Inversion of elastic parameters based on ray-path elastic impedance theory and its application in the prediction of tight sand reservoirs

Abstract

Compared with elastic impedance (EI), ray-path elastic impedance (REI) reduces the requirement for the Vp/Vs velocity ratio to be used as a constant parameter, leading to calculations of greater precision. Based on the REI formula, the analytic calculation of elastic parameters is derived from the objective function. It is not necessary to calculate the elastic parameter by means of iteration. As a result, the inversion of elastic parameters, in theory, is more precise and efficient. The AVO curve of the typical gas reservoir interface in the LD region of the Ordos Basin shows that the relative error of the reflection coefficient calculated by using REI is evidently smaller than that of the Shuey approximation formula. When the angle of incidence is 30°, the REI error is only 3%, whereas the error from the Shuey approximation formula is 13.2%. Therefore, the REI approach can better reflect the features of tight gas reservoirs. The example from the tight sand gas reservoir in the LD region shows that the result matches extremely well with the gas testing results of known wells. Introduction As a generalization of AI, elastic impedance (EI) as defined by Connolly (1999) takes into account the effect of P-wave reflectivity versus incident angle in order to solve the post-stack seismic trace inversion problem at large offsets. When the EI function is used in seismic trace inversion, the ratio of S-wave to P-wave velocities, γ=β/α, is assumed to be constant, and the seismic data are replaced with a common angle stack or an AVA fitting stack. Ray-path elastic impedance (REI; Wang, 2003; Ma and Morozov, 2004) eliminates the requirement for the Vp/Vs velocity ratio in the EI formula to be a constant variable. It is more precise than the EI formula, and better matches real-world scenarios. Pan et al. (2003) analyzed and compared some EI formulas, and suggest the GEI still has very high precision, even for the special case of REI. Wang (2003) was the first to use the REI formula, influencing many scholars to study similar approaches. Zhang et al. (2011) constructed a new parameter, which is the normalized EI with the strong points of both EI and REI, and used the estimated P-wave impedance. Liu et al. (2011) omitted the high-order term in the REI formula and derived a new REI formula as the function of the Pand Swave impedance. When the incidence angle is small, the precision is similar to that of the REI formula. However, when the incidence angle is large, the error is also large. As a result, it is only suitable for small incidence angles. Based on the REI formula, the analytic calculation formula of elastic parameters was derived from the objective function by Duan et al. (2013). As a result, the elastic parameter calculation is more precise and efficient, and the results match very closely with the gas testing results from wells in the LD region of the Ordos Basin. Definition of ray-path elastic impedance REI is defined along the ray path (Wang, 2003; Ma and Morozov, 2004) at the interface. The formula does not assume a constant incidence angle at each interface. As a result, it is more precise than the EI formula and is more representative of real-world scenarios. ) 2) 2(k 2 2 2 sin 1 cos + ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ − = i i i i i i i REI θ α β θ α ρ (1) Inversion of ray-path elastic impedance parameters REI includes not only acoustic parameters (e.g., P-wave and S-wave velocities), but also the Vp/ Vs ratio, and so on. This information is helpful in constraining fluids and lithologies. In the situation of three known elastic impedances of different angles: REI(θ1), REI(θ2), and REI(θ3), we can deduce an object Function (2) from Equation (1):