P-waves and S-waves propagate with different velocities, and those velocities are related to the elastic properties of the rocks. P-waves propagate with P-wave velocity. P-wave velocity is affected by two elastic moduli, the Bulk modulus and the Shear modulus. In other words, the Bulk modulus only affects the P-wave. The relationship between P-wave velocity and S-wave velocity is a fundamental parameter in AVO analysis.
Impedance Ip ; Is is the product of velocity times density. It is a fundamental property of the rock. The seismic experiment is controlled by the velocity of the waves in the subsurface. Because of the large wavelength of seismic waves in oil exploration in the order of meters , the velocity and density that we can measure from the seismic data reflects some average property of the rock.
It is a combination of the parameters of the rock matrix the grains and the fluids that fill the pore spaces which are in the scale of millimeters. It states that the bulk density of the rock is the average of the density of its components. This is because the Bulk modulus of oil is lower than water and the Bulk modulus of gas is lower than oil. Therefore the velocity of oil is lower than that of water.
The diagram in Fig.
There is one graph for oil and another for gas showing the decrease of P-wave velocity with the increase in hydrocarbons. The dashed line in Fig. The Gassman equation is formulated in terms of Bulk modulus of the different components. This means that the Gassman equation can be viewed as an extension of the formula that defined P-wave velocity in order to incorporate the fluid effects.
The Gassman equation predicts that upon an introduction of a very small amount of gas, the bulk P-wave velocity will drop. Increasing the amount of gas thereafter has only a small effect on the velocity. See the dashed line in Fig. This phenomena demonstrates that AVO technique can be useful in detecting hydrocarbons, but is not indicative enough to detect the amount of gas. We expect to see AVO anomalies even for low gas saturations.
Note that when oil is present there is a somewhat different situation because there is not such a large drop in velocity. This is why it is more difficult to predict oil with AVO compared to gas although in some cases it is possible. This is due to the effect of density and is not related to Bulk modulus.
As gas saturation increases, density is reduced. Since density is in the denominator, it causes Vs to increase slightly. The value of Vp responds mainly to the change in porosity and less to the change in pore fluids. Vp-Vs and Density Relationships Rock physics experiments show that for most sandstones there is a linear relationship between P-wave velocity and S-wave velocity for brine saturation. This relationship may vary for different rocks and regions. The amplitude varies with offset because the reflection coefficient varies when the angle of incidence of the wave at the interface varies.
The basic phenomena is described as follows: When a P-wave arrives at an interface between two layers, some of the energy reflects back to the surface and some is transmitted.
The amount reflected and the amount transmitted depend on the contrast in parameters of the two layers. When the wave arrives at the interface at non-normal incidence, some of the P wave energy is converted to shear. These variations are governed by the contrast in P-wave velocity and S-wave velocity at the interface. As previously stated, when there is gas in the layer, Vp drops whereas Vs does not change.
In principle AVO analysis should measure amplitude variations with angle of incidence. However, amplitude is measured with offset because usually as offset increases, the angle of incidence increases. We also assume that amplitude of the seismic data is proportional to the reflection coefficients. The Zoeppritz equations are quite complex. This may be the reason why AVO is a relatively new technique. AVO theory evolved only after approximations to the Zoeppritz equations were developed.
Relative change in Vp — Vp 2. Equation 22 is an approximation to the Zoeppritz equations.
Rearranging Equation 22 we get as shown in Fig. Amplitude Versus Angle AVO analysis should actually be called AVA analysis - amplitude versus angle-because it deals with the analysis of reflection coefficients which vary according to the angle of incidence and not according to the offset. We assume that for small angles, the offset is small and for large angles the offset is large. The resulting amplitude on an offset gather is negative reflection of near offset becoming more negative at the far offset, which is manifested with an absolute value of amplitude increase at large offsets.
This is shown in Fig.
The reflection coefficient of normal incidence is negative and becomes more negative at a large offset. Here normal incidence reflectivity is close to zero and becomes negative at larger offsets. Class II anomalies occur when gas sands have similar impedances to the neighboring shales as shown in Fig. It has positive normal incidence reflectivity which becomes smaller at larger offsets as shown in Fig.
The bright spots were large amplitude reflections on stack sections which often coincided with gas. When you stack them you get high stack amplitudes. If there is a phase reversal along offset axis, then when you stack all offsets, the near offsets cancel the far offsets and the result is a very low amplitude reflection on the stack section - the dim spot. In this step we attempt to convert the seismic data to different reflectivities which have clear physical meanings. In AVO inversion we take the seismic pre-stack data, which represents the reflection coefficient as a function of angle of incidence and, using the Zoeppritz equations, we try to convert this data to reflectivity.
Reflectivity means relative change in a rock parameter. Given the velocity model and the source receiver location, we can determine the angle of incidence using a ray tracing procedure. Note that we convert each offset to its corresponding angle using the ray tracing procedure. Member Section Member List. Links Data. Rock Physics Theses. Professional Societies.
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