An improved Butterworth gravity downward continuation method driven by entropy-PSO dual optimization

doi:10.11947/j.AGCS.2025.20250137

Abstract

Abstract:

In response to the challenges of high-frequency noise amplification and instability in downward continuation solutions influenced by gravity, this paper proposes an intelligent continuation method that integrates iterative Butterworth filtering with particle swarm optimization (PSO). The method introduces an improved Butterworth function to reconstruct the downward continuation operator and employs an iterative compensation mechanism to correct spectrum residuals. A particle swarm dual-parameter collaborative optimization method based on information entropy theory is designed to achieve adaptive optimization of the filter's cutoff frequency and order. Furthermore, a fitness feedback-driven dynamic adjustment strategy for inertia weight is proposed to balance global exploration capability and the efficiency of searching for local precise solutions. Experimental results demonstrate that compared to the hybrid domain iterative Tikhonov regularization method and improved derivative iterative method, the proposed method maintains good stability in continuation accuracy under varying noise levels, providing an effective solution for processing marine and aerial gravity data.

Key words: downward extension, wave number domain, Butterworth filter, particle swarm optimization algorithm, iterative approach

CLC Number:

P223

Han WANG, Yun XIAO, Huaikui GUAN, Weixuan SUN. An improved Butterworth gravity downward continuation method driven by entropy-PSO dual optimization[J]. Acta Geodaetica et Cartographica Sinica, 2025, 54(9): 1620-1632.

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种群规模	运行时间/s	性能指标	种群规模	运行时间/s	性能指标
10	5.45	2636	80	13.76	527
30	7.33	1318	100	20.89	615
50	11.43	791	150	50.67	1054

学习因子	运行时间/s	性能指标	学习因子	运行时间	性能指标
0.5	12.45	2636	2	13.87	123
1	13.77	703	3	12.74	1582
1.5	13.96	878	5	12.32	791

Z/km	Max/mGal	Min/mGal	Mean/mGal	SD/mGal
0	1.121	0.002	0.058	0.135
1	0.503	0.009	0.006	0.105

噪声水平/（%）	最小熵值	截断频率	阶次
2	15.55	0.0027	19
5	15.76	0.0023	20
10	15.83	0.0021	32

延拓方法	迭代次数	噪声水平/（%）	残差最大值/mGal	残差最小值/mGal	Mean/mGal	SD/mGal	RE/（%）	RMSE/mGal	Time/s
方法1	100	2	0.006	－0.007	3.61×10^－6	0.002	7.834	0.011	7.56
		5	0.018	－0.017	1.24×10^－5	0.004	7.845	0.011	8.73
		10	0.032	－0.037	1.87×10^－5	0.007	7.889	0.011	8.89
方法2	100	2	0.050	－0.054	3.22×10^－5	0.008	7.643	0.011	5.53
		5	0.088	－0.085	5.42×10^－5	0.012	7.865	0.021	5.59
		10	0.120	－0.117	6.52×10^－5	0.013	8.356	0.027	6.97
方法3	100	2	0.010	－0.028	9.71×10^－6	0.002	5.452	0.008	15.76
		5	0.013	－0.029	1.50×10^－5	0.019	5.970	0.008	17.98
		10	0.019	－0.043	3.02×10^－5	0.020	6.251	0.010	16.53