A significant problem with exploring for electrically conductive mineral deposits with airborne electromagnetic (AEM) methods is that many of the most valuable sulphide deposits are too conductive to be detected with conventional systems. High-grade sulphide deposits with bulk electrical conductivities on the order of 100,000 S/m can appear as “perfect conductors” to most EM systems because the decay of secondary fields (the “time constant” of the deposit) generated in the target by the system transmitter takes much longer than the short measuring time of EM systems. Their EM response is essentially undetectable with off-time measurements. One solution is to make measurements during the transmitter on-time when the secondary field of the target produced by magnetic flux exclusion is large. The difficulty is that the secondary field must be measured in the presence of a primary field which is orders of magnitude larger. The goal of this thesis is to advance the methodology of making AEM measurements during transmitter on-time by analysing experimental data from three different AEM systems. The first system analysed is a very large separation, two helicopter system where geometry is measured using GPS sensors. In order to calculate the primary field at the receiver with sufficient accuracy, the very large (nominally 400 m) separation requires geometry to be known to better than 1 m. Using the measured geometry to estimate and remove the primary field, I show that a very conductive target can be detected at depths of 200m using the total secondary field. I then used fluxgate magnetometers to correct for receiver rotation which allowed the component of the secondary field to be determined. The second system I examined was a large separation fixed-wing AEM system. Using a towed receiver bird with a smaller (˜ 135m) separation, the geometry must be known much more accurately. In the absence of direct measurement of this geometry, I used a least-squares prediction approach using measurements of aircraft manoeuvres which allowed primary field contamination to be estimated. Subtracting this estimate from the recorded signal increased the maximum time constant observed in a field survey for conductive targets by a factor of seven. Finally, a study of a nominally rigid helicopter EM system employing a bucking coil to cancel primary field showed that system geometry (specifically, the position of the receiver coil relative to the transmitter and bucking coils) must be known to better than 0.01 mm to detect deep targets. Again, direct measurements of system geometry were not available. A least-squares prediction filter using helicopter manoeuvre and system pitch and roll measurements was applied, but was not able to estimate primary field well enough to provide an accurate secondary on-time response. Direct measurements of relative motion of the system components might solve this problem.

A significant problem with exploring for electrically conductive mineral deposits with airborne electromagnetic (AEM) methods is that many of the most valuable sulphide deposits are too conductive to be detected with conventional systems. High-grade sulphide deposits with bulk electrical conductivities on the order of 100,000 S/m can appear as “perfect conductors” to most EM systems because the decay of secondary fields (the “time constant” of the deposit) generated in the target by the system transmitter takes much longer than the short measuring time of EM systems. Their EM response is essentially undetectable with off-time measurements. One solution is to make measurements during the transmitter on-time when the secondary field of the target produced by magnetic flux exclusion is large. The difficulty is that the secondary field must be measured in the presence of a primary field which is orders of magnitude larger. The goal of this thesis is to advance the methodology of making AEM measurements during transmitter on-time by analysing experimental data from three different AEM systems. The first system analysed is a very large separation, two helicopter system where geometry is measured using GPS sensors. In order to calculate the primary field at the receiver with sufficient accuracy, the very large (nominally 400 m) separation requires geometry to be known to better than 1 m. Using the measured geometry to estimate and remove the primary field, I show that a very conductive target can be detected at depths of 200m using the total secondary field. I then used fluxgate magnetometers to correct for receiver rotation which allowed the component of the secondary field to be determined. The second system I examined was a large separation fixed-wing AEM system. Using a towed receiver bird with a smaller (˜ 135m) separation, the geometry must be known much more accurately. In the absence of direct measurement of this geometry, I used a least-squares prediction approach using measurements of aircraft manoeuvres which allowed primary field contamination to be estimated. Subtracting this estimate from the recorded signal increased the maximum time constant observed in a field survey for conductive targets by a factor of seven. Finally, a study of a nominally rigid helicopter EM system employing a bucking coil to cancel primary field showed that system geometry (specifically, the position of the receiver coil relative to the transmitter and bucking coils) must be known to better than 0.01 mm to detect deep targets. Again, direct measurements of system geometry were not available. A least-squares prediction filter using helicopter manoeuvre and system pitch and roll measurements was applied, but was not able to estimate primary field well enough to provide an accurate secondary on-time response. Direct measurements of relative motion of the system components might solve this problem.

[ES] El objetivo de esta tesis es estudiar distintas propiedades de los operadores de composición ponderados en diferentes espacios ponderados de funciones analíticas. Dado un peso v estrictamente positivo y continuo en el disco complejo, consideramos unos ciertos espacios de Banach de funciones analíticas en el discto complejo. Estos espacios son los conjuntos de las funciones holomorfas en el disco f tales que el supremo, de los z en el disco, de v(z)|f(z)| es finito. También consideramos los espacios de las funciones holorfas f que cumplen que v(z)|f(z)| tiende a cero cuando |z| se acerca a 1. Dada una sucesión de pesos, trabajamos con los espacios formados por las intersecciones y uniones de los espacios de Banach ponderados determinados por los pesos de la sucesión. El espacio resultante de la intersección es un espacio de Fréchet y es el límite proyectivo de los espacios de Banach citados. Este espacio está provisto de la topología del límite proyectivo. El espacio resultante de la unión es un espacio LB (límite de Banach), y es el límite inductivo de los espacios citados, con la topología del límite inductivo. Cuando la sucesión de pesos viene determinada por los pesos (1-|z|)^n con n natural, el espacio resultante de la unión se llama espacio de Korenblum, que también es un límite inductivo. En la tesis estudiamos la continuidad, compacidad e invertibilidad de los operadores de composición ponderados en los espacios descritos arriba. También estudiamos algunas propiedades de su espectro y de su espectro puntual. / [CA] L'objectiu d'aquesta tesi és estudiar distintes propietats dels operadors de composició ponderats en diferents espais ponderats de funcions analítiques. Donat un pes v estrictament positiu i continu en el disc del pla complex, considerem uns certs espais de Banach de funcions analítiques en el disc complex. Aquests espais són els conjunts de les funcions holomorfes en el disc f tals que el suprem, dels z en el disc, de v(z)|f(z)| és finit. També considerem els espai de les funcions que verifiquen que v(z)|f(z)| tendeix a zero quan |z| s'apropa a 1. Donada una successió de pesos, treballem amb els espais formats per les interseccions i unions dels espais de Banach ponderats determinats pels pesos de la successió. L'espai resultant de la intersecció és un espai de Fréchet, i és el límit projectiu dels espais de Banach esmentats. Aquest espai està prove ̈ıt de la topologia del l ́ımit projectiu. L'espai resultant de la unió és un espai LB (límit de Banach), i és el límit inductiu dels espais esmentats, amb la topologia del límit inductiu. Quan la successió de pesos està determinada pels pesos (1-|z|)^n amb n natural, l'espai resultant de la unió s'anomena espai de Korenblum, que també és un límit inductiu. En al tesi estudiem la continu ̈ıtat, , compacitat i invertibilitat de l'operador de composició ponderat en els espais descrits abans. També estudiem algunes propietats del seu espectre i del seu espectre puntual. / [EN] The aim of this thesis is to study some properties of the weighted composition operators on different weighted spaces of analytic functions. Given a weight v strictly positive and continuous on the complex disc, we consider certain Banach spaces of analytic functions on the complex disc. These spaces are the sets of the holomorphic functions on the disc f such that the supremum, when z is in the disc, of v(z)|f(z)| is finite. We also consider the spaces of the holomorphic functions f such that v(z)|f(z)| tends to 0 whenever |z| goes to 1. Given a sequence of weights, we work with the spaces described by the intersection or union of the weighted Banach spaces determined by the weights in the sequence. The space of the intersection is a Fréchet space and it is the projective limit of the mentioned Banach spaces. This space is endowed with the projective limit topology. The space given by the union is an LB-space (limit of Banach), and it is the inductive limit of the mentioned spaces, with the inductive limit topology. When the sequence is given by the weights (1-|z|)^n with n natural, the space of the union is called Korenblum space, which is also an inductive limit. In the thesis we study the continuity, compactness and invertibility of the weighted composition operators on the spaces described above. We also study some properties of the spectrum and point spectrum. / Gomez Orts, E. (2022). Weighted Composition Operators on Spaces of Analytic Functions [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/183028 / TESIS