A Restoration Method for Impulsive Functions

A method is presented for enhancing the resolution of impulsive functions which have been degraded by a known convolutional disturbance and by the addition of white noise. An autoregressive model is employed to represent the spectrum of the ideally resolved impulsive function. The method is flexible in that it allows constraints to be incorporated into the resolution scheme. Two quite diverse examples are presented as illustration

L-moments and C-moments

It is well known that the computation of higher order statistics, like skewness and kurtosis, (which we call C-moments) is very dependent on sample size and is highly susceptible to the presence of outliers. To obviate these difficulties, Hosking (1990) has introduced related statistics called L-moments. We have investigated the relationship of these two measures in a number of different ways. Firstly, we show that probability density functions (pdf ) that are estimated from L-moments are superior estimates to those obtained using C-moments and the principle of maximum entropy. C-moments computed from these pdf's are not however, contrary to what one may have expected, better estimates than those estimated from sample statistics. L-moment derived distributions for field data examples appear to be more consistent sample to sample than pdf 's determined by conventional means. Our observations and conclusions have a significant impact on the use of the conventional maximum entropy procedure which typically uses C-moments from actual data sets to infer probabilities.Facultad de Ciencias Astronómicas y Geofísica

Simulated annealing ray tracing in complex 3-D media

Simulated annealing has been applied to seismic ray tracing to determine the minimum traveltime ray path connecting two points in complex 3-D media. In contrast to conventional ray tracing schemes such as shooting and bending, simulated annealing ray tracing (SART) overcomes some well-known difficulties regarding multipathing and take-off angle selection. These include local convergence (that is, failing to obtain the ray path with absolute minimum traveltime) and divergence of the take-off angle selection strategy. Under these circumstances, shooting and bending methods may not provide reliable results in highly variable 3-D media. A flexible model representation is used to accommodate a large class of velocity models.Facultad de Ciencias Astronómicas y Geofísica

Simulated annealing ray tracing in complex 3-D media

Simulated annealing has been applied to seismic ray tracing to determine the minimum traveltime ray path connecting two points in complex 3-D media. In contrast to conventional ray tracing schemes such as shooting and bending, simulated annealing ray tracing (SART) overcomes some well-known difficulties regarding multipathing and take-off angle selection. These include local convergence (that is, failing to obtain the ray path with absolute minimum traveltime) and divergence of the take-off angle selection strategy. Under these circumstances, shooting and bending methods may not provide reliable results in highly variable 3-D media. A flexible model representation is used to accommodate a large class of velocity models.Facultad de Ciencias Astronómicas y Geofísica

An Occam's razor view of the lead-lag dispute in global warming

There can surely be no doubt that the global-mean surface air temperature and the concentrations of greenhouse gases (esp. CO2) in the Earth's atmosphere are increasing quite rapidly. Whether the increase in anthropogenic CO2 is primarily responsible for an increase of our planet's global temperature is, in spite of considerable evidence, a point of constant and often virulent contention. Those who do not acquiesce to the theory that it is anthropogenic CO2 that is the culprit behind this temperature increase, we will call the nonanthropogenists (or NA's for brevity). This group, which clearly represents the minority scientific opinion 10 , utilize as a main weapon the argument that temperature leads CO2 in the climatic record. The principle of causality therefore, in their opinion, clearly points to the fact that it is some extra planetary source, (usually attributed to the solar flux) which is responsible for the undeniable global warming. For example, "The observation that two things have risen together for a period of time says nothing about one trend being the cause of the other. To establish a causal relationship it must be demonstrated that the presumed cause precedes the presumed effect" 1 . In other words, CO2 increases must precede temperature increases in order to prove anthropogenic forcing of the climate. The thrust of this article is to demonstrate, simply and parsimoniously, that the argument of causality, the 'precedes' issue, is irrelevant in the present debate. The temperature-CO2 cycle is a feedback cycle. Such mechanisms are always nonlinear and these nonlinearities may obliterate causality. We show this effect by way of a simple model-a model that mimics to some extent, the present day temperature-CO2 relationship. A related causality-correlation issue can be expressed by this often quoted statement, "Correlation does not prove causality, but non-correlation proves non-causality." 2 We discuss the fallacy of the second part of this statement, a discussion that should be of interest to all. We begin with the issue of lead-lag in the temperature record and follow by showing why the 'non-correlation=non-causality' statement is bogus. The Lead-Lag Dispute in Global Warming An excellent example of the debate between the NA's and the A's (the anthropogenists) is the recent congressional testimony of Al Gore