By William Menke
Please use extracts from experiences of first variation Key good points* up-to-date and punctiliously revised variation* extra fabric on geophysical/acoustic tomography* distinct dialogue of software of inverse thought to tectonic, gravitational and geomagnetic stories
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In regards to the ProductPublished by means of the yankee Geophysical Union as a part of the Geophysical Monograph sequence. content material:
Additional info for Geophysical Data Analysis: Discrete Inverse Theory
Noise causes the data to scatter about their mean value ( d ) . realization of the random variable will have a value in the neighborhood of d- the probability that the measurement is between d and d ad is P ( d ) dd (Fig. 2). We have used the partial derivative sign d only for the sake of clarity, to avoid adding another d to the notation. Since each measurement must have some value, the probability that d lies somewhere between -to and 00 is complete certainty (usually given the value of 100%or unity, which is written as + + The distribution completely describes the random variable.
It is appropriate to consider them deterministic quantities in some problems, and random variables in others. Estimates of the parameters, however, are always random variables. If the distribution of the data is known, then the distribution for any function of the data, including estimated model parameters, can be found. Consider two uncorrelated data that are known to have white distributions on the interval [0, I], that is, they can take on any value between 0 and 1 with equal probability (Fig.
The more complicated the distribution, the more difficult it is to chose an appropriate shape and calculate the probability within it. 1 The Lengths of Estimates The simplest of methods for solving the linear inverse problem Gm = d is based on measures of the size, or length, of the estimated model parameters mestand of the predicted data dPR = Gmest. To see that measures of length can be relevant to the solution of inverse problems, consider the simple problem of fitting a straight line to data (Fig.