Wavefront Curvature Correction Research Articles

Spaceborne/Stationary Bistatic SAR Imaging With TerraSAR-X as an Illuminator in Staring-Spotlight Mode

This paper addresses some important aspects for the spaceborne/stationary bistatic synthetic aperture radar (SAR) (SS-BiSAR) imaging with the transmitter, TerraSAR-X, operated in staring spotlight (ST) mode. With the large integration time reaching 7.5 s and the azimuth steering span reaching $\pm 2.2^{0}$ , several significant effects occur, including troposphere delay, precision phase and time synchronization, the curved orbit effect, azimuth spectrum aliasing problem, and efficient frequency domain focusing algorithm. To circumvent the main effects, corresponding solutions are proposed, including a precise synchronization strategy with troposphere delay correction based on the direct signal from the transmitter and a modified and integrative bistatic polar format algorithm (PFA). This paper covers the theoretical development, implementation, and analysis of the SS-BiSAR PFA based on 2-D fast Gaussian gridding nonuniform fast Fourier transform with wavefront curvature correction. Furthermore, the high-resolution ST-mode SS-BiSAR image processed by the proposed algorithm is acquired, and the differences of scattering behaviors between monostatic and bistatic SAR images are analyzed in detail.

Analytical wavefront curvature correction to plane‐wave reflection coefficients for a weak‐contrast interface

ABSTRACTMost amplitude versus offset (AVO) analysis and inversion techniques are based on the Zoeppritz equations for plane‐wave reflection coefficients or their approximations. Real seismic surveys use localized sources that produce spherical waves, rather than plane waves. In the far‐field, the AVO response for a spherical wave reflected from a plane interface can be well approximated by a plane‐wave response. However this approximation breaks down in the vicinity of the critical angle. Conventional AVO analysis ignores this problem and always utilizes the plane‐wave response. This approach is sufficiently accurate as long as the angles of incidence are much smaller than the critical angle. Such moderate angles are more than sufficient for the standard estimation of the AVO intercept and gradient. However, when independent estimation of the formation density is required, it may be important to use large incidence angles close to the critical angle, where spherical wave effects become important. For the amplitude of a spherical wave reflected from a plane fluid‐fluid interface, an analytical approximation is known, which provides a correction to the plane‐wave reflection coefficients for all angles. For the amplitude of a spherical wave reflected from a solid/solid interface, we propose a formula that combines this analytical approximation with the linearized plane‐wave AVO equation. The proposed approximation shows reasonable agreement with numerical simulations for a range of frequencies. Using this solution, we constructed a two‐layer three‐parameter least‐squares inversion algorithm. Application of this algorithm to synthetic data for a single plane interface shows an improvement compared to the use of plane‐wave reflection coefficients.

Wavefront curvature correction in one stationary bistatic SAR image focused via PFA

The wavefront curvature error in one stationary bistatic synthetic aperture radar (SAR) image focused via the polar format algorithm (PFA) is analysed and a space-variant filtering method for wavefront curvature correction is proposed. The correction method presented, extends the focused scene size when using the bistatic PFA effectively. Point target simulation validates the filtering method.

On: “Reflection of spherical seismic waves in elastic layered media” by P. M. Krail and H. Brysk (GEOPHYSICS, June 1983, p. 655–664).

This paper develops the wavefront curvature correction for the plane‐wave Zoeppritz coefficients. The authors imply that seismic reflection amplitude versus angle of incidence does not enhance detection of pore‐fluid‐caused amplitude anomalies (“bright spots”) as proposed in the scientific literature by Backus et al (1982), Ostrander (1982), and Stolt (1981). We believe certain parts of this discussion are incorrect. Points of disagreement are as follows. (1) The model parameters associated with Figure 6 (especially the values for the brine‐filled sandstone) are unrealistic and are not taken from Domenico (1977) as the authors have indicated. (2) The conclusion “… it is clear that the CMP gather by itself fails as a gas indicator” based on Figure 6 is incorrect. (3) A reflecting spherical wave having a radius of curvature equal to approximately one‐half wavelength (kr = 3) requires a shallow reflector unreasonable for petroleum exploration.

On the temporal coherence loss of strongly scintillating signals

In this paper, we have reprocessed a set of previously published intensity coherence time data to correct for wave front curvature. The spherical wave correction decreases the coherence time for a simple plane wave. Under conditions of strong scatter, theory predicts a simple power law relationship between the intensity coherence time and the phase turbulent strength. In the theory the power law index is simply related to the phase spectral index, which is usually assumed to be constant. Previously, this theory had been applied to test the consistency of the results. Evidence has recently come to light, however, that both the phase and in situ spectral indices vary systematically with changing perturbation strength. By accommodating this variation as well as the wave front curvature correction, we were able to greatly improve the theoretical fit to the intensity coherence time data.