Engineering topics

Turcotte, Donald L.

Publications and source records attributed to Turcotte, Donald L..

At least 19 records

NASA NTRS1994

Isostatic compensation of equatorial highlands on Venus

Spherical harmonic models for Venus' global topography and gravity incorporating Magellan data are used to test isostatic compensation models in five 30 deg x 30 deg regions representative of the main classes of equatorial highlands. The power spectral density for the harmonic models obeys a power-law scaling with spectral slope Beta approximately 2 (Brown noise) for the topography and Beta approximately 3 (Kaula's law) for the geoid, similar to what is observed for Earth. The Venus topography spectrum has lower amplitudes than Earth's which reflects the dominant lowland topography on Venus. Observed degree geoid to topography ratios (GTRs) on Venus are significantly smaller than degree GTRs for uncompensated topography, indicative of substantial compensation. Assuming a global Airy compensation, most of the topography is compensated at depths greater than 100 km, suggesting a thick lithosphere on Venus. For each region considered we obtain a regional degree of compensation C from a linear regression of Bouguer anomaly versus Bouguer gravity data. Geoid anomaly (N) versus topography variation (h) data for each sample were compared, in the least-squares sense, to theoretical correlations for Pratt, Airy, and thermal thinning isostasy models yielding regional GTR, zero-elevation crustal thickness (H), and zero elevation thermal lithosphere thickness (y(sub L(sub 0)), respectively. We find the regional compensation to be substantial (C approximately 52-80%), and the h, N data correlations in the chosen areas can be explained by isostasy models applicable on the Earth and involving variations in crustal thickness (Airy) and/or lithospheric (thermal thinning) thickness. However, a thick crust and lithosphere (y(sub L(sub 0)) approximately 300 km) must be assumed for Venus.

Kucinskas, Algis B.↗

NASA NTRS1994

Comment on 'An episodic hypothesis for Venusian tectonics' by Donald Turcotte

Turcotte (9193) proposes an episodic hypothesis regarding tectonics on Venus, wherein 'global subduction' alternates with quiescence and development of a thick strong lithosphere on a time scale of several hundred million years. Kaula (1994) argues that Turcotte's model is unpersuasive in several respects.

Turcotte, Donald L.↗

NASA NTRS1993

The spatial distribution of coronae and related features on Venus

Coronae are large quasi-circular geologica features that are common on Venus. They appear to be the surface tectonic and volcanic expressions of mantle diapirs that have impinged on the underside of the venusian lithosphere. We have investigated the spatial distribution of 335 coronae and related features identified in Magellan radar data. It is more clustered than a Poisson distribution, with a statistical certainty of more than 99%. It is dominated by a single large cluster centered near the equator at about 245 deg longitude. The features are preferentially found at elevation and geoid values close to the planetary mean, with a paucity at both the highest and lowest levels of topgraphy and geoid. Some coronae appear aligned in quasi-linear chains. We attribute the clustering of coronae and related features to preferential formation of these features above regions of broad-scale mantle upwelling, and suggest that a major mantle upwelling underlies the one large cluster. We suggest that coronae are rare at the lowest elevations because these may be regions of mantle downwelling. The shortage of coronae at the highest elevations may result both from obscuration by other intense tectonism there and from suppression there of their formation by an unusually thick crust. Corona chains may be produced by enhanced passive mantle uplift below failed or incipient rifts.

Squyres, Steven W.↗

NASA NTRS1993

A diffusion-limited aggregation model for the evolution of drainage networks

We propose a modified diffusion-limited aggregation (DLA) model for the evolution of fluvial drainage networks. Random walkers are introduced randomly on a grid, and each two-dimensional random walk proceeds until the walker finds a drainage network on which to accrete. This model for headward growth of drainage networks generates drainage patterns remarkably similar to actual drainages. The model also predicts statistical features which agree with actual networks, including the frequency-order (bifurcation) ratio (R(sub b) = 3.98) and the stream length-order (R(sub r) = 2.09). Using the definition of network fractal dimension D = log R(sub b)/log R(sub r), we find that our DLA model gives D = 1.87, near the observed range of D approximately equal to 1.80 - 1.85.

Masek, Jeffrey G.↗

NASA NTRS1993

Is there uniformitarian or catastrophic tectonics on Venus?

The distribution and modification of craters on Venus favors a near global, volcanic resurfacing event about 500 Myrs ago. Such an event indicates that the tectonic evolution of Venus was catastrophic rather than uniformitarian. The creation of a global, single-plate lithosphere on Venus about 500 Myrs ago can explain a variety of tectonic features on Venus that are not consistent with the thin lithosphere required by a uniformitarian hypothesis. A lithosphere on Venus that has thickened for 500 Myrs has a present thickness of about 300 km whereas steady-state heat loss from Venus requires a mean lithospheric thickness near 40 km. A thick lithosphere on Venus can support the high plateaus (elevations of 3-4 km) and mountain belts (up to 9 km) using the same isostatic compensation concepts applicable to the earth. If a thick lithosphere is thinned by a mantle plume, elevation is caused by thermal isostasy. The elevation due to the thinning of a 300 km thick lithosphere is about 3 km. Thus the domal elevation of Beta Regio can be explained by the same mechanism responsible for the elevation of the Hawaiian Swell. While the broad highland plateaus on Venus may be associated with thermal isostasy, the mountain belts in Ishtar Terra clearly cannot be. The high topography of Freyja Montes is almost certainly associated with underthrusting and the likely compensation mechanism is Airy isostasy associated with a thickened crust. With a density contrast delta, of 500 kg m(exp -3) an elevation of 9 km requires a crustal thickening of about 70 km. With a thick lithosphere there is no difficulty in supporting such a thick crust.

Turcotte, Donald L.↗

NASA NTRS1992

Fractal analysis of Venus topography in Tinatin Planitia and Ovda Regio

A one-dimensional fractal analysis is applied to Magellan altimetry data for two 20 x 20 deg equatorial regions on Venus. For the Ovda Regio, highlands the power spectra of the altimetry data correlate well with power law (fractal) statistics over the full range of wavelengths considered 36-703 km; the mean fractal dimension is D(Ovda) = 1.64. For the Tinatin Planitia lowlands, the power spectra consistently show a rollover at long wavelengths, (greater than 200 km), the long-wavelength topography in this region either never developed or has subsequently relaxed. The mean of the best fit fractal dimension for Tinatin is D(Tinatin) = 1.41. The measure of roughness (RA) correlates well with variations in relief, especially at short wavelengths (about 50 km). The quantitative analysis of Venus topography can be applied on a global scale. The one-dimensional method can be extended to two-dimensional space, yielding two-dimensional maps of regional D and RA, allowing a more complete use of regional two-dimensional altimetry data.

Kucinskas, Algis B.↗

NASA NTRS1991

Analysis of regional deformation and strain accumulation data adjacent to the San Andreas fault

A new approach to the understanding of crustal deformation was developed under this grant. This approach combined aspects of fractals, chaos, and self-organized criticality to provide a comprehensive theory for deformation on distributed faults. It is hypothesized that crustal deformation is an example of comminution: Deformation takes place on a fractal distribution of faults resulting in a fractal distribution of seismicity. Our primary effort under this grant was devoted to developing an understanding of distributed deformation in the continental crust. An initial effort was carried out on the fractal clustering of earthquakes in time. It was shown that earthquakes do not obey random Poisson statistics, but can be approximated in many cases by coupled, scale-invariant fractal statistics. We applied our approach to the statistics of earthquakes in the New Hebrides region of the southwest Pacific because of the very high level of seismicity there. This work was written up and published in the Bulletin of the Seismological Society of America. This approach was also applied to the statistics of the seismicity on the San Andreas fault system.

Turcotte, Donald L.↗

NASA NTRS1991

A scale-invariant cellular-automata model for distributed seismicity

In the standard cellular-automata model for a fault an element of stress is randomly added to a grid of boxes until a box has four elements, these are then redistributed to the adjacent boxes on the grid. The redistribution can result in one or more of these boxes having four or more elements in which case further redistributions are required. On the average added elements are lost from the edges of the grid. The model is modified so that the boxes have a scale-invariant distribution of sizes. The objective is to model a scale-invariant distribution of fault sizes. When a redistribution from a box occurs it is equivalent to a characteristic earthquake on the fault. A redistribution from a small box (a foreshock) can trigger an instability in a large box (the main shock). A redistribution from a large box always triggers many instabilities in the smaller boxes (aftershocks). The frequency-size statistics for both main shocks and aftershocks satisfy the Gutenberg-Richter relation with b = 0.835 for main shocks and b = 0.635 for aftershocks. Model foreshocks occur 28 percent of the time.

Barriere, Benoit↗

NASA NTRS1991

Implications of convection in the moon and the terrestrial planets

A comprehensive review is made of the thermal chemical evolution of the moon and the terrestrial planets. New results are presented which were obtained for Venus by the Magellan Mission the efforts were concentrated on this planet. Alternative models were examined for the thermal structure of the lithosphere of Venus. The statistical distribution was studied of the locations of the coronae on Venus. Models were examined for the patterns of faulting around the coronae on Venus. A series was considered of viscous models for the development and relaxation of elevation anomalies on Venus. And rates were studied of solidification of volcanic flows on Venus. Both radiative and convective heat transfer were considered.

Turcotte, Donald L.↗

NASA NTRS1991

Earthquake prediction

The state of the art in earthquake prediction is discussed. Short-term prediction based on seismic precursors, changes in the ratio of compressional velocity to shear velocity, tilt and strain precursors, electromagnetic precursors, hydrologic phenomena, chemical monitors, and animal behavior is examined. Seismic hazard assessment is addressed, and the applications of dynamical systems to earthquake prediction are discussed.

Turcotte, Donald L.↗

NASA NTRS1990

Fractal image analysis - Application to the topography of Oregon and synthetic images.

Digitized topography for the state of Oregon has been used to obtain maps of fractal dimension and roughness amplitude. The roughness amplitude correlates well with variations in relief and is a promising parameter for the quantitative classification of landforms. The spatial variations in fractal dimension are low and show no clear correlation with different tectonic settings. For Oregon the mean fractal dimension from a two-dimensional spectral analysis is D = 2.586, and for a one-dimensional spectral analysis the mean fractal dimension is D = 1.487, which is close to the Brown noise value D = 1.5. Synthetic two-dimensional images have also been generated for a range of D values. For D = 2.6, the synthetic image has a mean one-dimensional spectral fractal dimension D = 1.58, which is consistent with the results for Oregon. This approach can be easily applied to any digitzed image that obeys fractal statistics.

Huang, Jie↗

NASA NTRS1990

Are earthquakes an example of deterministic chaos?

A simple mass-spring model is used to systematically examine the dynamical behavior introduced by fault zone heterogeneities. The model consists of two sliding blocks coupled to each other and to a constant velocity driver by elastic springs. The state of this system can be characterized by the positions of the two blocks relative to the driver. A simple static/dynamic friction law is used. When the system is symmetric, cyclic behavior is observed. For an asymmetric system, where the frictional forces for the two blocks are not equal, the solutions exhibit deterministic chaos. Chaotic windows occur repeatedly between regions of limit cycles on bifurcation diagrams. The model behavior is similar to that of the one-dimensional logistic map. The results provide substantial evidence that earthquakes are an example of deterministic chaos.

Huang, Jie↗

NASA NTRS1989

The route to chaos in thermal convection at infinite Prandtl number. I - Some trajectories and bifurcations

The question of whether or not thermal convection in the earth's mantle is chaotic is addressed. It is suggested that the high Prandtl number/high Raleigh number thermal convection associated with mantle convection is chaotic. To test this hypothesis, the route to chaos in a fluid with infinite Prandtl number is examined, using the Saltzman (1962) equations and the Lorenz (1963) equations. It is concluded that thermal convection at infinite Prandtl number becomes chaotic by means of symmetry-breaking pitchfork bifurcations and the appearance of Hopf bifurcations which produce unstable periodic orbits.

Stewart, Cheryl A.↗

NASA NTRS1989

Fractals in geology and geophysics

The definition of a fractal distribution is that the number of objects N with a characteristic size greater than r scales with the relation N of about r exp -D. The frequency-size distributions for islands, earthquakes, fragments, ore deposits, and oil fields often satisfy this relation. This application illustrates a fundamental aspect of fractal distributions, scale invariance. The requirement of an object to define a scale in photograhs of many geological features is one indication of the wide applicability of scale invariance to geological problems; scale invariance can lead to fractal clustering. Geophysical spectra can also be related to fractals; these are self-affine fractals rather than self-similar fractals. Examples include the earth's topography and geoid.

Turcotte, Donald L.↗

NASA NTRS1989

Fractal applications to complex crustal problems

Complex scale-invariant problems obey fractal statistics. The basic definition of a fractal distribution is that the number of objects with a characteristic linear dimension greater than r satisfies the relation N = about r exp -D where D is the fractal dimension. Fragmentation often satisfies this relation. The distribution of earthquakes satisfies this relation. The classic relationship between the length of a rocky coast line and the step length can be derived from this relation. Power law relations for spectra can also be related to fractal dimensions. Topography and gravity are examples. Spectral techniques can be used to obtain maps of fractal dimension and roughness amplitude. These provide a quantitative measure of texture analysis. It is argued that the distribution of stress and strength in a complex crustal region, such as the Alps, is fractal. Based on this assumption, the observed frequency-magnitude relation for the seismicity in the region can be derived.

Turcotte, Donald L.↗

NASA NTRS1987

Implications of convection in the Moon and the terrestrial planets

The early thermal and chemical evolution of the Moon is discussed. The rubidium-strontium, neodymium-samarium, and uranium-thorium-lead systems were studied. The relation of source region heterogeneity to the mixing associated with mantle convection is considered. Work on the application of fractal concepts to planetary geology and geophysics is also discussed. The fractal concept was applied to fragmentation, including the frequency-size distribution of meteorites, asteroids and particulate matter produced by impacts.

Turcotte, Donald L.↗

NASA NTRS1987

A fractal interpretation of topography and geoid spectra on the earth, moon, Venus, and Mars

Global spectra are available for topography and geoid on the earth, Venus, Mars, and the moon. If the spectral energy density has a power law dependence on wave number, a fractal is defined. The topography spectrum for the earth is a well-defined fractal with D = 1.5; this corresponds to Brown noise with the amplitude proportional to the wavelength. Although there is more scatter for the other planetary bodies, the data for Mars and the moon correlate well with the data for the earth. Venus topography also exhibits a Brown noise behavior but with a smaller amplitude. The power law dependence of the earth's geoid is known as Kaula's law. It is shown that uncompensated Brown topography gives a geoid with a power law dependence that is in quite good agreement with Kaula's law. However, the required amplitude is only 8 percent of the observed topography. A similar result is found for the other bodies, with the ratio of the amplitude of topography required to explain the geoid to the observed topography increasing to 72 percent for the moon.

Turcotte, Donald L.↗

NASA NTRS1986

Correlation of data on strain accumulation adjacent to the San Andreas Fault with available models

Theoretical and numerical studies of deformation on strike slip faults were performed and the results applied to geodetic observations performed in the vicinity of the San Andreas Fault in California. The initial efforts were devoted to an extensive series of finite element calculations of the deformation associated with cyclic displacements on a strike-slip fault. Measurements of strain accumulation adjacent to the San Andreas Fault indicate that the zone of strain accumulation extends only a few tens of kilometers away from the fault. There is a concern about the tendency to make geodetic observations along the line to the source. This technique has serious problems for strike slip faults since the vector velocity is also along the fault. Use of a series of stations lying perpendicular to the fault whose positions are measured relative to a reference station are suggested to correct the problem. The complexity of faulting adjacent to the San Andreas Fault indicated that the homogeneous elastic and viscoelastic approach to deformation had serious limitations. These limitation led to the proposal of an approach that assumes a fault is composed of a distribution of asperities and barriers on all scales. Thus, an earthquake on a fault is treated as a failure of a fractal tree. Work continued on the development of a fractal based model for deformation in the western United States. In order to better understand the distribution of seismicity on the San Andreas Fault system a fractal analog was developed. The fractal concept also provides a means of testing whether clustering in time or space is a scale-invariant process.

Turcotte, Donald L.↗