Interpretation of 2D magnetic anomalies using wavelet transform

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Determination of the boundaries of anomaly-forming bodies (deep sources) is an important step in interpreting potential field anomalies during geophysical research. In this paper, a method based on continuous wavelet analysis of magnetic profiles is proposed to solve this problem. The connection between the parameters of simple bodies and the properties of the wavelet transformation of the field created by these bodies is shown. A technique has been developed for determining the boundaries of blocks of the magnetically active layer. The proposed method was tested on model data of the simplest single bodies and on a spreading model. The high resolution of the method is shown, which makes it possible to determine the boundaries of blocks of the spreading model with an accuracy of up to 400 m. The method was applied to a real magnetic profile crossing a typical oceanic structure: the mid-ocean Reykjanes Ridge. The results obtained confirm that the proposed method has a higher resolution compared to the analytical signal and allows the identification of narrow blocks. To clarify the boundaries of these blocks, it is planned to develop a methodology based on the modeling results.

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作者简介

S. Merkuriev

Pushkov Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation, Russian Academy of Sciences

编辑信件的主要联系方式.
Email: sam_hg@hotmail.com

St. Petersburg Branch

俄罗斯联邦, St. Petersburg

S. Ivanov

Pushkov Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation, Russian Academy of Sciences

Email: sergei.a.ivanov@mail.ru

St. Petersburg Branch

俄罗斯联邦, St. Petersburg

I. Demina

Pushkov Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation, Russian Academy of Sciences

Email: dim@izmiran.spb.ru

St. Petersburg Branch

俄罗斯联邦, St. Petersburg

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2. Fig. 1. Geometry and parameters of 2D geophysical models. (a) - quadrant, vertically and horizontally semi-infinite body; (b) - layer, horizontally semi-infinite layer; (c) - dike; (d) - block.

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3. Fig. 2. Wavelet spectra of the quadrant field for three Gaussian functions. (a) - m = 1, (b) - m = 2 and (c) - m = 3, respectively. Continuous lines are isolines of wavelet spectrum coefficients, dots are positions of local maxima at fixed scale.

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4. Fig. 3. Errors of determining the depth and thickness of the reservoir by the 3rd derivative. (a) - depth determination error, symbols show the dependence on thickness h in km: h = 0. 5 - ●, h = 1 - ◆, h = 2 - ▲, h = 3 - ”, h = 4 - □, h = 6 - ○, h = 7 - △, h = 8 - □; (b) - thickness determination error, symbols show dependence on z1 in km: z1 = 1 - ●, z1 = 2 - ▲, z1 = 4 -◆; (c) - relative thickness determination error in dimensionless units.

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5. Fig. 4. Error in determining the depth and half-width of the dike from the extrema of the 3rd derivative. (a) - error of z1 determination; (b) - error of half-width determination; (c) - the same as (a) after correction; (d) - the same as (b) after correction; symbols on (a) and (c) correspond to different half-widths, on (b) and (d) - dike depths.

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6. Fig. 5.Comparison of interpretation capabilities of the wavelet method and the analytical signal method.The solid line shows the theoretical dependence for the wavelet method, the dotted line - for the analytical signal, triangles - values obtained by the extrema of the 1st derivative, circles - the same by the extrema of the 3rd derivative.

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7. Fig. 6.The field created by the structure of 3 blocks, its derivatives and the result of interpretation.Bold black line shows the field, long dashed line - 1st derivative, short dashed line - 2nd derivative, solid gray line - 3rd derivative; (a) - given structure, (b) - initial estimation, (c) - after correction.

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8. Fig. 7.Comparison of two methods for determining the anomaly source boundaries for the spreading model.(a) -magnetic anomalies calculated from the spreading model, dark rectangles show the blocks of direct polarity, alphanumeric symbols - chron boundaries; (b) - analytical signal; (c) - comparison of the position of chron boundaries: segments with ▲ are the sought boundaries of the bodies, segments with ▼ are those found by wavelet analysis, segments with ◆ are those found by analytical signal; (d) - wavelet transform, isolines show the modulus of wavelet coefficients, dashed line - local extrema.

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9. Fig. 8.Magnetometer profile crossing the Reykjanes Ridge in the North Atlantic. (a) - bottom relief; (b) - magnetic anomalies measured on the KNOR24 profile, symbols - chrons; numbers - numbers of the main anomalies; (c) - shadow map of the bottom relief with the positions of isochrons and observed magnetic anomalies on the KNOR24 magnetometer profile, symbols are the same as in (b).

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10. Fig. 9. Comparison of two methods of determining the boundaries of magnetic anomaly sources for the KNOR24 profile. (a) - magnetic anomalies observed on the profile, dark rectangles show blocks of direct polarity, alphanumeric symbols - chron boundaries; (b) - analytical signal; (c) - comparison of the chron boundary positions; (d) - wavelet transformation.

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