Velocity and AVO analysis for the investigation of gas hydrate along a profile in the western continental margin of India

Abstract

The occurrence of gas hydrate has been inferred from the presence of Bottom-Simulating Reflectors (BSRs) along the western continental margin of India. In this paper, we assess the spatial and vertical distribution of gas hydrates by analyzing the interval velocities and Amplitude Versus Offset (AVO) responses obtained from multi-channel seismics (MCSs). The hydrate cements the grains of the host sediment, thereby increasing its velocity, whereas the free gas below the base of hydrate stability zone decreases the interval velocity. Conventionally, velocities are obtained from the semblance analysis on the Common Mid-Point (CMP) gathers. Here, we used wave-equation datuming to remove the effect of the water column before the velocity analysis. We show that the interval velocities obtained in this fashion are more stable than those computed from the conventional semblance analysis. The initial velocity model thus obtained is updated using the tomographic velocity analysis to account for lateral heterogeneity. The resultant interval velocity model shows large lateral velocity variations in the hydrate layer and some low velocity zones associated with free gas at the location of structural traps. The reflection from the base of the gas layer is also visible in the stacked seismic data. Vertical variation in hydrate distribution is assessed by analyzing the AVO response at selected locations. AVO analysis is carried out after applying true amplitude processing. The average amplitudes of BSRs are almost constant with offset, suggesting a fluid expulsion model for hydrate formation. In such a model, the hydrate concentrations are gradational with maxima occurring at the base of hydrate stability zone.

Appendix: interval velocity resolution of the target layer

The error of the RMS velocity obtained from the conventional velocity depends on the semblance function (Eq. 2). Let’s consider the semblance function for different depths of the overburden assuming a constant offset-to-depth ratio and for a fixed number of traces. The semblance is the measure of coherency along the hyperbolic trajectory defined by the trial velocity and the zero-offset traveltime. If we assume that the wavelet does not change as the wavefield is propagated downward then the semblance depends on the traveltime difference between the hyperbolic trajectory of the RMS velocity and the trial velocity.

Let’s consider the traveltime difference between the RMS velocity of the target layer (V _rms2) and the overburden velocity V _rms1 at the zero-offset traveltime of the target layer (t ₀),

$$ \Delta t = t_0 \left( \sqrt{1+\frac{x^2}{t_0^2 V_{rms2}^2}} - \sqrt{1+\frac{x^2}{t_0^2 V_{rms1}^2}} \right). $$

(5)

The RMS velocity of the target layer can be expressed in terms of the overburden velocity (V _rms1) and the interval target layer velocity (V _int ),

$$ V_{rms2} = \sqrt \frac{V_{rms1}^2 t_1 + V_{int}^2 t_2}{t_1+t_2}, $$

(6)

where t _1,2 are the zero-offset traveltimes of the overburden and the target layer respectively. Assuming z ≈ V _rms1 t ₁/2, the ratio of the zero-offset traveltimes can be expressed as,

$$ \frac{t_1}{t_2}\approx \frac{z V_{int}}{h V_{rms1}}, $$

(7)

where z and h represent the thicknesses of the overburden and the target layer respectively.

The interval velocity can be represented as V _int =  V _rms1 +  ΔV and under the assumption of small velocity perturbation ($\frac{\Delta V}{V_{rms1}} \ll 1$), Eq. (6) can be simplified as,

$$ V_{rms2} = V_{rms1} \sqrt{\left[ \frac{1+ \frac{t_2}{t_1} + \frac{2 \Delta V t_2}{V_{rms1} t_1}}{1+ \frac{t_2}{t_1}}\right]} $$

(8)

$$ \approx V_{rms1} \left[ 1 + \frac{\Delta V h}{V_{rms1} (z+h)}\right] $$

(9)

Similarly, the zero-offset traveltime can be approximated as,

$$ t_0 \approx 2 \left[ \frac{z}{V_{rms1}} + \frac{h}{V_{rms1}+\Delta V} \right] $$

(10)

$$ \approx 2 \left[ \frac{z+h}{V_{rms1}} - \frac{h \Delta V} {V_{rms1}^2} \right]. $$

(11)

Substituting the approximate value of the RMS velocity from Eq. (9) into Eq. (5) and further simplifying,

$$ \Delta t \approx \frac{\Delta V h}{V_{rms1}^2 (z+h)} \frac{x^2} {\sqrt{t_0^2 V_{rms1}^2 + x^2}}. $$

(12)

Substituting the approximate value of the zero-offset traveltime from Eq. (11) into Eq. (12) and further simplifying,

$$ \Delta t \approx \frac{\Delta V h}{V_{rms1}^2} \frac{x^2}{2 (z+h)^2} \frac{1}{\sqrt{1+\frac{x^2}{2 (z+h)^2}}}. $$

(13)

Since the offset-to-depth ratio of the target layer [x/(z + h)] is assumed to be a constant, the traveltime difference is independent of the depth. As a result, all the semblance curve shown in Figure 1 passes through a constant given by Eq. (15). As discussed in the text, the above property can be used to approximate the semblance curve using a Gaussian function.

In the presence of random noise, the conventional semblance analysis will yield a range of velocities. Let’s say that all the velocities which lie within the p % of the maximum amplitude are acceptable. Then the error in estimating the RMS velocity can be quantified from Eq. (3),

$$ p = exp [-K^2 \sigma_{V_{rms}}^2], $$

(14)

where the difference between the RMS velocity and the velocity corresponding to the p % of the maximum semblance value is taken as the standard deviation of the RMS velocity (σ _{V rms} ). The constant C can also be expressed as,

$$ C \approx \frac{M (M-1)}{2} exp [-K^2 (V_{rms2}-V_{rms1})^2]. $$

(15)

Combining Eqs. (14) and (15), the σ _rms can be expressed as,

$$ \begin{aligned} \sigma_{V_{rms}} &\approx K^{\prime} (V_{rms2}-V_{rms1}), \\ K^{\prime} &= \sqrt{\frac{\ln p}{\ln \frac{2 C}{M (M-1)}}}. \end{aligned} $$

(16)

Substituting the approximate value of the RMS velocity from Eq. (9) into Eq. (16), the simplified expression for the standard deviation is obtained,

$$ \sigma_{V_{rms}} \approx K^{\prime} \frac{\Delta V h}{(h+z)} $$

(17)

The error in the interval velocity can be obtained by substituting Eq. (17) into (1),

$$ \sigma_{V_{int}} (z)\approx K^{\prime}\frac{\Delta V (\sqrt{2} z +h)}{(z+h)}. $$

(18)