The Building Technology Of High-accuracy Wavefield Extrapola Tion Operators In Frequency Domain

With the deepening of oil and gas exploration and development, exploration tar-gets and conditions have become more and more complex, which includes the explo-ration and development of complex structure oil and gas reservoirs, lithological res-ervoirs and fractured reservoirs. Therefore, there is a higher requirement of seismic migration imaging accuracy.This paper based on the building technology of high-accuracy wave field extrap-olation operators in frequency domain raises two high-precision wave field continua-tion operators: PADE high-order approximate operator and rational fraction approxi-mation operator. We compared high-accuracy wave field extrapolation operators with general operator in frequency domain in methodology, accuracy analysis, computa-tional efficiency and selection of reference velocity. The results show that they have high imaging accuracy and efficiency, and they are of great value. This paper contains the following specific aspects:Frist, methodology: For non-uniform medium wave equation, in order to avoid k_z ( zi) =0, the normal approximation is Taylor expansion and PADE expansion. PADE high-order approximate operator uses a new PADE expansion method, which has a higher accuracy compared with the conventional PADE expansion. Rational fraction approximation operator uses fraction approximation at the first-order and parabolic approximation at the second-order. Coefficient is determined with the given lateral velocity contrast, which meets the minimum error dispersion. Than we de-compose k₀( zi ) / k_z ( zi )with1+a. Though deduction, one-way wave equation can be expressed as a split-step framework similar to SSF and be expressed as two-step ex-tension: Frequency shift and interpolation in time shift, which is greatly improved the computational efficiency.Second, accuracy analysis: From the relationship of lateral velocity contrast, transmission angle, the relative error and error analysis of the dispersion, we com-pared the accuracy of SSF operator, PADE high-order approximate operator and ra-tional fraction approximation operator. The results show that the imaging precision of PADE high-order approximate operator and the rational fraction approximation oper-ator have a great improver then SSF operator. PADE high-order approximate operator adapts medium of lateral velocity contrast. The rational fraction approximation oper-ator adapts medium of strong lateral velocity. From the imaging precision of SEG / EAGE model, we can see PADE high-order approximate operator, the rational frac-tion approximation operator can achieve a considerable imaging precision of migra-tion compared with the FFD operator.Third, computational efficiency: SSF operator needs two FFT in one extension, PADE high-order approximate operator and rational fraction approximation operator need three FFT and one interpolation. The FFD operator needs five FFT, which is in-cluded with two FFT and one FD. Under the same hardware, we test on the same model. the CPU time of PADE high-order approximate operator caused 31% compu-ting time more than SSF operator, and rational fraction approximation operator caused 44% computing time more than SSF operator.Fourth, selection of reference velocity: From the reference velocities is larger or smaller than true velocities, the paper studies the influence of SSF operator, PADE high-order approximate operator and the rational fraction approximation operator in reference velocities selection. The results show that whether the reference velocities is larger or smaller than true velocities, the imaging precision of PADE high-order ap-proximate operator and the rational fraction approximation operator have a great im-prover than SSF operator.Fifth, numerical simulation of the actual data: This paper uses high-precision wave field continuation operator to do numerical simulation of reef reservoir and J well. Simulation of seismic profile has a high degree of the original agreement. It de-scribes the geological model of the modeling and numerical simulation is accurate, it also proved accurate imaging capabilities of frequency domain wave field continua-tion operator in the actual data.