razil finds itself in an advanced phase of the process of demographic transition. The shrinking of the base of the aging pyramid and the growth of its vertex are already noticeable. This essay intends to compare the migration flow figures of two distinct periods: 1995/200 and 2005/2010, in order to ascertain what kind of migration flows is occurring in this period, that could eventually explain some of its migration behavior.(Figures 1-7)

A new phenomena that concern these migratory fluctuations has been taken to note and has been the studies of various research projects in the academic environment: a decline in net migration rate from traditionally underdeveloped regions (mainly the northeast) to more industrialized regions (primarily the southeast).

This decline in the net migration rate can be partly explained by return migration. Considering that fact, it is of fundamental importance to know migratory patterns of the population so as to foresee the spatial redistribution of the population in general that will eventually result in the reformulation of social policy to better regionally allocate national resources.

Spatial analysis and GIS are widely used in order to study such events (Bailey and Gatrell, 1996). Specifically in this case, Tobler's approach is used (Tobler, 1976) for mapping the flows and, for the identification of migration patterns.

If a potential migrant is taken at random in a population sample and is "thrown in the air", there will be a general migration tendency that this person will follow. Tobler calls this tendency a "wind" (Tobler, 1976). He has focused on the difficulties associated with the symmetry of the gravity model and tried to remove this problem introducing the "wind" in order to account for interaction in particular directions. The approach facilitates the description of large flow matrices by analyzing the asymmetric part of the from-to-tables.

It is interesting to see that the antecedents of the approach were motivated by the calculation of geographical locations from data on separations or on interaction. The inversion of models was used: for example, the social gravity model can be written as:

The problem was that the social gravity model is symmetric, i. e, D ij = D ji and M ij must be equal to M ij . In practice the data are different (M ij ? M ji ). This would imply that if the model is inverted, D ij ? D ji .

He stated that has "the consequence that the tri-lateration solution can result in more than one geometrical configuration or that the standard errors of the position determination are increased" (Tobler, 1976. p. 2).

To overcome this problem, a "wind" was introduced in order to facilitate interaction in some direction. This vector is estimated by the data. In its formal aspect, each location i, with coordinates (x, y), has associated with a vector with magnitude and direction:

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. For the complete algebraic development, see Tobler (1979).

Sometimes we have an incomplete matrix for a set of data, so in order to overcome this situation a complete set of data is generated, using Baxter entropy program (Tobler, 1976). The program follows Wilson's derivations of the gravity model using entropymaximizing techniques. It has three variations and one can use a complete matrix or only the marginals as input. The program permits two variations with the gravity model or with the entropy model.

In the research described here we have used a

In the comparison of the data migration between the periods of 1995/2000 and 2005/2010 for the Northern region, the States of Rondônia, Amazonas, Roraima, Amapá and Tocantins continued to receive immigrants, showing a positive balance for both periods, with the exception of the States of Acre and Pará that continued to show a negative balance, but with a significant decrease in the number of emigrants in the comparison between the two periods considered.

In the Northeast region it was observed a quite expressive negative balance for almost all States, especially for the States of Bahia and Maranhão, who contributed with significant numbers of emigrants by repeating the tendency observed in the 1995/2000 period, without major modifications. The States of Piauí, Ceará and Alagoas kept negative figures, but decreased their numbers in absolute values for both periods, perhaps showing some modification in their migratory pattern, which should be better measured in the future. Only the States of Sergipe and Rio Grande do Norte presented a positive migratory balance, perhaps due to new investments in the tourism sector, typical of these States.

In the Southeast region the negative highlights went to the State of Minas Gerais, which was the only one to make a considerable change in its demographic profile presenting, in the 1995/2000 period, an expressive number of immigrants, but in the period 2005/2010 presented a negative number in its migratory balance. The State of Espírito Santo showed a significant increase of immigrants, nearly doubling its values of the previous decade, probably due to the new investments in oil extraction and in agribusiness. The States of Rio de Janeiro and São Paulo also presented a positive migratory balance, but with much smaller values than the previous decade, perhaps explained by the so called return migration, which has been shown to be significant in Brazil in the past two decades.

In the Southern region the Santa Catarina State occupies a prominent position showing an expressive positive migratory balance, almost tripling the number of immigrants in the last decade. The States of Paraná and Rio Grande do Sul have maintained the tendency of negative balances in the last two decades, but the State of Rio Grande do Sul, presented an even more expressive negative balance for the last evaluated period.

All This decrease is also well perceived in interregional migration. According to the 2000 Census, 3.3 million people had changed regions in the five previous years. The national survey samples (PNAD) of 2004 already shows a reduction to 2.8 million. Finally, the National Household Survey of 2009 shows that just over 2 million people had chosen another region to live.

In the South, the States of Paraná and Rio Grande do Sul perceived a considerable flow of return migration, while Santa Catarina is the southern State that attracts more new immigrants -its current migratory balance is 80 thousand immigrants. The same process can be observed in the Midwestern region, being the region that more retains its immigrants. According to the 2009 PNAD, in absolute terms, São Paulo remains as the State that receives more immigrants (535.000), followed by Minas Gerais (288.000), Goiás (264.000) Bahia and Paraná (both with 203.000 new immigrants). On the other hand, São Paulo is also the place that Migration Flows in Brazil: A Spatial Analysis using Tobler´S Approach generates more emigrants (588.000), followed by Bahia (312.000), Minas Gerais (276.000), Paraná (171.000) and Rio de Janeiro (165.000). (Figures 1-3).