta_{2}^{2} - \rho_{1} \beta_{1}^{2} ). \\ \end{aligned} $$

(19)

$$ \begin{aligned} E & = b\frac{{\cos i_{1} }}{{\alpha_{1} }} + c\frac{{\cos i_{2} }}{{\alpha_{2} }},\quad F = b\frac{{\cos j_{1} }}{{\beta_{1} }} + c\frac{{\cos j_{2} }}{{\beta_{2} }}, \\ G & = a - d\frac{{\cos i_{1} }}{{\alpha_{1} }}\frac{{\cos j_{2} }}{{\beta_{2} }},\quad H = a - d\frac{{\cos i_{2} }}{{\alpha_{2} }}\frac{{\cos j_{1} }}{{\beta_{1} }}, \\ D & = EF + GHp^{2} . \\ \end{aligned} $$

(20)

where i ₁, i ₂, j ₁, and j ₂ are defined in terms of the ray trajectories, reflection and transmission angles of P-wave and S-wave, respectively. ρ ₁, α ₁, β ₁, ρ ₂, α ₂, and β ₂ are the density, P-wave and S-wave velocity for the upper and lower media of the interface.