P-SV Wave Prestack Inversion Based on Hybrid Algorithm

doi:10.19596/j.cnki.1001-246x.8730

Abstract

Abstract:

The simulated annealing method is introduced into genetic algorithm to form a hybrid algorithm, which can overcome the defects of genetic algorithm in optimization and avoid the premature phenomenon. According to the approximate formula of reflection coefficient of P-SV wave, the objective function of anisotropy parameter inversion is established. The anisotropy parameter inversion of TTI medium is achieved by using single algorithm and mixed algorithm respectively. The results show that the mixed algorithm inversion accuracy is higher and the process is more stable. Furthermore, Gaussian white noise with a signal-to-noise ratio of 5 is added to the data of the theoretical model to test the anti-noise property. The error of the inversion results is small and the anti-noise ability is good. Finally, the anisotropic parameter inversion of the modified Hess model is carried out, and the inversion profile is obtained, which is in good agreement with the original profile, and the effectiveness of the hybrid algorithm is verified. In addition, the research area is selected to perform inversion test on the actual data. The inversion results are good and the accuracy is high, which verifies the effectiveness of the hybrid algorithm in practical application.

Key words: genetic algorithm, simulated annealing method, hybrid algorithm, converted wave, prestack inversion

CLC Number:

P631

Qin LI, Min ZHANG, Ying XU. P-SV Wave Prestack Inversion Based on Hybrid Algorithm[J]. Chinese Journal of Computational Physics, 2024, 41(3): 380-391.

Figures/Tables 18

Fig.1 Schematic of simulated annealing algorithm searching for optimal solution

Table 1 Model parameters of three sets of two-layer media

介质结构	ε	δ	γ	θ₂	φ
ISO/TTI	0/0.2	0/0.1	0/0.11	0/60	0/30
TTI/ISO	0.2/0	0.1/0	0.11/0	60/0	30/0
TTI/TTI	0.1/0.2	0.1/0.1	0.15/0.11	45/60	30/45

Fig.2 Approximate reflection coefficients of the medium models

Table 2 Anisotropic parameters of two-layer medium model

介质结构	ε	δ	γ	θ₂	φ
	0.1~0.4	0.1	0.11
ISO/TTI	0.2	0.05~0.2	0.11	0/60	0/30
	0.2	0.1	0.06~0.21
	0.1~0.4	0.1	0.11
TTI/ISO	0.2	0.05~0.2	0.11	60/0	30/0
	0.2	0.1	0.06~0.21
	0.1~0.4	0.1	0.11
TTI/TTI	0.2	0.05~0.2	0.11	45/60	30/45
	0.2	0.1	0.06~0.21

Fig.3 Effects of anisotropic parameters ε, δ, γ on RPS in three models (a) ISO/TTI(ε); (b) ISO/TTI(δ); (c) ISO/TTI(γ); (d) TTI/ISO(ε); (e) TTI/ISO(δ); (f) TTI/ISO(γ); (g) TTI/TTI(ε); (h) TTI/TTI(δ); (i) TTI/TTI(γ)

Table 3 ISO/TTI media model parameters

介质	V_P/(m·s^-1)	V_S/(m·s^-1)	ρ/(g·cm^-3)	ε	δ	γ	θ₂	φ
ISO	3 000	1 750	2.4	0	0	0	0	0
TTI	2 900	1 650	2.6	0.43	0.35	0.11	60	30

Fig.4 TTI medium P-SV wave inversion by single algorithm with ε, δ, γ (a) GA (ε); (b) GA (δ); (c) GA (γ); (d) SA (ε); (e) SA (δ); (f) SA (γ)

Table 4 Anisotropy parameter inversion results in TTI medium (GA, SA)

反演参数	GA			SA
反演参数	ε	δ	γ	ε	δ	γ
理论值	0.430	0.350	0.110	0.430	0.350	0.110
反演值	0.432	0.339	0.106	0.430 7	0.351 4	0.112
相对误差/%	0.469	3.143	3.290	0.166	0.408	1.950

Fig.5 TTI medium P-SV wave inversion by hybrid algorithm with ε, δ, γ (a) HGA(ε); (b) HGA(δ); (c)HGA(γ)

Table 5 Anisotropy parameter inversion results in TTI medium (HGA)

	ε	δ	γ
理论值	0.430 0	0.350 0	0.110 0
反演值	0.429 6	0.350 6	0.110 6
相对误差/%	0.080 9	0.185 7	0.536 0

Fig.6 Corner track set of white Gaussian noise with signal to noise ratio of 5 dB

Table 6 Inversion results of anisotropy parameters in TTI media with noise

	ε	δ	γ
理论值	0.430	0.350	0.110
反演值	0.452	0.313	0.119
相对误差/%	5.116	10.571	8.181

Table 7 With N = 50 or 100, T = 100, inversion results of genetic algorithm, simulated annealing algorithm and hybrid genetic algorithm

反演参数	GA		SA		HGA
反演参数	N=50	N=100	N=50	N=100	N=50	N=100
A/%	1.132	0.233	3.257	4.298	2.182	0.573
B/%	2.571	1.577	0.637	1.566	1.595	1.771
C/%	4.590	1.682	8.496	3.980	3.612	1.305

Table 8 With T = 50 or 100, N=80, inversion results of genetic algorithm, simulated annealing algorithm and hybrid genetic algorithm

反演参数	GA		SA		HGA
反演参数	T=50	T=150	T=50	T=150	T=50	T=150
A/%	0.264	0.256	3.488	4.235	0.343	0.003
B/%	1.103	0.409	0.192	1.514	1.218	1.761
C/%	0.349	3.490	2.410	2.563	2.727	0.666

Fig.7 Hess-TTI medium model and inversion region

Fig.8 Profile of anisotropy parameters of the Hess-TTI model (Color bar on the right represents interval of anisotropy parameter.) (a) ε original profile; (b) δ original profile; (c) γ original profile; (d) ε inversion profile; (e) δ inversion profile; (f) γ inversion profile

Fig.9 Selected study block data (a) wave impedance inversion profile; (b) synthetic corner track set

Fig.10 Anisotropy parameter inversion profile of actual data (Color bar on the right represents interval of anisotropic parameter.) (a) ε inversion profile; (b) δ inversion profile; (c) γ inversion profile

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