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A large number of Rayleigh wave dispersion curves recorded at twenty three seismic stations was used to investigate the 3-D shear wave velocity structure of the northeastern Brazilian lithosphere. A simple procedure to generate a three-dimensional image of Mohorovi
ci
c； discontinuity was applied in northeastern Brazil and the Moho 3-D image was in agreement with several isolated crustal thicknesses obtained with different geophysical methods. A detailed 3-D S wave velocity model is proposed for the region. In the crust, our model is more realist than CRUST2.0 global model, because it shows more details either laterally or in depth than global model,
*i*.
*e*., clear lateral variation and gradual increase of S wave velocity in depth. Down to 100 km depth, the 3-D S wave velocity model in northeastern Brazil is dominated by low velocities and this is consistent either with heat flow measurements or with measurements of the flexural strength of the lithosphere developed in the South American continent. Our 3-D S wave velocity model was also used to obtain the lithosphere thickness in each cell of the northeastern Brazil and the results were consistent with global studies about the Lithosphere-Asthenosphere Boundary worldwide.

The small quantity and the poor distribution of seismic stations in the Brazilian territory can be considered the major factors for the poor knowledge of the earth’s interior in the last decades. The major part of the regional surface wave investigations in Brazil and surrounding areas ( [

The recent installation of modern seismic stations in the South America continent, as initiative of international institutions (IRIS, GEOFON, GEOSCOPE, etc.) and, mainly, with the seismic data available to the seismological community, has allowed the development of more detailed studies about the earth’s interior in Brazil. The free access to those high quality seismic data has allowed the development of some 3-D shear wave velocity studies in both southeastern and northeastern Brazil ( [

In the recent years, the general aspects of the shear wave velocity structure of the South America continent has been studied via surface waves ( [

Our objective is to present the results of a detailed 3-D shear wave velocity structure study in northeastern Brazil. It is well known, in the seismological literature, that a 3-D shear wave velocity structure study, via surface waves, is commonly divided into two main steps. In the first step, the source-station dispersion curves are used in a 2-D inversion process (i.e., a regionalization process or a phase and/or group-velocity tomography) to get a dispersion curve representative of each element of the total area (i.e. a cell). In the second step, the dispersion curve of each cell is used in a 1-D inversion process to obtain the shear wave velocity structure in depth, so that a 3-D S wave velocity model of the region can be constructed from the spatial representation of those 1-D inversions.

In this study, a large quantity of Rayleigh wave group-velocities, recorded at several seismic stations of Incorporated Research Institutions for Seismology (IRIS) Consortium, was used to investigate the 3-D shear wave velocity structure of the northeastern Brazilian lithosphere. The methodology used in the estimation of the Rayleigh wave group-velocities in northeastern Brazil is presented in the Section 2. In Section 3, both data and its processing, to get the dispersion curves from source to station, are presented and discussed. The Section 4 is dedicated to the quantitative analysis of the spatial resolution of the regionalized Rayleigh wave group-velocities, which are directly related to the estimated shear wave velocity structure in northeastern Brazil. In both Sections 5.1 and 5.2, respectively, a 3-D image of Mohorovičić Discontinuity and the 3-D shear wave velocity structure of northeastern Brazil are proposed and analyzed in detail, by using previous studies available in the seismological literature. The main conclusions of our study are condensed in Section 6.

The region limited by the geographical coordinates (−125, 45) and (25, −75) is, initially, divided into square cells of 2˚ × 2˚ (^{th} path and a given period (T), we can write ( [

where v_{j}(T) is an attributed group-velocity for the j^{th} cell, V_{i}(T) is the source-station group-velocity for the i^{th} path calculated from attributed v_{j}(T), U_{i}(T) is the observed source-station group-velocity for the i^{th} path, u_{j}(T) is the group-velocity for the j^{th} cell, d_{ij} is the length of the i^{th} path in the j^{th} cell, and D_{i} is the source-station distance of the i^{th} path.

At this time, a relevant point, which is related to the computation of both partial and total source-station distances (i.e., the terms d_{ij} and D_{i} in Equation (1)) should be cited. In this case, to obtain precise partial and total source-station distances, an ellipsoidal earth model and Rudoe’s formula were applied ( [

Our objective is to estimate the group-velocity for each cell of _{j}(T), by using the Equation (1). Thus, for a particular period (T), the following procedures were applied in the solution of the equation system:

1―To get the best solution of the equation system (1), a group-velocity range (Δc) covering a large interval of group-velocities (c_{n},

2―The first value of the group-velocity range (i.e., a constant group-velocity value?c_{1}) is then attributed in all cells of the grid (v_{j} values);

3―With the v_{j} values of the previous item, the V_{i} values are then calculated;

4―As the terms U_{i}, d_{ij} and D_{i} are known, then the equation system is solved (for the particular group-velocity c_{1}?item 2) and the values of u_{j} are computed via Equation (3). In this step, both resolution and covariance matrices are also computed by using Equations (4) and (5);

5―With the u_{j} values obtained in the previous step, the source-station travel times for all paths are then calculated and they are compared with the observed source-station travel times, so that a set of time residuals (tr_{i}) is estimated and a root mean square of those values is calculated and storage in a vector (q_{n},

6―The next value of the group-velocity range (i.e., c_{2} = c_{1} + ζ) is attributed and the whole process starts again, i.e., it goes to step 3;

7―When the group-velocity range (Δc) is completed (p iterations), the set of root mean square values storage in the item 5 (vector q_{n}) is used to find the minimum one or the best solution of the tomographic problem.

The result of the procedure aforementioned is a Rayleigh wave dispersion curve for each cell of

where y is a residual vector (m ´ 1), x is a vector with the unknown parameters (n ´ 1) and A is a m ´ n matrix relating model parameters to observations. In terms of damped least-squares ( [

where A^{T} is the transpose of matrix A,

where σ^{2} is the variance in the observations. The standard deviations of the estimated group-velocities at each cell of the northeastern Brazil are obtained in the diagonal elements of the covariance matrix. Furthermore, several factors can contribute to uncertainties in group-velocity estimation ( [^{2} term of the covariance matrix (C).

As our goal is to investigate northeastern Brazil (

In order to have a good path coverage of the target are (i.e. northeastern Brazil), a large quantity of earthquakes recorded at twenty three seismic stations (from 1988 to 1998 [

Many digital seismograms, related to seismic events with focal depth shallower than 120 km and magnitude higher than 5.0 m_{b}, were requested and received from IRIS. The Seismic Analysis Code (SAC) package ( [

Twenty two periods, ranging from 10 to 102s (i.e., 10.04, 12.05, 14.03, 16.00, 18.29, 20.08, 24.38, 28.44, 32.00, 36.57, 42.67, 46.55, 51.20, 56.89, 60.24, 64.00, 68.27, 73.14 78.77, 85.33, 93.09 102.40s), were selected to compose the source-station dispersion curves. This computation produced 3134 source-station Rayleigh wave group-velocity dispersion curves. In the next section, these dispersion curves are used to get a dispersion curve representative of each element of the total area (i.e., a cell of 2˚ × 2˚).

In this study, the methodology proposed by [

where c is a parameter obtained after two main procedures, i.e., a linearization of the estimated resolving kernels (Equation (4)) followed by a quadratic least-squares fit ( [

The Equation (6) was used to get the spatial resolution of the estimated Rayleigh wave group-velocities at each cell of the northeastern Brazil. As the region under investigation is formed by 49 cells (

A few cases displayed in

The results displayed in

Despite the fast reduction in the Rayleigh wave paths quantity in NE Brazil, when the period increases (

Furthermore, our spatial resolution range is also in agreement with the theoretical restrictions associated with the influence zone or the first Fresnel zone, which is defined as an area (around a surface wave path) where surface wave phases are coherent and there is only constructive interference from scattered waves ( [

source-station path is supposed to be like a delta function. Nevertheless, actual surface waves with finite frequency sample a finite region around a ray path (physical ray [_{F}) of the first Fresnel zone (in radians) is given by the following expression

where λ is the wavelength (in radians) and Δ is the epicentral distance. Equation (7) shows that Fresnel’s zones width increases with increasing wavelength and epicentral distance. According to [_{F}/3).

In order to investigate Fresnel’s zone width in this study, we considered the data set associated with two periods (10.04 s and 102.40 s). The epicentral distances of the Rayleigh wave paths that crossed northeastern Brazilian region were classified into several distinct classes (

Δ (degrees) | c = 2.94 km/s T = 10.04 s | c = 4.09 km/s T = 102.40 s |
---|---|---|

20 | L_{F}/3 = 0.7˚ | L_{F}/3 = 2.5˚ |

80 | L_{F}/3 = 1.5˚ | L_{F}/3 = 5.5˚ |

120 | L_{F}/3 = 2.1˚ | L_{F}/3 = 7.9˚ |

In order to understand the dynamics of several geological processes (i.e., mountain ranges, subduction, rifting and basin formation) it is fundamental to have information about crustal thickness in distinct geotectonic provinces. Seismic reflection and refraction data are the best way of getting both precise and reliable determinations of such parameter. However, in general, the practical procedures to obtain those data are very expensive. In this context, surface wave data can be an inexpensive alternative way to get information about crustal thickness in any place of the world.

In the recent years, surface wave data (dispersion and waveform) have been used to provide information about crustal thickness in the earth’s interior. The major part of those studies is based on Genetic Algorithms (GA) applied into local and regional surface wave waveform ( [

Two important points must be observed in the procedure adopted in this study. First, each dispersion curve is sensitive to the lithosphere structure beneath the area that it represents (i.e. a cell) and the period range of the dispersion curve (from 10 to 102 s) is suitable for identification of Mohorovičić Discontinuity (MD) depth. Second, for a dispersion curve (i.e., a dispersion curve which should be, theoretically, strongly affected by local shear wave velocity in depth) a S wave velocity contrast at MD depth is out of question remarkable, and such information is certainly present in the dispersion data.

A simple procedure, which can be summarized into two main steps well consolidated in the surface wave studies, defines the methodology used in this study to generate the 3-D image of Mohorovičić Discontinuity in northeastern Brazil. In the first step, the source-station Rayleigh wave group-velocities are used in a 2-D inversion process in order to get a dispersion curve representative of each cell of the NE Brazilian region. In the second step, the dispersion curve of a given cell is 1-D shear wave velocity inverted many times (i.e. a dispersion curve for such cell is inverted for a limited quantity of crustal models, where the thickness of the models varies from thin to thick) to find the best fit between observed and theoretical dispersion curves. The best fit, which is characterized by the minimum Root Mean Square (RMS) between observed and theoretical Rayleigh wave group velocities, provides both the S wave velocity structure in depth and its corresponding crustal thickness of such cell.

The first step was described, in detail, in the section 3. Therefore, the dispersion curves in each cell of the northeastern Brazil are ready to be used. It should be noted that the target area is composed of three types of cells (

In the continent, we generated 69 crustal models, by combining layers of the upper crust (2, 3, 4, 5, 6, 7, 8, 9, 10, 15 or 20 km thickness) with layers of the lower crust (5, 10, 15 or 20 km thickness), so that each crustal model has a distinct crustal thickness. In the ocean, we generated 150 crustal models, by combining layers of water (1, 2, 3, 4 or 5 km thickness), layers of sediments (0.5, 1, 2, 4, 6, or 8 km thickness) and layers of lower crust (2, 4, 6, 8, or 10 km thickness), so that each crustal model has a different crustal thickness. The above combinations allow for crustal thickness varies from 18 to 66 km (in the continent) and from 3.5 to 23 km (in the ocean). The upper mantle is common for both continental and oceanic structures and it is represented by eight layers of 20 km thickness, and the layer thicknesses are fixed during dispersion inversion. Thus, only S wave velocities in depth are inverted in the upper mantle. Examples of crustal models used in the dispersion inversion procedures are shown in

To estimate the S wave velocity structure in depth, at each cell of the target area (

In conclusion, our procedure looks for the best combination of crustal S wave velocities layers in depth through a simple RMS value between theoretical and observed dispersion curves in a given cell. Thus, for a particular cell, the dispersion curve is then inverted (69, 150 or 219 times) and the minimum Root Mean Square (RMS) between observed and theoretical Rayleigh wave dispersion curves is identified to find its corresponding S wave velocity structure in depth and crustal thickness.

An example of this procedure for a continental cell (corners (−39, −5) and (−37, −7)―

The methodology described previously was applied at each cell of the northeastern Brazil (

CONTINENT | |||||
---|---|---|---|---|---|

MODEL 3 | MODEL 17 | MODEL 34 | MODEL 43 | MODEL 55 | MODEL 68 |

4 | 7 | 2 | 15 | 5 | 9 |

4 | 7 | 2 | 15 | 5 | 9 |

4 | 7 | 2 | 20 | 5 | 9 |

4 | 7 | 2 | 20 | 5 | 20 |

4 | 10 | 2 | 20 | 20 | 20 |

5 | 10 | 20 | 20 | 20 | 20 |

5 | 20 | 20 | 20 | 20 | 20 |

5 | 20 | 20 | 20 | 20 | 20 |

5 | 20 | 20 | 20 | 20 | 20 |

20 | 20 | 20 | 20 | 20 | 20 |

20 | 20 | 20 | 20 | 20 | 20 |

20 | 20 | 20 | ∞ | 20 | ∞ |

20 | 20 | 20 | ∞ | ||

20 | 20 | 20 | |||

20 | ∞ | ∞ | |||

20 | |||||

20 | |||||

∞ | |||||

OCEAN | |||||

MODEL 4 | MODEL 40 | MODEL 77 | MODEL 114 | MODEL 129 | MODEL 149 |

1 | 2 | 3 | 4 | 5 | 5 |

0.5 | 1 | 4 | 6 | 1 | 8 |

8 | 10 | 4 | 8 | 8 | 8 |

20 | 20 | 20 | 20 | 20 | 20 |

20 | 20 | 20 | 20 | 20 | 20 |

20 | 20 | 20 | 20 | 20 | 20 |

20 | 20 | 20 | 20 | 20 | 20 |

20 | 20 | 20 | 20 | 20 | 20 |

20 | 20 | 20 | 20 | 20 | 20 |

20 | 20 | 20 | 20 | 20 | 20 |

20 | 20 | 20 | 20 | 20 | 20 |

∞ | ∞ | ∞ | ∞ | ∞ | ∞ |

was used to produce a 3-D image of Moho Discontinuity (

The variations of the three-dimensional Moho image in northeastern Brazil are either smooth or uniform throughout the study area. There are clear differences in Moho depth from one geological province to another, which shows that the methodology applied was sensitive to the local variations in the MD thickness. According to our 3-D MD image, the Moho depth varies from 14 to 45 km in northeastern Brazil. Several isolated crustal thicknesses estimates available in the literature, obtained with different geophysical methods and data types, were superimposed to the 3-D Moho image (

As CRUST2.0 global model ( [

The forty nine 1-D shear wave velocity models in depth, obtained in the previous section, were spatially represented, and this procedure generated a 3-D shear wave velocity model. Afterwards, this three-dimensional S wave velocity model was horizontally sliced at twelve different depths (3.5, 5.5, 13.5, 26, 32.5, 47, 53, 61, 84, 102, 144 and 164 km―

In order to help us in the interpretation of the different horizontal slices of the three-dimensional S wave velocity model in northeastern Brazil (

In 13.5 km depth (

should not be analyzed. The same analysis must be applied in the two crystalline nuclei located at São Francisco and Borborema provinces (

At 26 km depth (

At 32.5 km depth (

From 32.5 to 47 km depth (

LAYER | CRUST2.0 (38.5W,7.5S) (km/s) | ak135 (km/s) | iasp91 (km/s) | PREM (km/s) |
---|---|---|---|---|

Soft sediment | 1.20 | |||

Hard sediment | 2.10 | |||

Upper crust | 3.60 | 3.46 | 3.36 | 3.20 |

Middle crust | 3.60 | |||

Lower crust | 3.80 | 3.85 | 3.75 | 3.90 |

Upper mantle | » 4.50 (from 35 to 210 km) | » 4.50 (from 35 to 210 km) | » 4.50 (from 24.4 to 115 km) |

LAYER | S wave velocity (km/s) |
---|---|

Sedimentary sequence | 2.23 |

High velocity sedimentary rocks, crystalline basement or both | 3.20 |

Lower crust | 3.77 |

Upper mantle | 4.63 |

Low velocity channel | 4.20 |

cally higher than in the ocean (»3.60 km/s). At 53 km depth, the transition between continent and ocean coincides, in general, with its geographical transition and it can be easily identified through its clear difference in the S wave velocity.

At 61 and 84 km depths (

The 1-D S wave velocity models in depth were used to analyze some aspects related to the lithosphere’s thickness in northeastern Brazil. As pointed out by [

resolved (i.e., they show a narrower Gaussian behavior) before the lithosphere’s base region, at this region and after it. In those specific cells (blue values―

A global study about the Lithosphere-Asthenosphere Boundary (LAB) worldwide, by using P-to-S conversions at 169 single stations ( [

It is well known in the seismological literature that S waves provide valuable information about temperature (specially for depths ≤ 180 km) and this relationship has been used to expand the heat-flow measurements to regions where such measurements are rare or absent ( [^{2}. Despite of these heat flow evidences and the well known relationship between S wave and temperature, none of the previous surface waves studies in the South American continent has observed low S wave velocities down to 100 km ( [

Another important information comes from measurements of the flexural strength of the lithosphere in the South American continent ( [

In conclusion, our 3-D S wave velocity structure are in agreement with both heat flow and flexural strength studies in the South America continent and with the general characteristics of global S wave models found in the seismological literature.

A large number of Rayleigh wave dispersion curves recorded at twenty three seismic stations of IRIS Consortium was used to investigate the 3-D shear wave velocity structure of the northeastern Brazilian lithosphere. A simple procedure was used to generate a three-dimensional image of Mohorovičić Discontinuity (by using Rayleigh wave group-velocities) in northeastern Brazil and it was in agreement with several isolated crustal thicknesses obtained with different geophysical methods. A detailed three-dimensional S wave velocity model is proposed for the northeastern Brazilian lithosphere. In the crust, our 3-D model is more real than CRUST2.0 global model, because it shows more details either laterally or in depth than global model, i.e., clear lateral variation and gradual increase of shear wave velocity in depth. Down to 100 km depth, the 3-D S wave velocity model in northeastern Brazil is dominated by low velocities and this is consistent either with heat flow measurements or measurements of the flexural strength of the lithosphere developed in the South American continent. The 3-D shear wave velocity model was also used to obtain the lithosphere thickness in each cell of the northeastern Brazil. The results are consistent with recent global studies about the Lithosphere-Asthenosphere Boundary worldwide.

This research was developed by using data from GSN and GTSN seismic networks available at IRIS. The authors would like to thank these institutions for providing all seismic data. They also thank Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro (FAPERJ) for financial support during the development of this study (Process #: E-26/170.407/2000). JLS and NPS thank Observatório Nacional for all support and CSV thanks Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) by providing a fellowship for development of this research. Several figures were prepared with the software Generic Mapping Tools ( [

Jorge Luis de Souza,Newton Pereira dos Santos,Carlos da Silva Vilar,1 1, (2016) Three-Dimensional Shear Wave Velocity Structure of the Northeastern Brazilian Lithosphere. International Journal of Geosciences,07,849-872. doi: 10.4236/ijg.2016.76063