Support minimized inversion of acoustic and elastic wave scattering

Inversion of limited data is common in many areas of NDE such as X-ray Computed Tomography (CT), Ultrasonic and eddy current flaw characterization and imaging;In many applications, it is common to have a bias toward a solution with minimum (L[superscript]2)[superscript]2 norm without any physical justification. When it is a priori known that objects are compact as, say, with cracks and voids, by choosing Minimum Support functional instead of the minimum (L[superscript]2)[superscript]2 norm, an image can be obtained that is equally in agreement with the available data, while it is more consistent with what is most probably seen in the real world;We have utilized a minimum support functional to find a solution with the smallest volume. This inversion algorithm is most successful in reconstructing objects that are compact like voids and cracks. To verify this idea, we first performed a variational nonlinear inversion of acoustic backscatter data using minimum support objective function. A full nonlinear forward model was used to accurately study the effectiveness of the minimized support inversion without error due to the linear (Born) approximation. After successful inversions using a full nonlinear forward model, a linearized acoustic inversion was developed to increase speed and efficiency in imaging process. The results indicate that by using minimum support functional, we can accurately size and characterize voids and/or cracks which otherwise might be uncharacterizable;An extremely important feature of support minimized inversion is its ability to compensate for unknown absolute phase (zero-of-time). Zero-of-time ambiguity is a serious problem in the inversion of the pulse-echo data. The minimum support inversion was successfully used for the inversion of acoustic backscatter data due to compact scatterers without the knowledge of the zero-of-time;The main drawback to this type of inversion is its computer intensiveness. In order to make this type of constrained inversion available for common use, work needs to be performed in three areas: (1) exploitation of state-of-the-art parallel computation, (2) improvement of theoretical formulation of the scattering process for better computation efficiency, and (3) development of better methods for guiding the non-linear inversion. (Abstract shortened by UMI.

Support minimized nonlinear acoustic inversion with absolute phase error correction

The predominant factors which prohibit the inversion of acoustic scattering data for the purposes of flaw characterization are 1) limited angular access to the flaw, 2) limited temporal frequency signal bandwidth, and 3) lack of absolute phase information between individual measurements (zero of time problem). An additional complication which impedes the data inversion is the non-linear dependence of the scattering data on the scattering object. This problem must be handled by either linearizing the problem or by applying an iterative procedure which may have questionable convergence properties. An approach to data inversion is presented here which shows potential in overcoming the aforementioned difficulties. This approach compensates for the lack of data by constructing a solution which yields simulated scattering consistent with the measured data, while simultaneously minimizing a functional measure of the support (i.e. volume) of the flaw. Such an approach to limited data inversion has proven effective in limited view X-ray CT applications when reconstructing discontinuous boundary flaws such as cracks and inclusions [1, 2, 3]. The application presented here is by-and-large analogous to the X-ray CT application, except for the additional complication of the lack of absolute phase between measurements. This zero-of-time problem is handled here by treating the absolute phase of each measurement as a variable in the minimization of the flaw support

SHARAD radar sounding of the Vastitas Borealis Formation in Amazonis Planitia

Amazonis Planitia has undergone alternating episodes of sedimentary and volcanic infilling, forming an interleaved sequence with an upper surface that is very smooth at the kilometer scale. Earlier work interprets the near-surface materials as either young, rough lava flows or ice-rich sediment layers, overlying a basement comprising the Vastitas Borealis Formation and earlier Hesperian plains. Sounding radar profiles across Amazonis Planitia from the Shallow Radar (SHARAD) instrument on the Mars Reconnaissance Orbiter reveal a subsurface dielectric interface that increases in depth toward the north along most orbital tracks. The maximum depth of detection is 100–170 m, depending upon the real dielectric permittivity of the materials, but the interface may persist at greater depth to the north if the reflected energy is attenuated below the SHARAD noise floor. The dielectric horizon likely marks the boundary between sedimentary material of the Vastitas Borealis Formation and underlying Hesperian volcanic plains. The SHARAD-detected interface follows the surface topography across at least one of the large wrinkle ridges in north central Amazonis Planitia. This conformality suggests that Vastitas Borealis sediments, at least in this region, were emplaced prior to compressional tectonic deformation. The change in radar echo strength with time delay is consistent with a loss tangent of 0.005–0.012 for the column of material between the surface and the reflector. These values are consistent with dry, moderate-density sediments or the lower end of the range of values measured for basalts. While a component of distributed ice in a higher-loss matrix cannot be ruled out, we do not find evidence for a dielectric horizon within the Vastitas Borealis Formation that might suggest an abrupt change from an upper dry layer to an ice-rich lower deposit

Subsurface structure of Planum Boreum from Mars Reconnaissance Orbiter Shallow Radar soundings

We map the subsurface structure of Planum Boreum using sounding data from the Shallow Radar (SHARAD) instrument onboard the Mars Reconnaissance Orbiter. Radar coverage throughout the 1,000,000- km2 area reveals widespread reflections from basal and internal interfaces of the north polar layered deposits (NPLD). A dome-shaped zone of diffuse reflectivity up to 12 ls (1-km thick) underlies twothirds of the NPLD, predominantly in the main lobe but also extending into the Gemina Lingula lobe across Chasma Boreale. We equate this zone with a basal unit identified in image data as Amazonian sand-rich layered deposits [Byrne, S., Murray, B.C., 2002. J. Geophys. Res. 107, 5044, 12 pp. doi:10.1029/2001JE001615; Fishbaugh, K.E., Head, J.W., 2005. Icarus 174, 444–474; Tanaka, K.L., Rodriguez, J.A.P., Skinner, J.A., Bourke, M.C., Fortezzo, C.M., Herkenhoff, K.E., Kolb, E.J., Okubo, C.H., 2008. Icarus 196, 318–358]. Elsewhere, the NPLD base is remarkably flat-lying and co-planar with the exposed surface of the surrounding Vastitas Borealis materials. Within the NPLD, we delineate and map four units based on the radar-layer packets of Phillips et al. [Phillips, R.J., and 26 colleagues, 2008. Science 320, 1182– 1185] that extend throughout the deposits and a fifth unit confined to eastern Gemina Lingula. We estimate the volume of each internal unit and of the entire NPLD stack (821,000 km3), exclusive of the basal unit. Correlation of these units to models of insolation cycles and polar deposition [Laskar, J., Levrard, B., Mustard, J.F., 2002. Nature 419, 375–377; Levrard, B., Forget, F., Montmessin, F., Laskar, J., 2007. J. Geophys. Res. 112, E06012, 18 pp. doi:10.1029/2006JE002772] is consistent with the 4.2-Ma age of the oldest preserved NPLD obtained by Levrard et al. [Levrard, B., Forget, F., Montmessin, F., Laskar, J., 2007. J. Geophys. Res. 112, E06012, 18 pp. doi:10.1029/2006JE002772]. We suggest a dominant layering mechanism of dust–content variation during accumulation rather than one of lag production during periods of sublimation

Radar sounding evidence for buried glaciers in the southern mid-latitudes of Mars

Lobate features abutting massifs and escarpments in the middle latitudes of Mars have been recognized in images for decades, but their true nature has been controversial, with hypotheses of origin such as ice-lubricated debris flows or glaciers covered by a layer of surface debris. These models imply an ice content ranging from minor and interstitial to massive and relatively pure. Soundings of these deposits in the eastern Hellas region by the Shallow Radar on the Mars Reconnaissance Orbiter reveal radar properties entirely consistent with massive water ice, supporting the debris-covered glacier hypothesis. The results imply that these glaciers formed in a previous climate conducive to glaciation at middle latitudes. Such features may collectively represent the most extensive nonpolar ice yet recognized on Mars

Shallow radar (SHARAD) sounding observations of the Medusae Fossae Formation, Mars

The SHARAD (shallow radar) sounding radar on the Mars Reconnaissance Orbiter detects subsurface reflections in the eastern and western parts of the Medusae Fossae Formation (MFF). The radar waves penetrate up to 580 m of the MFF and detect clear subsurface interfaces in two locations: west MFF between 150 and 155◦ E and east MFF between 209 and 213◦ E. Analysis of SHARAD radargrams suggests that the real part of the permittivity is ∼3.0, which falls within the range of permittivity values inferred from MARSIS data for thicker parts of the MFF. The SHARAD data cannot uniquely determine the composition of the MFF material, but the low permittivity implies that the upper few hundred meters of the MFF material has a high porosity. One possibility is that the MFF is comprised of low-density welded or interlocked pyroclastic deposits that are capable of sustaining the steep-sided yardangs and ridges seen in imagery. The SHARAD surface echo power across the MFF is low relative to typical martian plains, and completely disappears in parts of the east MFF that correspond to the radar-dark Stealth region. These areas are extremely rough at centimeter to meter scales, and the lack of echo power is most likely due to a combination of surface roughness and a low near-surface permittivity that reduces the echo strength from any locally flat regions. There is also no radar evidence for internal layering in any of the SHARAD data for the MFF, despite the fact that tens-of-meters scale layering is apparent in infrared and visible wavelength images of nearby areas. These interfaces may not be detected in SHARAD data if their permittivity contrasts are low, or if the layers are discontinuous. The lack of closely spaced internal radar reflectors suggests that the MFF is not an equatorial analog to the current martian polar deposits, which show clear evidence of multiple internal layers in SHARAD dat

Support minimized inversion of acoustic and elastic wave scattering

Inversion of limited data is common in many areas of NDE such as X-ray Computed Tomography (CT), Ultrasonic and eddy current flaw characterization and imaging;In many applications, it is common to have a bias toward a solution with minimum (L[superscript]2)[superscript]2 norm without any physical justification. When it is a priori known that objects are compact as, say, with cracks and voids, by choosing "Minimum Support" functional instead of the minimum (L[superscript]2)[superscript]2 norm, an image can be obtained that is equally in agreement with the available data, while it is more consistent with what is most probably seen in the real world;We have utilized a minimum support functional to find a solution with the smallest volume. This inversion algorithm is most successful in reconstructing objects that are compact like voids and cracks. To verify this idea, we first performed a variational nonlinear inversion of acoustic backscatter data using minimum support objective function. A full nonlinear forward model was used to accurately study the effectiveness of the minimized support inversion without error due to the linear (Born) approximation. After successful inversions using a full nonlinear forward model, a linearized acoustic inversion was developed to increase speed and efficiency in imaging process. The results indicate that by using minimum support functional, we can accurately size and characterize voids and/or cracks which otherwise might be uncharacterizable;An extremely important feature of support minimized inversion is its ability to compensate for unknown absolute phase (zero-of-time). Zero-of-time ambiguity is a serious problem in the inversion of the pulse-echo data. The minimum support inversion was successfully used for the inversion of acoustic backscatter data due to compact scatterers without the knowledge of the zero-of-time;The main drawback to this type of inversion is its computer intensiveness. In order to make this type of constrained inversion available for common use, work needs to be performed in three areas: (1) exploitation of state-of-the-art parallel computation, (2) improvement of theoretical formulation of the scattering process for better computation efficiency, and (3) development of better methods for guiding the non-linear inversion. (Abstract shortened by UMI.)</p

Restoration of Limited View-Angle Image with a Line-by-Line Kalman Filter

Image reconstruction using limited data is a necessity in a variety of applications. These applications include CT and NMR imaging in medical and industrial applications, and synthesis imaging in radio astronomy. In X-ray CT, the incompleteness of the data can be interpreted as a lack of sampling in the spatial Fourier domain. We will show that the distortion in a limited view-angle x-ray CT imaging can be formulated as a linear distortion. An estimation procedure to restore the distorted image will be presented. Finally, we will present the results of this estimation process to X-ray CT.</p