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Robert K. Mark

Publications and source records attributed to Robert K. Mark.

11 recordsLinked to original sources

Mediterranean seabed in digital shaded relief

Relief-shaded images made from a large digital depth model (DDM) provide a fresh view of regional tectonism and submarine geomorphology in the central Mediterranean. The 1-km spatial resolution is better than that afforded by the 5-arc-minute worldwide digital bathymetry (DBDB5). These computer pictures enable information on seafloor morphology to be visualized and communicated in much the same way that relief maps made from digital elevation models are used to interpret subaerial topography. The images shown here (partially joined along 19°E) were taken from a new shaded-relief map of the entire Mediterranean seafloor and parts of the Bay of Biscay and Black Sea between latitude 307deg;–46°N and longitude 6°W–37°E.

Aegean Sea, Mediterranean Sea, Tyrhennian Sea

Mapping debris-flow hazard in Honolulu using a DEM

A method for mapping hazard posed by debris flows has been developed and applied to an area near Honolulu, Hawaii. The method uses studies of past debris flows to characterize sites of initiation, volume at initiation, and volume-change behavior during flow. Digital simulations of debris flows based on these characteristics are then routed through a digital elevation model (DEM) to estimate degree of hazard over the area.

Conference Paper

Morphology of the island of Hawaii

Digital elevation data for the island of Hawaii from the U.S. Geographical Survey gridded at 30 m spacing was used to generate a slope map, a shaded relief map, and plots that compare slope and elevation for each of the five volcanoes that compose the island.These computer- generated products are useful in analyzing the morphology of the sland. The volcanoes become steeper with increasing age. The five volcanoes, in order of increasing age, are Kilauea, Mauna Lao, Hualalai, Mauna Kea and Kohala; their average slopes are 3.3, 5.4, 6.6, 7.0, and 11.3, respectively. This relation apparently results from growth of the late, steeper alkali cap on the older volcanoes that include more viscous, thicker flows, flows that are smaller hence tend to pile up more near the summit vents, and volatile- rich lavas that commonly produce steep sided cinder cones at summit vents. The cause of the gentler slopes of younger volcanoes include the high proportion of exposed fluid lava flows from the shield building stage, the ponding of lava against earlier volcanoes, and the grading of lava to sea level; subsidence of the older volcanoes have cause these gently dipping near-seas-level lava flows to subside below the sea. Finally, steep erosional canyons have developed in large areas of the older volcanoes (notably Kohala). Virtually all of the major fault systems on the sland appear to be related to the upper parts of giant landslides, most of which are hidden below sea level on the submarine flanks of the volcanoes. These are generally normal faults in the tensional regime at the heads and upper parts of the landslides Subtle changes in slope hint at buried landslide related faults scarps that have been covered by subsequent lava flows. Major erosional canyons are present in only two places, each presumed to be in the amphitheaters of the major landslides. The probably formed in this setting because steam erosion is favored by the steep sloped generated at the heads of landslides. The slope map clearly displays two bands of steep slope on Mauna Kea that mark the terminal moraines at the edges of the last two advances of the Pleistocene ice cap.

Hawaii

Statistical relations among earthquake magnitude, surface rupture length, and surface fault displacement

In order to refine correlations of surface-wave magnitude, fault rupture length at the ground surface, and fault displacement at the surface by including the uncertainties in these variables, the existing data were critically reviewed and a new data base was compiled. Earthquake magnitudes were redetermined as necessary to make them as consistent as possible with the Gutenberg methods and results, which make up much of the data base. Measurement errors were estimated for the three variables for 58 moderate to large shallow-focus earthquakes. Regression analyses were then made utilizing the estimated measurement errors. The regression analysis demonstrates that the relations among the variables magnitude, length, and displacement are stochastic in nature. The stochastic variance, introduced in part by incomplete surface expression of seismogenic faulting, variation in shear modulus, and regional factors, dominates the estimated measurement errors. Thus, it is appropriate to use ordinary least squares for the regression models, rather than regression models based upon an underlying deterministic relation in which the variance results primarily from measurement errors. Significant differences exist in correlations of certain combinations of length, displacement, and magnitude when events are grouped by fault type or by region, including attenuation regions delineated by Evernden and others. Estimates of the magnitude and the standard deviation of the magnitude of a prehistoric or future earthquake associated with a fault can be made by correlating M s with the logarithms of rupture length, fault displacement, or the product of length and displacement. Fault rupture area could be reliably estimated for about 20 of the events in the data set. Regression of M s on rupture area did not result in a marked improvement over regressions that did not involve rupture area. Because no subduction-zone earthquakes are included in this study, the reported results do not apply to such zones.

Bulletin of the Seismological Society of America

Application of linear statistical models of earthquake magnitude versus fault length in estimating maximum expectable earthquakes

Correlation or linear regression estimates of earthquake magnitude from data on historical magnitude and length of surface rupture should be based upon the correct regression. For example, the regression of magnitude on the logarithm of the length of surface rupture L can be used to estimate magnitude, but the regression of log L on magnitude cannot. Regression estimates are most probable values, and estimates of maximum values require consideration of one-sided confidence limits.

Geology