Spectral analysis of vector magnetic field profiles

Abstract

Abstract. We investigate the power spectra and cross spectra derived from the three components of the vector magnetic field measured on a straight horizontal path above a statistically stationary source. All of these spectra, which can be estimated from the recorded time series, are related to a single two-dimensional power spectral density via integrals that run in the across-track direction in the wavenumber domain. Thus the measured spectra must obey a number of strong constraints: for example, the sum of the two power spectral densities of the two horizontal field components equals the power spectral density of the vertical component at every wavenumber and the phase spectrum between the vertical and along-track components is always n/2. These constraints provide powerful checks on the quality of the measured data; if they are violated, measurement or environmental noise should be suspected. The noise due to errors of orientation has a clear characteristic; both the power and phase spectra of the components differ from those of crustal signals, which makes orientation noise easy to detect and to quantify. The spectra of the crustal signals can be inverted to obtain information about the cross-track structure of the field. We illustrate these ideas using a high-altitude Project Magnet profile flown in the southeastern Pacific Ocean.

Equatorial Pacific magnetic anomalies identified from vector aeromagnetic data

“…Additional tests of our interpretation of these profiles as recorders of seafloor-spreading anomalies can be obtained from cross-spectra (Parker & O'Brien 1997). We find that the mean coherence between the X and Z components over wavenumber band A (0.0064 < k x < 0.0541 km −1 ), the wavenumber band over which the power sum rule holds, is 0.82 ± 0.038 (Fig.…”

“…Parker & O'Brien (1997) developed a method of spectral analysis of residual vector magnetic profiles to determine the noise content of the data and to extract, if present, the signal of the crustal magnetic fields. Parker & O'Brien (1997) developed a method of spectral analysis of residual vector magnetic profiles to determine the noise content of the data and to extract, if present, the signal of the crustal magnetic fields.…”

“…3a) is, to a first approximation, a downward-trending straight line with slope −4π h, where h is the height of the magnetometer above the source (Spector & Grant 1970;Parker & O'Brien 1997). 3a) is, to a first approximation, a downward-trending straight line with slope −4π h, where h is the height of the magnetometer above the source (Spector & Grant 1970;Parker & O'Brien 1997).…”

“…A test of the self-consistency of the data is whether the PSD of the residual vertical component equals the sum of the PSDs of the two residual horizontal components at every wavenumber for a vector magnetic profile along a horizontal straight line above a statistically stationary source (Parker & O'Brien 1997). We applied this 'power sum rule' to the residual components of profile 0550-047 and found excellent agreement for wavenumbers between 0.0064 and 0.0541 km −1 , corresponding to wavelengths between 18.5 and 156.3 km (Fig.…”

Characteristics of crustal magnetic structures in the Tsushima (Ulleung) and Japan Basins from vector magnetic anomalies

“…To evaluate whether the observed anomalies are generated by 2-D magnetic structure, we adopted the method suggested by Isezaki (1986b). This method is based on the characteristics of a magnetic field generated by 2-D magnetic structure: the amplitude of the horizontal component parallel to the strike is zero, and the horizontal component normal to the strike and the vertical component have a constant phase difference of π/2 (Blakely et al, 1973;Isezaki, 1986b;Parker and O'Brien, 1997). We first converted X and Y components to two horizontal components (named H 1 and H 2) by minimizing root mean square (RMS) of H 2.…”