Modeling currents at satellite altitudes

A mathematical formalism for modeling the poloidal magnetic field and current density at satellite altitudes is presented

Comparing hard and soft prior bounds in geophysical inverse problems

In linear inversion of a finite-dimensional data vector y to estimate a finite-dimensional prediction vector z, prior information about X sub E is essential if y is to supply useful limits for z. The one exception occurs when all the prediction functionals are linear combinations of the data functionals. Two forms of prior information are compared: a soft bound on X sub E is a probability distribution p sub x on X which describeds the observer's opinion about where X sub E is likely to be in X; a hard bound on X sub E is an inequality Q sub x(X sub E, X sub E) is equal to or less than 1, where Q sub x is a positive definite quadratic form on X. A hard bound Q sub x can be softened to many different probability distributions p sub x, but all these p sub x's carry much new information about X sub E which is absent from Q sub x, and some information which contradicts Q sub x. Both stochastic inversion (SI) and Bayesian inference (BI) estimate z from y and a soft prior bound p sub x. If that probability distribution was obtained by softening a hard prior bound Q sub x, rather than by objective statistical inference independent of y, then p sub x contains so much unsupported new information absent from Q sub x that conclusions about z obtained with SI or BI would seen to be suspect

Reverse Engineering the Yield Curve

Prices of riskfree bonds in any arbitrage-free environment are governed by a pricing kernel: given a kernel, we can compute prices of bonds of any maturity we like. We use observed prices of multi-period bonds to estimate, in a log-linear theoretical setting, the pricing kernel that gave rise to them. The high-order dynamics of our estimated kernel help to explain why first-order, one-factor models of the term structure have had difficulty reconciling the shape of the yield curve with the persistence of the short rate. We use the estimated kernel to provide a new perspective on Hansen-Jagannathan bounds, the price of risk, and the pricing of bond options and futures.

Dynamics of the trade balance and the terms of trade: the S-curve

We provide a theoretical interpretation of two features of international data: the countercyclical movements in net exports and the tendency for the trade balance to be negatively correlated with current and future movements in the terms of trade, but positively correlated with past movements. We document these same properties in a two-country stochastic growth model in which trade fluctuations reflect, in large part, the dynamics of capital formation. We find that the general equilibrium perspective is essential: The relation between the trade balance and the terms of trade depends critically on the source of fluctuations.Balance of trade

Relative price movements in dynamic general equilibrium models of international trade

We examine the behavior of international relative prices from the perspective of dynamic general equilibrium theory, with particular emphasis on the variability of the terms of trade and the relation between the terms of trade and net exports. We highlight aspects of the theory that are critical in determining these properties, contrast our perspective with those associated with the Marshall-Lerner condition and the Harberger-Laursen-Metzler effect, and point out features of the data that have proved difficult to explain within existing dynamic general equilibrium models.International trade

Does the geoid drift west?

In 1970 Hide and Malin noted a correlation of about 0.8 between the geoid and the geomagnetic potential at the Earth's surface when the latter is rotated eastward in longitude by about 160 degrees and the spherical harmonic expansions of both functions are truncated at degree 4. From a century of magnetic observatory data, Hide and Malin inferred an average magnetic westward drift rate of about 0.27 degrees/year. They attributed the magnetic-gravitational correlation to a core event at about 1350 A.D. which impressed the mantle's gravity pattern at long wavelengths onto the core motion and the resulting magnetic field. The impressed pattern was then carried westward 160 degrees by the nsuing magnetic westward drift. An alternative possibility is some sort of steady physical coupling between the magnetic and gravitational fields (perhaps migration of Hide's bumps on the core-mantle interface). This model predicts that the geoid will drift west at the magnetic rate. On a rigid earth, the resulting changes in sea level would be easily observed, but they could be masked by adjustment of the mantle if it has a shell with viscosity considerably less than 10 to the 21 poise. However, steady westward drift of the geoid also predicts secular changes in g, the local acceleration of gravity, at land stations. These changes are now ruled out by recent independent high-accuracy absolute measurements of g made by several workers at various locations in the Northern Hemisphere

Investigation of terrestrial photovoltaic power systems with sunlight concentration

An analytical model of the silicon solar cells for high illumination is being used to design cells for different concentration factors. It is shown that a cell design using one centimeter length grid fingers would have an efficiency at 100 suns that is 90% of the efficiency of a typical cell at one sun. This may require about 30 fingers per centimeter. A decrease in efficiency comes from the greater coverage of the surface with grids as the concentration increases. The importance of base material resistivity on cell design for high concentration is outlined

Contributions from geomagnetic inverse theory to the study of hydromagnetic conditions near the core-mantle boundary

The Final Report on contributions from geomagnetic inverse theory to the study of hydromagnetic conditions near the core-mantle boundary (CMB) is presented. The original proposal was to study five questions concerning what the surface and satellite magnetic data imply about hydromagnetic and electromagnetic conditions near the CMB. The five questions are: (1) what do the surface and satellite data imply about the geomagnetic field B near the surface of the earth; (2) how does one extrapolate B down through the conducting mantle to the CMB; (3) if B on the CMB is visible, how accurately does it satisfy the frozen-flux approximation; (4) if frozen flux is a good approximation on the CMB, what can be inferred about the fluid velocity v in the upper core; and (5) if v at the CMB is visible, does it suggest any dynamical properties of the core, such as vertical advection, Alfven-inertial waves, link instabilities, or mantle effects. A summary of the research is provided

Confidence set inference with a prior quadratic bound

In the uniqueness part of a geophysical inverse problem, the observer wants to predict all likely values of P unknown numerical properties z = (z sub 1,...,z sub p) of the earth from measurement of D other numerical properties y(0)=(y sub 1(0),...,y sub D(0)) knowledge of the statistical distribution of the random errors in y(0). The data space Y containing y(0) is D-dimensional, so when the model space X is infinite-dimensional the linear uniqueness problem usually is insoluble without prior information about the correct earth model x. If that information is a quadratic bound on x (e.g., energy or dissipation rate), Bayesian inference (BI) and stochastic inversion (SI) inject spurious structure into x, implied by neither the data nor the quadratic bound. Confidence set inference (CSI) provides an alternative inversion technique free of this objection. CSI is illustrated in the problem of estimating the geomagnetic field B at the core-mantle boundary (CMB) from components of B measured on or above the earth's surface. Neither the heat flow nor the energy bound is strong enough to permit estimation of B(r) at single points on the CMB, but the heat flow bound permits estimation of uniform averages of B(r) over discs on the CMB, and both bounds permit weighted disc-averages with continous weighting kernels. Both bounds also permit estimation of low-degree Gauss coefficients at the CMB. The heat flow bound resolves them up to degree 8 if the crustal field at satellite altitudes must be treated as a systematic error, but can resolve to degree 11 under the most favorable statistical treatment of the crust. These two limits produce circles of confusion on the CMB with diameters of 25 deg and 19 deg respectively