Due to the sparsity of space probes, it is still not clear on how the magnetic structure of the magnetotail looks like and how it evolves when the interplanetary magnetic field (IMF) directs northward. This simulation study uses two different global magnetosphere magnetohydrodynamics (MHD) models to simulate two northward IMF events and study the evolution of the magnetotail. Both models show that the magnetotail may form a structure that is composed of a dawnside tail lobe and a duskside tail lobe, under northward IMF conditions with significant By, instead of a northern tail lobe and a southern tail lobe under southward IMF conditions. In this magnetic configuration, a tail lobe extends a domain from northern (southern) cusp to southern (northern) IMF. The larger the magnitude of IMF clock angle, the longer and wider the magnetotail. Such magnetic configuration suggests that magnetotail reconnection is possible to occur when the dawnside tail lobe contacts with the duskside tail lobe and thus a substorm is also possible to occur under northward IMF conditions with significant By.

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We analyzed the numerical forward methods in the Fourier domain for potential fields. Existing Fourier-domain forward methods applied the standard fast Fourier transform (FFT) algorithm to inverse transform a conjugate symmetrical spectrum into a real field. It had significant speed advantages over space-domain forward methods but suffered from problems including aliasing, imposed periodicity, and edge effect. Usually, grid expansion was needed to reduce these errors, which was equivalent to the numerical evaluation of the oscillatory Fourier integral using the trapezoidal rule with smaller steps. We tested a high-precision Fourier-domain forward method based on a combined use of shift-sampling technique and Gaussian quadrature theory. The trapezoidal rule applied by the standard FFT algorithm to evaluate the continuous Fourier transform was modified by introducing a shift parameter [Formula: see text]. By choosing optimum values of [Formula: see text] as Gaussian quadrature nodes, we developed a Gauss-FFT method for Fourier forward modeling of potential fields. No grid expansion was needed, the sources can be set near the boundary of the fields or even go beyond the boundary. The Gauss-FFT method converged to the space-domain solution much faster than the standard FFT method with grid expansion. Forward modeling results almost identical to space-domain ones can be obtained in less time. Numerical examples, of both simple and complex 2D and 3D source forward modeling, revealed the reliability and adaptability of the method.

Most of the disturbances in space environment can be explained under the framework theory of open magnetosphere and Dungey cycle (Dungey, 1961). This theory is sketched in Figure 1 which is similar to Dungey's original figure. Under southward IMF (SIMF) conditions, magnetic reconnection occurs first at the nose of the magnetopause (Figure 1c) where IMF field lines interconnect with dayside geomagnetic closed field lines. Such reconnection creates a northern set and a southern set of open field lines that consequently convect toward nightside and form into a north-south tail lobe magnetotail configuration (Figures 1a and 1b). Then the northern open field lines interconnect with the southern open field lines in the tail (Figure 1d), creating new closed field lines and new IMF field lines. These two magnetic reconnection processes thus form a Dungey cycle, during which the topology of involved geomagnetic field lines changes from closed to open in dayside and then changes back from open to closed in nightside. This cycle causes solar wind mass and energy to enter into the magnetosphere and the ionosphere, resulting in disturbances such as magnetic storm, substorm, aurora, and so on.

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Prismatic bodies with variable density contrasts are very useful in modeling and inversion of gravity anomalies for sedimentary basins, in which some simple mathematical functions offer better approximations for the density-depth relationship of the basin fill than a constant density model. We have explored Fourier-domain modeling of vector and tensor gravity anomalies due to 2D and 3D prismatic bodies following a wide class of variable density functions. We placed the emphasis on general polynomial models because they provided a flexible way to approximate arbitrary density functions. The recently proposed Gauss-fast Fourier transform method was applied to improve the accuracy of inverse Fourier transform. The numerical performance of the presented method was examined by comparing with space-domain analytical, seminumerical, or completely numerical solutions. Singularity and numerical stability of the algorithm were also analyzed with ranges of numerical stability for polynomial density models of different orders specified. Truncation errors of Fourier forward methods were estimated quantitatively using relevant model parameters, and the behavior was observed through theoretical analysis and model tests. Synthetic models, of 2D and 3D prisms with variable density contrasts, found the accuracy, efficiency, and flexibility of the method. We also interpreted a real data example of the gravity profile across the San Jacinto graben.

Parker's method (Parker, 1973), initially introduced by the author for the rapid calculation of gravitational and magnetic anomalies, of 2D and 3D complexly layered models based on the FFT algorithm, is by no doubt one of the most widely applied algorithms in potential field data processing and interpretation (Nabighian, Ander, et al., 2005;. By raising the interface functions of a layered model to the E n th power and transforming into Fourier series using the FFT algorithm, potential anomalies on a horizontal plane above the layered model can be computed much more efficiently than using space-domain numerical integration techniques. The method has been proved particularly useful in solving forward problems such as gravimetric terrain correction and isostatic correction (

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