Abstract:
we re-derive the solution for scattering and diffraction of elastic waves by a single spherical obstacle. a complete catalog for the coefficients in the series' expansions of scattered waves is presented. the classical solution is a superposition of incident and diffracted fields. plane p- or s-waves are assumed. they are expressed as expansions of spherical wave functions which are tested against exact results. the diffracted field is calculated from the analytical enforcing of boundary conditions at the scatterer-matrix interface. the spherical obstacle is a cavity, an elastic inclusion or a fluid-filled zone. a complete set of wave functions is given in terms of spherical bessel and hankel radial functions. legendre and trigonometric functions are used for the angular coordinates. results are shown in time and frequency domains. diffracted displacement amplitudes versus normalized frequency and radiation patterns at low, intermediate and high frequencies are reported. synthetic seismograms for some relevant cases are computed.

Abstract:
We re-derive the solution for scattering and diffraction of elastic waves by a single spherical obstacle. A complete catalog for the coefficients in the series’ expansions of scattered waves is presented. The classical solution is a superposition of incident and diffracted fields. Plane P- or S-waves are assumed. They are expressed as expansions of spherical wave functions which are tested against exact results. The diffracted field is calculated from the analytical enforcing of boundary conditions at the scatterer-matrix interface. The spherical obstacle is a cavity, an elastic inclusion or a fluid-filled zone. A complete set of wave functions is given in terms of spherical Bessel and Hankel radial functions. Legendre and trigonometric functions are used for the angular coordinates. Results are shown in time and frequency domains. Diffracted displacement amplitudes versus normalized frequency and radiation patterns at low, intermediate and high frequencies are reported. Synthetic seismograms for some relevant cases are computed.

Abstract:
we study the multiple scattering of elastic waves by a finite linear array of regularly distributed cylindrical obstacles. the transient response of the system for incident anti-plane shear waves is given in detail. we present an extension of an original solution for rigid cylinders, developed by some of us in 1983. the solution is formally obtained for harmonic excitation and fourier analysis provides the transient response. material properties of the cylindrical inclusions are considered. a 2-d formulation is constructed by superposition of the incident field upon the waves diffracted by each obstacle. the solutions for each obstacle are constructed as expansions of cylindrical wave functions, after imposing continuity conditions for the displacements and tractions at the scatterers matrix interfaces with the aid of graf's addition theorem. thus, the total field can be referred to any cylindrical coordinates. the infinite system is approximated by a finite one and numerical results are obtained for different values of the parameters. various cases of cavities and inclusions are studied. a double effect is produced by different filling materials, f. e. amplification at the incidence side and reductions at the far side, or vice versa. synthetic seismograms and snapshots are computed to illustrate the complex features of wave propagation for this inhomogeneous model.

Abstract:
several crack configurations are considered in order to show the importance of the cracks' geometry on the rayleigh-wave propagation. we use the indirect boundary element method, this numerical technique is based on an integral representation of the diffracted wave field, which has been reduced from somigliana's identity. the method allows us to evaluate the complete displacement field by the superposition of the free field and the diffracted field. it is remarkable that the free field is specified as incident rayleigh- waves, making the assumption of absence of cracks. the diffracted field is obtained from the integral representation by means of the presence of cracks. our results are compared with those previously published. we emphasize the amplitude reduction of rayleigh- waves while the interaction with the cracks take place. conspicuous wave amplification at the crack neighborhood is observed immediately after such interaction. this information may give us a way to characterize crack's depth and orientations from the analysis of the diffracted field.

Abstract:
an analytic formulation oriented to understand the diffraction, dispersion and attenuation of borehole propagation modes is presented. the main aim of this article is to report to the scientific community the fundamentals of the seismic response at the well neighborhood, excited by an internal point source and present novelty simulation results compared against real data. an important, but not widely exploited technique to carefully investigate the elastic wave propagation in petroleum wells is the logging of sonic waveforms. the appropriate treatment and adequate processing of such microseismograms allow the extraction of useful information to characterize and understand the rock formation and is crucial on taking of decisions in the hydrocarbon production chain. in this work, the study of borehole wave propagation is based in the performing numerical simulations with the so-called discrete wave-number method applied to various cases of representative wells in mexican reservoirs. the contributions of this investigation are: (1) to evince in the seismograms the strong effect of diffraction and dispersion of elastic waves, even working with the homogeneous isotropic case, (2) to describe in frequency and time domains, the propagation of waves generated by a point source in a cylindrical borehole filled with fluid, and 3) to compare controlled simulation results versus real data from geophysical logs. to validate our computations, time histories and dispersion curves are compared with down-hole sonic waveforms for several types of lithologies. the set of results reported here may be helpful for understanding and predicting the effects produced by the presence of fractures and heterogeneities over the wave propagation. it is expected that in the near future, mathematical modeling of sonic waveform logs can be established as a trustworthy technique.

Abstract:
Several crack configurations are considered in order to show the importance of the cracks’ geometry on the Rayleigh-wave propagation. We use the Indirect Boundary Element Method, this numerical technique is based on an integral representation of the diffracted wave field, which has been reduced from Somigliana′s identity. The method allows us to evaluate the complete displacement field by the superposition of the free field and the diffracted field. It is remarkable that the free field is specified as incident Rayleigh- waves, making the assumption of absence of cracks. The diffracted field is obtained from the integral representation by means of the presence of cracks. Our results are compared with those previously published. We emphasize the amplitude reduction of Rayleigh- waves while the interaction with the cracks take place. Conspicuous wave amplification at the crack neighborhood is observed immediately after such interaction. This information may give us a way to characterize crack’s depth and orientations from the analysis of the diffracted field.

Abstract:
We study the multiple scattering of elastic waves by a finite linear array of regularly distributed cylindrical obstacles. The transient response of the system for incident anti-plane shear waves is given in detail. We present an extension of an original solution for rigid cylinders, developed by some of us in 1983. The solution is formally obtained for harmonic excitation and Fourier analysis provides the transient response. Material properties of the cylindrical inclusions are considered. A 2-D formulation is constructed by superposition of the incident field upon the waves diffracted by each obstacle. The solutions for each obstacle are constructed as expansions of cylindrical wave functions, after imposing continuity conditions for the displacements and tractions at the scatterers matrix interfaces with the aid of Graf’s addition theorem. Thus, the total field can be referred to any cylindrical coordinates. The infinite system is approximated by a finite one and numerical results are obtained for different values of the parameters. Various cases of cavities and inclusions are studied. A double effect is produced by different filling materials, f. e. amplification at the incidence side and reductions at the far side, or vice versa. Synthetic seismograms and snapshots are computed to illustrate the complex features of wave propagation for this inhomogeneous model.

Abstract:
Evaluating the proportion in which waters from different origins are mixed in a given water sample is relevant for many hydrogeological problems, such as quantifying total recharge, assessing groundwater pollution risks, or managing water resources. Our work is motivated by urban hydrogeology, where waters with different chemical signature can be identified (losses from water supply and sewage networks, infiltration from surface runoff and other water bodies, lateral aquifers inflows, ...). The relative contribution of different sources to total recharge can be quantified by means of solute mass balances, but application is hindered by the large number of potential origins. Hence, the need to incorporate data from a large number of conservative species, the uncertainty in sources concentrations and measurement errors. We present a methodology to compute mixing ratios and end-members composition, which consists of (i) Identification of potential recharge sources, (ii) Selection of tracers, (iii) Characterization of the hydrochemical composition of potential recharge sources and mixed water samples, and (iv) Computation of mixing ratios and reevaluation of end-members. The analysis performed in a data set from samples of the Barcelona city aquifers suggests that the main contributors to total recharge are the water supply network losses (22%), the sewage network losses (30%), rainfall, concentrated in the non-urbanized areas (17%), from runoff infiltration (20%), and the Besòs River (11%). Regarding species, halogens (chloride, fluoride and bromide), sulfate, total nitrogen, and stable isotopes (18O, 2H, and 34S) behaved quite conservatively. Boron, residual alkalinity, EDTA and Zn did not. Yet, including these species in the computations did not affect significantly the proportion estimations.

Abstract:
Evaluating the proportion in which waters from different origins are mixed in a given water sample is relevant for many hydrogeological problems, such as quantifying total recharge, assessing groundwater pollution risks, or managing water resources. Our work is motivated by urban hydrogeology, where waters with different chemical signature can be identified (losses from water supply and sewage networks, infiltration from surface runoff and other water bodies, lateral aquifers inflows, ...). The relative contribution of different sources to total recharge can be quantified by means of solute mass balances, but application is hindered by the large number of potential origins. Hence, the need to incorporate data from a large number of conservative species, the uncertainty in sources concentrations and measurement errors. We present a methodology to compute mixing ratios and end-members composition, which consists of (i) Identification of potential recharge sources, (ii) Selection of tracers, (iii) Characterization of the hydrochemical composition of potential recharge sources and mixed water samples, and (iv) Computation of mixing ratios and reevaluation of end-members. The analysis performed in a data set from samples of the Barcelona city aquifers suggests that the main contributors to total recharge are the water supply network losses (22%), the sewage network losses (30%), rainfall, concentrated in the non-urbanized areas (17%), from runoff infiltration (20%), and the Besòs River (11%). Regarding species, halogens (chloride, fluoride and bromide), sulfate, total nitrogen, and stable isotopes (18O2H, and 34S) behaved quite conservatively. Boron, residual alkalinity, EDTA and Zn did not. Yet, including these species in the computations did not affect significantly the proportion estimations.

Abstract:
this research aimed at determining the most striking leadership characteristics of teachers in the first stage of basic education. it employed the bass and avolio (1991 b) instrument, which makes it possible to distinguish among three constructs: the transformational leader, the transactional leader, and the laisser faire leader. the instrument is an adaptation consisting of 87 items in two formats: one for self-evaluation, to be filled out by the teacher, and another to be filled by the student who will appraise his/her teacher. the present study is oriented by its objectives toward a case study method. a study was carried out among the "a" and "b" section third grade teachers at maría inmaculada school, and their students. this institution actively participates in the pedagogical projects stipulated in the national basic curriculum (education ministry, 1998). the highest frequency of behaviors was found to be related to the presence of transformational leader-type teachers, and teachers of this kind were found to inspire trust and respect, according to the children's opinion, and to induce commitment in the teachers' judgment. both of these features are consistent with what is to be expected of an effective transformational leader.