Pitfalls in Nonlinear Inversion

— We discuss and illustrate graphically with simple 2-D problems, four common pitfalls in geophysical nonlinear inversion. The first one establishes that the Lagrange multiplier, used to incorporate a priori information in the geophysical inverse problem, should be the largest value still compatible with a reasonable data fitting. This procedure should be used only when the interpreter is sure about the importance of the a priori information used to stabilize the inverse problem relative to the geophysical observations. Because this is rarely the case, the user should use the smallest Lagrange multiplier still producing stable solutions. The second pitfall is an attempt to automatically estimate the Lagrange multiplier by decreasing it along the iterative process used to solve the nonlinear optimization problem. Consequently, at the last iteration, the Lagrange multiplier may be so small that the problem may become ill-posed and any computed solution in this case is meaningless. The third pitfall is related to the incorporation of a priori information by a technique known as “Jumping.” This formulation, from the viewpoint of the class of Acceptable Gradient Methods, is incomplete and may lead to a premature halt in the iteration, and, consequently, to solutions far from the true one. Finally, the fourth pitfall is an inadequate convergence criterion which stops the iteration when the data misfit drops just below the noise level, irrespective of the fact that the functional to be minimized may not have attained its minimum. This means that the a priori information has not been completely incorporated, so that this stopping criterion partially neutralizes the effect of the stabilizing functional, and opens the possibility of obtaining unstable, meaningless estimates.     

Long-term changes in water quality and phytoplankton characteristics in port shelter, Hong Kong, from 1988-1998.

This study analysed monthly physico-chemical and phytoplankton data collected from 10 marine monitoring stations in Port Shelter Hong Kong, from 1988 to 1998. Cluster analysis based on all water quality parameters measured shows that the 10 monitoring stations can be grouped into three clusters: Cluster I consists of stations located in Outer Port Shelter; Cluster II consists of stations located in Inner Port Shelter and Cluster III consists of a single station in Hebe Heaven, a well-sheltered Bay in Inner Port Shelter. Factor analysis shows high positive loadings for nutrients and nutrient ratios in the first two factors of the three clusters, which indicates that the stations of the three clusters were primarily grouped according to their respective nutrient conditions. In Inner Port Shelter, and particularly Station PM5 in the sheltered Hebe Haven, the influence of surface runoff and pollution loading from the surrounding catchment area was apparent. Five stations located along a transect from Inner to Outer Port Shelter were selected for trend analysis. An increasing trend for temperature and a decreasing trend for pH are observed in all Stations except PM10 which is at the mouth of Port Shelter. The results of canonical analysis revealed that temperature and pH could also play an important role in determining the density and biovolume of the minor algal groups in Port Shelter.     

Anthropogenic organic matter in the Great Marsh of the Indiana Dunes National Lakeshore and its implications

Cores from the Great Marsh area of the Indiana Dunes National Lakeshore were examined in order to document variations in concentration, type and size of anthropogenic organic matter (A_nOM—coal, coke, etc.) and discuss their relationship to the concentration of such trace elements as Pb, Zn, and Mn in the near-surface sediment section. The results indicate that the first appearance of A_nOM corresponds to the onset of industrialization in the area. There is also a general relationship between the occurrence of A_nOM and Zn, Pb, and Mn. Trace metals were likely transported from the industrial sites to the area of their deposition as sulfur-bearing coatings on small anthropogenic particles. After deposition, these sulfur-bearing compounds reacted with organic matter within the marsh. As a result of bacterial reduction, the pyrite was produced, as suggested by a close relationship between the pyrite and A_nOM. Distance from the industrial complex upwind as well as local hydrologic conditions are among the major factors controlling distribution of A_nOM and trace elements. At the same distance from the source, types and sizes of A_nOM are influenced by the duration and frequency of flooding.     

Variations in heavy metals concentrations in Antarctic snows from 1940 to 1980

Concentrations of Pb, Cd, Cu and Zn have been measured using improved ultraclean procedures in a succession of twenty six snow samples integrating a 40 yr time sequence from 1940 to 1980 which were collected from the walls of a 6 m deep pit at stake D 55 in Adelie Land, East Antarctica. Measured concentrations, which are among the lowest ones ever measured in Antarctic snows, are found not to have significantly increased during the investigated time period, with the possible exception of Pb for which there might have been a significant increase after the mid 1960's. For this last metal, measured concentrations in the 1940's are about 6-fold higher than in Antarctic Holocene ice several thousand years old, which indicates that a large fraction of the anthropogenic increase for Pb probably occurred before the 1940's.