Approximate inversion of the wave-equation Hessian via randomized matrix probing

We present a method for approximately inverting the Hessian of full waveform inversion as a dip-dependent and scale-dependent amplitude correction. The terms in the expansion of this correction are determined by least-squares fitting from a handful of applications of the Hessian to random models — a procedure called matrix probing. We show numerical indications that randomness is important for generating a robust preconditioner, i.e., one that works regardless of the model to be corrected. To be successful, matrix probing requires an accurate determination of the nullspace of the Hessian, which we propose to implement as a local dip-dependent mask in curvelet space. Numerical experiments show that the novel preconditioner fits 70% of the inverse Hessian (in Frobenius norm) for the 1-parameter acoustic 2D Marmousi model.National Science Foundation (U.S.); Alfred P. Sloan Foundatio

Digital filters and applications to seismic detection and discrimination

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Geology and Geophysics, 1963."February 1963."Includes bibliographical references (leaf 89).The first part of this thesis is concerned with the mathematics of filtering in discrete time. Filters are defined for the purposes of 1) condensing waveforms into impulsive functions 2) wave shaping 3) noise suppression 4) signal detection according to the criterion of maximum signal-to-noise output at an instant and 5) the same over an interval. The behavior of the complex Fourier transforms of some of these filters is considered and connection is made with the theory of orthogonal polynomials. This leads to the possibility of a feed back representation of these filters. In the second part, computational experiments are described in which digital filters are applied to seismic body waves to i) try to determine whether the first arrival is up or down on a seismogram corrupted with microseismic noise, 2) increase signal-to-noise ratio on seismograms where noise has almost obliterated signal 3) assign polarity to each of two seismic first motion wavelets so they can be termed "same" or "opposite," 4) remove spectrum of seismometer from data, 5) investigate the time varying spectral structure of underground nuclear shot seismograms.by Jon F. Claerbout.M.S

Electromagnetic effects of atmospheric gravity waves,

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Geology and Geophysics, 1967.Vita.Bibliography: leaves 169-172.by Jon F. Claerbout.Ph.D

Seed biology of Physaria ludoviciana (silvery bladderpod; Brassicaceae ), an endangered species in sand prairies of the Midwest

Physaria ludoviciana (Nuttal) O\u27Kane & Al-Shehbaz (silvery bladderpod) is a state endangered species in Illinois, Minnesota and Wisconsin, the eastern edge of its range. Our goal was to investigate its seed biology (production, dispersal, seed bank longevity, afterripening, seed longevity after storage using germination and emergence, and seedling establishment). This information will be useful for conservation efforts of this endangered species. Over a ten-year period, various seed biology parameters were measured. Infructescences were counted to estimate seed production with 110–744 seeds per reproductive plant. Soil samples were collected at various distances to estimate dispersal where seeds dispersed less than a meter, and also at various times to estimate longevity in the seed bank where only 4% as many seeds were found in November as in June. After-ripening tests used seeds imbibed every two months after harvest for ten months where germination rates increased when imbibition was delayed at least six months. Germination and emergence of stored seed was measured to estimate longevity. Seeds stored at 4 °C and 40–50% relative humidity remained viable for at least six years. For establishment and plant density, seedlings, vegetative plants, and reproductive plants were counted. For establishment, densities were 0–11 seedlings m−2. This seed biology information could be applied to conservation efforts for this endangered species

INVESTIGATION OF INSECT VISITS TO FLOWERS OF STYLISMA PICKERINGII (PATTERSON BINDWEED), AN ENDANGERED PLANT OF ILLINOIS SAND PRAIRIES

Little is known about the reproductive biology of Stylisma pickeringii var. pattersonii, an endangered plant in Illinois occurring in only three counties (Cass, Henderson, and Mason). The objective of this study was to estimate flower densities and temporal (time of day and seasonal) differences in insect visitation to flowers of S. pickeringii in 2002 for native populations in Henderson and Mason Counties. A 50 m transect was located where S. pickeringii was most abundant and quadrats (0.25 m2) were placed on alternate sides of the tape measure at every meter at random distances from the transect. The number of flowers was estimated for both Mason and Henderson Counties in July and August 2002. For insect visitations, three plots (1 m2) were located in patches where open S. pickeringii flowers were abundant. Insects visiting flowers were collected within the same plots for one hour starting at 10:00 A.M., 12:30 P.M., and 3:00 P.M. on July 9, 2002 (Henderson County) and on July 10, 2002 (Mason County). On August 21, 2002 in Mason County only, plots were observed for one hour starting only at 12:30 P.M.. Insects were collected with nets and placed in killing jars containing cyanide. The number of each insect species visiting flowers of S. pickeringii was recorded for each time. Pollen from the bodies of four insect visitors was compared to that from flowers. Mason County had significantly higher flower density with a mean of 131 6 17 flowers/m2. July is peak flowering time for S. pickeringii in Mason County, Illinois. Insect diversity was greater in Henderson County than in Mason County. No differences were noted for insect visits to flowers during different times of day in July at Henderson County, but visits were greatest from 3:00 to 4:00 P.M. at Mason County. Pollen collected from all insect visitors that were checked was similar in color, shape and size to pollen from flowers of S. pickeringii. These findings increase the understanding of plant-pollinator interactions for S. pickeringii and will support more informed management decisions