The probability tomography approach developed for the scalar resistivity method is here extended to the 2D tensorial apparent resistivity acquisition mode. The rotational invariant derived from the trace of the apparent resistivity tensor is considered, since it gives on the datum plane anomalies confined above the buried objects. Firstly, a departure function is introduced as the difference be...

We survey recent results on the structure of the range of the derivative of a smooth mapping f between two Banach spaces X and Y . We recall some necessary conditions and some sufficient conditions on a subsetA of (X ,Y) for the existence of a Fréchet differentiable mapping f from X into Y so that f ′(X)= A. Whenever f is only assumed Gâteaux differentiable, new phenomena appear: for instance, ...

approximating the solution of differential equations of fractional order is necessary because fractional differential equations have extensively been used in physics, chemistry as well as engineering fields. in this paper with central difference approximation and newton cots integration formula, we have found approximate solution for a class of boundary value problems of fractional order. three...

potential field methods such as gravity and magnetic methods are among the most applied geophysical methods in mineral exploration. a high-resolution technique is developed to image geologic boundaries such as contacts and faults. potential field derivatives are the basis of many interpretation techniques. in boundary detection, the analytic signal quantity is defined by combining the val...

We prove a Lusternik-Schnirelmann type theorem for <em>C</em><sup>1</sup>- function φ : M → R, where is connected infinite dimensional Frechet manifold of class <em>C</em><sup>1</sup>. To this end, in context we the so-called Deformation Lemma and by using it derive result generalizing Minimax Principle.

Sparsity-promoting terms are incorporated into the objective functions of optimal control problems in order to ensure that controls vanish on large parts underlying domain. Typical candidates for those integral Lebesgue spaces based $\ell_p$-metric $p\in[0,1)$ which nonconvex as well non-Lipschitz and, thus, variationally challenging. In this paper, we derive exact formulas Frechet, limiting, a...

This paper presents a new traveltime inversion method based on the wave equation. In this new method, designated as wave-equation traveltime inversion (WT), seismograms are computed by any full-wave forward modeling method (we use a finitedifference method). The velocity model is perturbed until the traveltimes from the synthetic seismograms are best fitted to the observed traveltimes in a leas...

In this paper we discuss one dimensional scattering and inverse scattering for the Helmholtz equation on the half line from the point of view of the layer stripping. By full or nonlinear scattering, we mean the transformation between the index of refraction (actually half of its logarithmic derivative) and the reflection coefficient. We refer to this mapping as nonlinear scattering, because the...