Engineering topics
Publications and source records attributed to Richards, M. A..
A modal radar cross section (RCS) of arbitrary wire scatterers is constructed in terms of SEM parameters. Numerical results are presented for both straight and L-shaped wire targets and are compared to computations performed in the frequency domain using the method of moments.
Seismic tomography and fluid dynamical models are extended to include a detailed and realistic parameterization of the viscosity structure of the mantle. The model also includes the effects of heterogeneity inferred from surface-wave studies of upper-mantle structure. It is found that about 90 percent of the observed geoid may be explained by density anomalies inferred from tomography, a model of subducted slabs, and an earth model with a low-viscosity asthenosphere over a moderate-viscosity lower mantle.
Hotspots are associated with long wavelength geoid highs, an association that is even stronger when the geoid highs associated with subduction zones are removed. These associations are quantified by expanding the hotspot distribution in spherical harmonics and calculating correlation coefficients as a function of harmonic degree. The hotspot distribution spectrum is essentially white, with peaks at degrees 2 and 6. It is correlated positively with the slab residual geoid for degrees 2 to 6, with low seismic velocity in the lower mantle at degree 2, and with low seismic velocity in the upper mantle at degree 6. A variety of fluid mechanical models were tested for hotspots, including lithospheric delamination and hot plumes, by calculating their predicted dynamic geoid responses and comparing them to the observations. These models include the effects of temperature dependent rheology. The preferred hotspot model, based on observations of the geoid and seismic tomography, has plumes preferentially occurring in regions of large scale background temperature highs in a mantle with substantial viscosity increase with depth, although other models are possible.
Unlike Earth, long wavelength gravity anomalies and topography correlate well on Venus. Venus's admittance curve from spherical harmonic degree 2 to 18 is inconsistent with either Airy or Pratt isostasy, but is consistent with dynamic support from mantle convection. A model using whole mantle flow and a high viscosity near surface layer overlying a constant viscosity mantle reproduces this admittance curve. On Earth, the effective viscosity deduced from geoid modeling increases by a factor of 300 from the asthenosphere to the lower mantle. These viscosity estimates may be biased by the neglect of lateral variations in mantle viscosity associated with hot plumes and cold subducted slabs. The different effective viscosity profiles for Earth and Venus may reflect their convective styles, with tectonism and mantle heat transport dominated by hot plumes on Venus and by subducted slabs on Earth. Convection at degree 2 appears much stronger on Earth than on Venus. A degree 2 convective structure may be unstable on Venus, but may have been stabilized on Earth by the insulating effects of the Pangean supercontinental assemblage.
The long wavelength components of the Earth's gravity field result mainly from density contrasts associated with convection in the mantle. Direct interpretation of the geoid for mantle convection is complicated by the fact that convective flow results in dynamically maintained deformation of the surface of the Earth, the core mantle boundary (CMB), and any interior chemical boundaries which might exist. These boundary deformations effect the geoid opposite in sign and are comparable in magnitude to those of the interior density contrasts driving the flow. The total difference of two relatively large quantities.
Density contrasts in the lower mantle, recently imaged using seismic tomography, drive convective flow which results in kilometers of dynamically maintained topography at the core-mantle boundary and at the earth's surface. The total gravity field due to interior density constrasts and boundary topography predicts the largest wavelength components of the geoid remarkably well. Neglecting dynamic surface deformation leads to geoid anomalies of opposite sign than are observed.
Unlike Earth, on Venus long wavelength geoid anomalies correlate well with topography. Venus's admittance curve between harmonic degrees 3 and 18 is inconsistent with Airy isostasy but is consistent with dynamic support from convection being the dominant mechanism of compensation on Venus. We model dynamic compensation on Venus using simple flow models which assume a spherically symmetric Newtonian mantle viscosity profile. Preliminary models parameterize the viscosity variation with depth as a 2 layer model with a boundary at 720 km depth. A model in which viscosity in the lower mantle is a factor of 10 lower than in the upper mantle can explain Venus's observed admittance curve for degrees 3 through 18. Dynamic models which include a chemical boundary between the upper and lower mantle do not successfully explain the observed admittance curve, indicating that Venus does not have a chemically layered mantle.
Unlike Earth, long wavelength gravity anomalies and topography correlate well on Venus. Venus's admittance curve from spherical harmonic degree 2 to 18 is inconsistent with either Airy or Pratt isostasy, but is consistent with dynamic support from mantle convection. A model using whole mantle flow and a high viscosity near surface layer overlying a constant viscosity mantle reproduces this admittance curve. On Earth, the effective viscosity deduced from geoid modeling increases by a factor of 300 from the asthenosphere to the lower mantle. These viscosity estimates may be biased by the neglect of lateral variations in mantle viscosity associated with hot plumes and cold subducted slabs. The different effective viscosity profiles for Earth and Venus may reflect their convective styles, with tectonism and mantle heat transport dominated by hot plumes on Venus and by subducted slabs on Earth. Convection at degree 2 appears much stronger on Earth than on Venus. A degree 2 convective structure may be unstable on Venus, but may have been stabilized on Earth by the insulating effects of the Pangean supercontinental assemblage.
Potential and surface deformation Love numbers for internal loading have been calculated in order to obtain a dynamically consistent relationship between the geoid and the earth's response to internal buoyancy forces. These quantities depend on the depth and harmonic degree of loading, and can be integrated as Green functions to obtain the dynamic response due to an arbitrary distribution of internal density contrasts. Constructing a series of spherically symmetric, self-gravitating flow models for a variety of radial Newtonian viscosity variations and flow configurations, and calculating relaxation times for spherically symmetric viscous earth models, it is demonstrated that boundary deformation due to internal loading reaches its equilibrium value on the same time scale as postglacial rebound; this is much less time than the time scale for significant change in the convective flow pattern.
Density contrasts in the lower mantle, recently imaged using seismic tomography, drive convective flow which results in kilometers of dynamically maintained topography at the core-mantle boundary and at the Earth's surface. The total gravity field due to interior density contrasts and boundary topography predicts the largest wavelength components of the geoid remarkably well. Neglecting dynamic surface deformation leads to geoid anomalies of opposite sign than are observed.
A linear empirical model has been developed for the correction of sea state bias effects, in Seasat altimetry data altitude measurements, that are due to (1) electromagnetic bias caused by the fact that ocean wave troughs reflect the altimeter signal more strongly than the crests, shifting the apparent mean sea level toward the wave troughs, and (2) an independent instrument-related bias resulting from the inability of height corrections applied in the ground processor to compensate for simplifying assumptions made for the processor aboard Seasat. After applying appropriate corrections to the altimetry data, an empirical model for the sea state bias is obtained by differencing significant wave height and height measurements from coincident ground tracks. Height differences are minimized by solving for the coefficient of a linear relationship between height differences and wave height differences that minimize the height differences. In more than 50% of the 36 cases examined, 7% of the value of significant wave height should be subtracted for sea state bias correction.