Uma investigação histórica sobre os logaritmos com sugestões didáticas para a sala de aula

This study was conducted from a preliminary research to identify the conceptual and didactic approach to the logarithms given in the main textbooks adopted by the Mathematics teachers in state schools in the School of Natal, in Rio Grande do Norte. I carried out an historical investigation of the logarithms in order to reorient the math teacher to improve its educational approach this subject in the classroom. Based on the research approach I adopted a model of the log based on three concepts: the arithmetic, the geometric and algebraic-functional. The main objective of this work is to redirect the teacher for a broad and significant understanding of the content in order to overcome their difficulties in the classroom and thus realize an education that can reach the students learning. The investigative study indicated the possibility of addressing the logarithms in the classroom so transversalizante and interdisciplinary. In this regard, I point to some practical applications of this matter are fundamental in the study of natural phenomena as earthquakes, population growth, among others. These practical applications are connected, approximately, Basic Problematization Units (BPUs) to be used in the classroom. In closing, I offer some activities that helped teachers to understand and clarify the meaningful study of this topic in their teaching practice

Uma sequência didática a partir da temática terremotos com ênfase em CTS

Throughout its history the population of the region of Mato Grande, which includes the city of João Câmara, in Rio Grande do Norte, was subject to earthquakes. These events are caused by a geological fault, known as fault Samambaia. In the 1980s there was an intensification of this phenomenon culminating in an earthquake 5.1 on the Richter scale in the early hours of November 30, 1986, causing researchers from Brazil and other countries to shift to the region to conduct research in Seismology. During this period there was a strong interaction between scientists and local people. With the aim of studying how people experienced that moment that marked the history of the city of João Câmara, from interviews with some individuals who witnessed the incident, is that this research was developed. Taking as a theoretical approach to Science, Technology and Society (STS), aimed to thus carry the theme in a systematic way to the classroom, promoting ways to help teachers with the scientific training and guidance to students in case of occurrence of earthquakes

Caracterização estatística de processos sísmicos via Distribuição Generalizada de Pareto. Estudo de caso: João Câmara-RN

The work is to make a brief discussion of methods to estimate the parameters of the Generalized Pareto distribution (GPD). Being addressed the following techniques: Moments (moments), Maximum Likelihood (MLE), Biased Probability Weighted Moments (PWMB), Unbiased Probability Weighted Moments (PWMU), Mean Power Density Divergence (MDPD), Median (MED), Pickands (PICKANDS), Maximum Penalized Likelihood (MPLE), Maximum Goodness-of-fit (MGF) and the Maximum Entropy (POME) technique, the focus of this manuscript. By way of illustration adjustments were made for the Generalized Pareto distribution, for a sequence of earthquakes intraplacas which occurred in the city of João Câmara in the northeastern region of Brazil, which was monitored continuously for two years (1987 and 1988). It was found that the MLE and POME were the most efficient methods, giving them basically mean squared errors. Based on the threshold of 1.5 degrees was estimated the seismic risk for the city, and estimated the level of return to earthquakes of intensity 1.5°, 2.0°, 2.5°, 3.0° and the most intense earthquake never registered in the city, which occurred in November 1986 with magnitude of about 5.2º

Estudo da atividade sísmica em São Caetano-PE em 2007

In this dissertation we studied the seismic activity in the São Caetano county, Pernambuco State, Northeastern Brazil, located near the Pernambuco Lineament. The Pernambuco Lineament is a one of Neoproterozoic continental-scale shear zones that deforms the Borborema province. The seismicity estudied occurred in a NE trending branch of Pernambuco Lineament. The seismic activity in São Caetano started in 2006 and in May 20th, 2006 a 4,0 mb earthquake hit there. This was the largest earthquake ever reported in Pernambuco State. This dissertation is the result of a campaign done in the period from Februay 1th 2007 to July 31 th 2007. In this campaign up to nine three-component digital seismographic stations were deployed and the collected data was used to determine hypocenters and focal mechanism. A total of 214 earthquakes, recorded at least by three stations, were analyzed. To determine hypocenters and time origin the HYPO71 program was used assuming a half-space model with parameters : VP (P-wave velocity) equal to 5.90 km/s and the ratio VP/VS 1.70, where VS is the S-wave velocity. The earthquakes hypocentral distribution was approximately 4 km long and agrees with the NE-SW direction of the Pernambuco Lineamento branch. Hypocentres depth range from 2 to 8 km. The composed focal mechanism was made from a group of 14 selected earthquakes. We try firstly to find the fault plane solution matching the polarity distribution at stations, using the FPFIT program. The result was 43 deg ± 15 deg for strike, 59 deg ± 9 deg for dip and -142 deg ± 15 deg for rake. We also fitted a plane using the hypocentral distribution to obtain the dip and azimuth of the hypocentral distribution. The results obtained by this fit were 58 deg for the azimuth, 55 deg for the dip and -155 deg for rake. This result shows a mechanism of a strike-slip dextral fault with a normal component. This dissertation shows, once more, that there is a good correlation between the seismic activity and geological features in the region near the Pernambuco Lineament and its NE branches

Parâmetros de fonte de microterremotos em Cascavel-CE

In this dissertation it was studied the rupture characteristic of earthquakes of the Town of Cascavel CE, Northeastern Brazil. Located on the border of the Potiguar Basin, the Town of Cascavel is one of the most seismically active intraplate areas in the country. In this town, on November 20th, 1980 a 5,2mb earthquake occurred. This was the largest earthquake ever reported in Northeast Brazil. Studies of this region using instruments were possible after 1989, with several campaigns being done using seismographic networks. From the beginning of the monitoring to April 2008 more than 55,000 events were recorded. With the data collected by a network with six 3-components digital seismographic stations during the campaigns done from September 29th, 1997 to March 5th, 1998, estimates of source parameters were found fitting the displacement spectra in the frequency domain for each event. From the fitting of the displacement spectra it was possible to obtain the corner frequency ( ) c f and long period amplitude ( ) W0 . Source parameters were determined following Brune (1970) and Madariaga (1976) models. Twenty-one seismic events were analyzed (0.7 £ £ 2.1) b m in order to estimate the source dimension (r ), seismic moment ( ) M0 , static stress drop (Ds ), apparent stress ( ) a s , seismic energy ( ) S E and moment magnitude ( ) W M for each of the events. It was observed that the ratio between radiated seismic energy and moment seismic (apparent stress) increases with increasing moment and hence magnitude at the observed range. As suggested by Abercrombie (1995), also in this work there is a breakdown in the scaling for earthquakes with magnitudes smaller than three ( < 3.0) W M , so that the rupture physics is different for larger events. If this assumption is valid, the earthquakes analyzed in this work are not selfsimilar. Thus, larger events tend to radiated more energy per unit area than smaller ones.

Estudo sísmico no açude Tucunduba, Senador Sá, CE

The Tucunduba Dam, is west of Fortaleza, Ceará State. The seismic monitoring of the area, with an analogical station and seven digital stations, had beginning on June 11, 1997. The digital stations, operated from June to November 1997. The data collected in the period of digital monitoring was analyzed for determination of hypocenters, focal mechanisms, and shear-wave anisotropy analysis. For determination of hypocenters, it was possible to find an active zone of nearly 1 km in length, with depth between 4.5 and 5.2 km. A 60AZ/88SE fault plane was determined using the least-squares method and hypocenters of a selected set of 16 earthquakes recorded. Focal mechanisms were determined, in the composite fault plane solution, a strike-slip fault, trending nearly E-W, was found. Single fault plane solutions were obteined to some earthquakes presented mean values of 65 (azimuth), and 80 (dip). Shear-wave anisotropy was found in the data. Polarization directions and travel time delays, between S spliting waves, were determined. It was not possible to obtain any conclusion on the cause of the observed anisotropy. It is not clear if there is correlation between seismicity and mapped faults in the area, although the directions obtained starting from the hipocentros and focal mechanism are they are consistent with directions, observed in the area, photo, topographic and fractures directions observed in the area

Estudoda sismicidade na região de Sobral - CE em 2008

The town of Sobral is located at the northwest part of the Ceará State, 250 km away from its capital, Fortaleza. In January 2008, an intense seismic activity began near Sobral with one event with magnitude 4,2mb on May 21. Since the start of its seismic activity, all events were recorded by the SBBR station (located on EMBRAPA Caprinos Farm), which operates in the region since August 2007. After this event, monitoring the seismic activity was carried out with the deployment of a local three component digital seismographic network, from June 5, 2008 until September 24. Initially, this network was composed of six seismographic stations. Later additional five stations were deployed until August 26 2008. This local network detected approximately 2,800 earthquakes. In this study we analyzed 581 earthquakes recorded by at least three stations for hypocentral and focal mechanism determination, and to contribute to a better explanation of the seismicity which in this region. To determine the hypocenters, we used a half-space model, with vP = 6,00 km/s and vP/vS = 1,71. From the hypocentral determination, it was revealed an active seismic zone with depth ranging between 1 and 8 km, 6 km long in E - W direction. The determination of fault planes and focal mechanism was obtained using the programs FPFIT and PLAN, which allowed comparison between their respective results in order to obtain more accurate results. A set of 24 earthquakes were selected to determine fault using PLAN planes and focal mechanisms using FPFIT. With the aid of detailed map of hypocenters this set, it was possible to identify three structures. Therefore, the set of 24 earthquakes were divided into three subsets. The type of mechanism was predominantly strike-slip with a dextral direction. Although the region has two tectonic structures near the site of the study area: the Café- Ipueiras Fault (normal fault) and the Sobral-Pedro II Lineament (dextral strike-slip fault) it was not possible to correlate the seismicity founded with those structures

Metodologia para implantação de um sistema de disposição de rejeitos em minério de ferro na região do semiárido: estudo de caso

Tailings dams are structures that aims to retain the solid waste and water from mining processes. Its analysis and planning begins with searching of location for deployment, step on which to bind all kinds of variables that directly or indirectly influence the work, such as geological, hydrological, tectonic, topographic, geotechnical, environmental, social characteristics, evaluation security risks, among others. Thus, this paper aims to present a study on the most appropriate and secure type of busbar to design a layout structure of iron ore tailings, taking into account all the above mentioned variables. The case study involves the assessment of sites for location of dams of tailings disposal beneficiation of iron mine to be built in Bonito, in the municipality of Jucurutu in Seridó Potiguar. For site selection among alternatives, various aspects of the current state of the art were considered, one that causes the least environmental impact, low cost investment, adding value to the product and especially the safety of the implanted structure mitigates the concern about induced earthquakes as a result of liquefaction wastes somatized by dams in the region, as the tilling of Mina Bonito is located practically in the hydraulic basin dam Armando Ribeiro in environmental protection (APA). The methodology compares induced by dams in the semiarid region with the characteristics of the waste disposal and sterile seismicity, taking into account the enhancement of liquefaction by the action of seismicity in the Mina Bonito region. With the fulcrum in the methodology, we indicated the best busbar type for disposal of tailings from iron ore or combination of them, to be designed and built in semiarid particularly for Mina Bonito. Also presents a number of possible uses for the tailings and in engineering activities, which may cause processing to the common good.

Estudo da estrutura subsuperficial da província Borborema com correlação de ruído sísmico

Ambient seismic noise has traditionally been considered as an unwanted perturbation in seismic data acquisition that "contaminates" the clean recording of earthquakes. Over the last decade, however, it has been demonstrated that consistent information about the subsurface structure can be extracted from cross-correlation of ambient seismic noise. In this context, the rules are reversed: the ambient seismic noise becomes the desired seismic signal, while earthquakes become the unwanted perturbation that needs to be removed. At periods lower than 30 s, the spectrum of ambient seismic noise is dominated by microseism, which originates from distant atmospheric perturbations over the oceans. The microsseism is the most continuous seismic signal and can be classified as primary – when observed in the range 10-20 s – and secondary – when observed in the range 5-10 s. The Green‘s function of the propagating medium between two receivers (seismic stations) can be reconstructed by cross-correlating seismic noise simultaneously recorded at the receivers. The reconstruction of the Green‘s function is generally proportional to the surface-wave portion of the seismic wavefield, as microsseismic energy travels mostly as surface-waves. In this work, 194 Green‘s functions obtained from stacking of one month of daily cross-correlations of ambient seismic noise recorded in the vertical component of several pairs of broadband seismic stations in Northeast Brazil are presented. The daily cross-correlations were stacked using a timefrequency, phase-weighted scheme that enhances weak coherent signals by reducing incoherent noise. The cross-correlations show that, as expected, the emerged signal is dominated by Rayleigh waves, with dispersion velocities being reliably measured for periods ranging between 5 and 20 s. Both permanent stations from a monitoring seismic network and temporary stations from past passive experiments in the region are considered, resulting in a combined network of 33 stations separated by distances between 60 and 1311 km, approximately. The Rayleigh-wave, dispersion velocity measurements are then used to develop tomographic images of group velocity variation for the Borborema Province of Northeast Brazil. The tomographic maps allow to satisfactorily map buried structural features in the region. At short periods (~5 s) the images reflect shallow crustal structure, clearly delineating intra-continental and marginal sedimentary basins, as well as portions of important shear zones traversing the Borborema Province. At longer periods (10 – 20 s) the images are sensitive to deeper structure in the upper crust, and most of the shallower anomalies fade away. Interestingly, some of them do persist. The deep anomalies do not correlate with either the location of Cenozoic volcanism and uplift - which marked the evolution of the Borborema Province in the Cenozoic - or available maps of surface heat-flow, and the origin of the deep anomalies remains enigmatic.

Utilização de sismos regionais para a determinação de um modelo 1D de velocidades da onda P na Província Borborema - NE do Brasil

In this work it was performed a study to obtain parameters for an 1D regional velocity model for the Borborema Province, NE Brazil. It was used earthquakes occurred between 2001 and 2013 with magnitude greater than 2.9 mb either from epicentres determined from local seismic networks or by back azimuth determination, when possible. We chose seven events which occurred in the main seismic areas in the Borborema Province. The selected events were recorded in up to 74 seismic stations from the following networks: RSISNE, INCT-ET, João Câmara – RN, São Rafael – RN, Caruaru - PE, São Caetano - PE, Castanhão - CE, Santana do Acarau - CE, Taipu – RN e Sobral – CE, and the RCBR (IRIS/USGS—GSN). For the determination of the model parameters were inverted via a travel-time table and its fit. These model parameters were compared with other known model (global and regional) and have improved the epicentral determination. This final set of parameters model, we called MBB is laterally homogeneous with an upper crust at 11,45 km depth and total crustal thickness of 33,9 km. The P-wave velocity in the upper crust was estimated at 6.0 km/s and 6.64 km/s for it lower part. The P-wave velocity in the upper mantle we estimated at 8.21 km/s with an VP/VS ratio of approximately 1.74.

Utilização de sismos regionais para a determinação de um modelo 1D de velocidades da onda P na Província Borborema - NE do Brasil

In this work it was performed a study to obtain parameters for an 1D regional velocity model for the Borborema Province, NE Brazil. It was used earthquakes occurred between 2001 and 2013 with magnitude greater than 2.9 mb either from epicentres determined from local seismic networks or by back azimuth determination, when possible. We chose seven events which occurred in the main seismic areas in the Borborema Province. The selected events were recorded in up to 74 seismic stations from the following networks: RSISNE, INCT-ET, João Câmara – RN, São Rafael – RN, Caruaru - PE, São Caetano - PE, Castanhão - CE, Santana do Acarau - CE, Taipu – RN e Sobral – CE, and the RCBR (IRIS/USGS—GSN). For the determination of the model parameters were inverted via a travel-time table and its fit. These model parameters were compared with other known model (global and regional) and have improved the epicentral determination. This final set of parameters model, we called MBB is laterally homogeneous with an upper crust at 11,45 km depth and total crustal thickness of 33,9 km. The P-wave velocity in the upper crust was estimated at 6.0 km/s and 6.64 km/s for it lower part. The P-wave velocity in the upper mantle we estimated at 8.21 km/s with an VP/VS ratio of approximately 1.74.

Medium change monitoring using ambient seismic noise and coda wave interferometry: examples from intraplate NE Brazil and the Mid-Atlantic Ridge

This thesis presents and discusses the results of ambient seismic noise correlation for two different environments: intraplate and Mid-Atlantic Ridge. The coda wave interferometry method has also been tested for the intraplate data. Ambient noise correlation is a method that allows to retrieve the structural response between two receivers from ambient noise records, as if one of the station was a virtual source. It has been largely used in seismology to image the subsurface and to monitor structural changes associated mostly with volcanic eruptions and large earthquakes. In the intraplate study, we were able to detect localized structural changes related to a small earthquake swarm, which main event is mR 3.7, North-East of Brazil. We also showed that the 1-bit normalization and spectral whitening result on the loss of waveform details and that the phase auto-correlation, which is amplitude unbiased, seems to be more sensitive and robust for our analysis of a small earthquake swarm. The analysis of 6 months of data using cross-correlations detect clear medium changes soon after the main event while the auto-correlations detect changes essentially after 1 month. It could be explained by fluid pressure redistribution which can be initiated by hydromechanical changes and opened path ways to shallower depth levels due to later occurring earthquakes. In the Mid-Atlantic Ridge study, we investigate structural changes associated with a mb 4.9 earthquake in the region of the Saint Paul transform fault. The data have been recorded by a single broadband seismic station located at less than 200 km from the Mid-Atlantic ridge. The results of the phase auto-correlation for a 5-month period, show a strong co-seismic medium change followed by a relatively fast post-seismic recovery. This medium change is likely related to the damages caused by the earthquake’s ground shaking. The healing process (filling of the new cracks) that lasted 60 days can be decomposed in two phases, a fast recovery (70% in ~30 days) in the early post-seismic stage and a relatively slow recovery later (30% in ~30 days). In the coda wave interferometry study, we monitor temporal changes of the subsurface caused by the small intraplate earthquake swarm mentioned previously. The method was first validated with synthetics data. We were able to detect a change of 2.5% in the source position and a 15% decrease of the scatterers’ amount. Then, from the real data, we observed a rapid decorrelation of the seismic coda after the mR 3.7 seismic event. This indicates a rapid change of the subsurface in the fault’s region induced by the earthquake.

Medium change monitoring using ambient seismic noise and coda wave interferometry: examples from intraplate NE Brazil and the Mid-Atlantic Ridge

This thesis presents and discusses the results of ambient seismic noise correlation for two different environments: intraplate and Mid-Atlantic Ridge. The coda wave interferometry method has also been tested for the intraplate data. Ambient noise correlation is a method that allows to retrieve the structural response between two receivers from ambient noise records, as if one of the station was a virtual source. It has been largely used in seismology to image the subsurface and to monitor structural changes associated mostly with volcanic eruptions and large earthquakes. In the intraplate study, we were able to detect localized structural changes related to a small earthquake swarm, which main event is mR 3.7, North-East of Brazil. We also showed that the 1-bit normalization and spectral whitening result on the loss of waveform details and that the phase auto-correlation, which is amplitude unbiased, seems to be more sensitive and robust for our analysis of a small earthquake swarm. The analysis of 6 months of data using cross-correlations detect clear medium changes soon after the main event while the auto-correlations detect changes essentially after 1 month. It could be explained by fluid pressure redistribution which can be initiated by hydromechanical changes and opened path ways to shallower depth levels due to later occurring earthquakes. In the Mid-Atlantic Ridge study, we investigate structural changes associated with a mb 4.9 earthquake in the region of the Saint Paul transform fault. The data have been recorded by a single broadband seismic station located at less than 200 km from the Mid-Atlantic ridge. The results of the phase auto-correlation for a 5-month period, show a strong co-seismic medium change followed by a relatively fast post-seismic recovery. This medium change is likely related to the damages caused by the earthquake’s ground shaking. The healing process (filling of the new cracks) that lasted 60 days can be decomposed in two phases, a fast recovery (70% in ~30 days) in the early post-seismic stage and a relatively slow recovery later (30% in ~30 days). In the coda wave interferometry study, we monitor temporal changes of the subsurface caused by the small intraplate earthquake swarm mentioned previously. The method was first validated with synthetics data. We were able to detect a change of 2.5% in the source position and a 15% decrease of the scatterers’ amount. Then, from the real data, we observed a rapid decorrelation of the seismic coda after the mR 3.7 seismic event. This indicates a rapid change of the subsurface in the fault’s region induced by the earthquake.

Estudo da sismicidade na barragem do Açu no período de 2012 a 2013

The seismic activity in the Northeastern of Brazil has been a constant target of study, since it is the most active region of the country. However, some areas have their earthquakes related to human action, what means they are induced. The Açu dam is a classic example of reservoir-induced seismicity and it has been the subject of several studies. Recently, after a considerable period of inactivity, the LabSis / UFRN recorded events related to the dam, which led to the installation of a network around the reservoir. From the data provided by this network, it was observed that the seismic activity is related to a new epicental area inside the lake. The epicentral parameters and the focal mechanism were determined. It was found that the events were related to the reactivation of a basement structure in a new seismogenic subvertical fault with NE-SW-striking subparallel to the São Rafael Fault. These results were used in the preparation of a scientific paper, which discussed the relationship between this seismicity with the geology of the region and with the reservoir water level. The paper showed that the diffusion of pore pressure was the main mechanism that controlled the triggering of the induced seismicity at the reservoir.

Estudo da sismicidade na barragem do Açu no período de 2012 a 2013

The seismic activity in the Northeastern of Brazil has been a constant target of study, since it is the most active region of the country. However, some areas have their earthquakes related to human action, what means they are induced. The Açu dam is a classic example of reservoir-induced seismicity and it has been the subject of several studies. Recently, after a considerable period of inactivity, the LabSis / UFRN recorded events related to the dam, which led to the installation of a network around the reservoir. From the data provided by this network, it was observed that the seismic activity is related to a new epicental area inside the lake. The epicentral parameters and the focal mechanism were determined. It was found that the events were related to the reactivation of a basement structure in a new seismogenic subvertical fault with NE-SW-striking subparallel to the São Rafael Fault. These results were used in the preparation of a scientific paper, which discussed the relationship between this seismicity with the geology of the region and with the reservoir water level. The paper showed that the diffusion of pore pressure was the main mechanism that controlled the triggering of the induced seismicity at the reservoir.