An iterative scheme for use in MT 2D forward modelling — to speed up production of the Jacobian and to improve accuracy of the inverse matrix

An important stage in two-dimensional magnetotelluric modelling is the calculation of the Earth's response functions for an assumed conductivity model and the calculation of the associated Jacobian relating those response functions to the model parameters. The efficiency of the calculation of the Jacobian will affect the efficiency of the inversion modelling. Rodi (1976) produced all the Jacobian elements by inverting a single matrix and using an approximate first-order algorithm. Since only one inverse matrix required calculation the procedure speeded up the inversion. An iterative scheme to improve the approximation to the Jacobian information is presented in this paper. While this scheme takes a little longer than Rodi's algorithm, it enables a more accurate determination of the Jacobian information. It is found that the Jacobian elements can be produced in 10% of the time required to calculate an inverse matrix or to calculate a 2D starting model. A modification of the algorithm can further be used to improve the accuracy of the original inverse matrix calculated in a 2D finite difference program and hence the solution this program produces. The convergence of the iteration scheme is found to be related both to the originally calculated inverse matrix and to the change in the newly formed matrix arising from perturbation of the model parameter. A ridge regression inverse algorithm is used in conjunction with the iterative scheme for forward modelling described in this paper to produce a 2D conductivity section from field data.     

Mutual Potential of Homogeneous Polyhedra

The mutual gravitational potential between a pair of homogeneous polyhedra is expressed using an infinite series. The nested volume integrals are evaluated analytically and result in simple tensor expressions containing no special functions. However, complexity increases as O(6 ⁿ ), where n is the term degree. An alternate formulation due to Liebenthal is also presented.     

Volatile retention from cometary impacts on the Moon

Impacts of comets and asteroids play an important role in volatile delivery on the Moon. We use a novel method for tracking vapor masses that reach escape velocity in hydrocode simulations of cometary impacts to explore the effects of volatile retention. We model impacts on the Moon to find the mass of vapor plume gravitationally trapped on the Moon as a function of impact velocity. We apply this result to the impactor velocity distribution and find that the total impactor mass retained on the Moon is approximately 6.5% of the impactor mass flux. Making reasonable assumptions about water content of comets and the comet size-frequency distribution, we derive a water flux for the Moon. After accounting for migration and stability of water ice at the poles, we estimate a total 1.3×10⁸-4.3×10⁹ metric tons of water is delivered to the Moon and remains stable at the poles over 1 Ga. A factor of 30 uncertainty in the estimated cometary impact flux is primarily responsible for this large range of values. The calculated mass of water is sufficient to account for the neutron fluxes poleward of 75° observed by Lunar Prospector. A similar analysis for water delivery to the Moon via asteroid impacts shows that asteroids provide six times more water mass via impacts than comets.     

Subsurface electric fields of a grounded cable of finite length for both frequency and time domain

Summary The subsurface electric fields of a current-carrying cable are examined for both steady-state and transient situations. Closed form expressions are obtained for two of the electric field components, and a numerical integration is used to obtain the third component. Waveforms for a stepfunction current excitation are displayed. The results have possible application to pulsed downlink communication in mine rescue operations.     

Overview of US Minerals Management Service Activities in Deepwater Research

The US Minerals Management Service (MMS) is responsible for safe and environmentally sound management of offshore oil and gas resources. In recent years, there has been a tremendous increase in both activities and plans for deepwater development of these resources in the Gulf of Mexico (GOM). As the industry meets the enormous technical challenges involved, there is a concomitant effort to assure environmental protection of deep-ocean and coastal resources. This paper will outline the research planning and program currently underway to assess impacts, identify potential problems, and discover more about unknown resources of the deep ocean.     

The glacilacustrine sedimentary environment of Bowser Lake in the northern Coast Mountains of British Columbia, Canada

Bowser Lake, a fiord lake in the northern Coast Mountains of British Columbia, contains a thick Holocene fill consisting mainly of silt and clay varves. These sediments were carried into the lake by proglacial Bowser River which drains a high-energy, heavily glacierized basin. Sedimentation in the lake is controlled by seasonal snow and ice melt, by autumn rainstorms, and by rare, but very large jökulhlaups from glacier-dammed lakes in the upper Bowser River basin which complicate environmental inferences from the sedimentary record. Sediment is dispersed through the deep western part of the lake by energetic turbidity currents. The turbidity currents apparently do not overtop a sill that separates the western basin from much shallower areas to the east. Large amounts of silt and clay are deposited from suspension in the eastern part of the lake, but sediment accumulation rates there are much lower than to the west. Several strong acoustic reflectors punctuate the varved fill in the western basin; these may be thick or relatively coarse beds deposited during jökulhlaups or exceptionally large storms. The contemporary sediment yield to Bowser Lake, estimated from sediments in the lake, is about 360 t km^-2a^-1. This is a relatively high value, but it is less than yields insome other, similar montane basins with extensive snow and ice cover.The most likely explanation for the difference is that large amounts of sediment have been, and continue to be, stored on the Bowser delta andin small proglacial lakes.