Rayleigh-Wave, Group-Velocity Tomography of the Borborema Province,

NE Brazil, from Ambient Seismic Noise

RAFAELA CARREIRO DIAS,1 JORDI JULIA,1,2 and MARTIN SCHIMMEL3

Abstract—Ambient seismic noise has traditionally been

regarded as an unwanted perturbation that ‘‘contaminates’’ earth-

quake data. Over the last decade, however, it has been shown that

consistent information about subsurface structure can be extracted

from ambient seismic noise. By cross-correlation of noise simul-

taneously recorded at two seismic stations, the empirical Green’s

function for the propagating medium between them can be recon-

structed. Moreover, for periods less than 30 s the seismic spectrum

of ambient noise is dominated by microseismic energy and,

because microseismic energy travels mostly as surface-waves, the

reconstruction of the empirical Green’s function is usually pro-

portional to the surface-wave portion of the seismic wavefield. In

this paper, we present 333 empirical Green’s functions obtained

from stacked cross-correlations of one month of vertical compo-

nent ambient seismic noise for different pairs of seismic stations in

the Borborema Province of NE Brazil. The empirical Green’s

functions show that the signal obtained is dominated by Rayleigh

waves and that dispersion velocities can be measured reliably for

periods between 5 and 20 s. The study includes permanent stations

from a monitoring seismic network and temporary stations from

past passive experiments in the region, resulting in a combined

network of 34 stations separated by distances between approxi-

mately 40 and 1,287 km. Fundamental-mode group velocities were

obtained for all station pairs and then tomographically inverted to

produce maps of group velocity variation. For short periods

(5–10 s) the tomographic maps correlate well with surface geology,

with slow velocities delineating the main rift basins (Potiguar,

Tucano, and Reconcavo) and fast velocities delineating the location

of the Precambrian Sao Francisco craton and the Rio Grande do

Norte domain. For longer periods (15–20 s) most of the velocity

anomalies fade away, and only those associated with the deep

Tucano basin and the Sao Francisco craton remain. The fading of

the Rio Grande do Norte domain fast-velocity anomaly suggests

this is a supracrustal structure rather than a lithospheric terrain,

and places new constraints on the Precambrian evolution of the

Borborema Province.

Key words: Seismic interferometry, Ambient seismic noise,

Rayleigh-wave dispersion, surface wave tomography, Borborema

Province.

1. Introduction

Seismic noise has traditionally been regarded as

an unwanted signal in seismic recordings of the

Earth’s ground motion and has frequently been

omitted from detailed analysis. In recent years,

however, it has been shown that the empirical

Green’s function of the propagating medium between

two points can be reconstructed by cross-correlating

seismic noise recorded simultaneously at those two

points (LOBKIS and WEAVER 2001; CAMPILLO and PAUL

2003; SHAPIRO and CAMPILLO 2004; SNIEDER 2004;

SHAPIRO et al. 2005). Similar to recorded seismo-

grams, cross-correlations of ambient seismic noise

contain information about the distribution of seismic

velocities within the propagating medium, and ana-

lysis of ambient noise cross-correlations is now

routinely used to infer subsurface velocity structure

(SHAPIRO et al. 2005; SABRA et al. 2005; MOTTAGHI

et al. 2013). Moreover, because ambient noise pro-

files are dominated by microseismic peaks at

approximately 0.05–0.10 and 0.1–0.2 Hz, and mi-

croseisms propagate predominantly as Rayleigh

waves (LACOSS et al. 1969; FRIEDRICH et al. 1998;

BROMIRSKI 2001; BROMIRSKI and DUENNEBIER 2002;

STEHLY et al. 2006), results from cross-correlation of

seismic ambient noise are dominated by the surface-

wave portion of the Green’s function within those

frequency ranges. Dispersion velocities can thus be

measured in the cross-correlated time-series and, if

enough stations are available, tomographic inversion

1 Programa de Pos-Graduacao em Geodinamica e Geofısica,

Universidade Federal do Rio Grande do Norte, Natal, Brazil.

E-mail: cdias.rafaela@gmail.com; jordi@geofisica.ufrn.br2 Departamento de Geofısica, Universidade Federal do Rio

Grande do Norte, Natal, Brazil.3 Institut de Ciencies de la Terra ‘‘Jaume Almera’’, Centro

Superior de Investigaciones Cientıficas, Barcelona, Spain.

Pure Appl. Geophys.

� 2014 Springer Basel

DOI 10.1007/s00024-014-0982-9 Pure and Applied Geophysics

can be used to develop images of dispersion velocity

variation (SHAPIRO et al. 2005; SABRA et al. 2005;

VILLASENOR et al. 2007; BENSEN et al. 2008; MOT-

TAGHI et al. 2013).

In the work reported here ambient noise tomog-

raphy was used to develop high-resolution

tomographic images of fundamental-mode, Rayleigh-

wave, group-velocities for the Borborema Province

of NE Brazil, with the objective of mapping shallow,

sub-surface velocity variations in the region. Surface-

wave tomographic images of the Borborema Province

published so far are only available from a few con-

tinental-scale studies of South America (FENG 2004;

FENG et al. 2007; LLOYD et al. 2010; ASSUMPCAO

et al. 2013), and are of low-resolution in the Province

because of the limited data available for the region. In

recent years, however, the Borborema Province has

been the focus of large multi-institutional, inter-dis-

ciplinary projects. Those include the Institutos do

Milenio—Tectonic and Geophysical Studies in the

Borborema Province and the Instituto Nacional de

Ciencia e Tecnologia para Estudos Tectonicos

(INCT-ET), both funded by the Brazilian Centro

Nacional de Desenvolvimento Cientıfico e Tec-

nologico (CNPq), which deployed several temporary

broadband networks in the region. Moreover, since

2011, the seismicity in NE Brazil has been monitored

by use of the Rede Sismografica do Nordeste

(RSISNE), a permanent network of 16 broadband

stations supported by the Brazilian oil company

Petrobras. In total, the combined network of perma-

nent and temporary stations now available in the

Borborema Province and surrounding regions con-

sists of 34 broadband stations with inter-station

distances between 40 and 1,287 km, approximately.

This dramatic increase in the seismic coverage of the

Borborema Province provides a unique opportunity

for passive imaging of the Province’s subsurface

structure with unprecedented detail.

Our study includes 333 cross-correlations

obtained from 1 month of continuous seismic noise

recordings at several pairs of broadband stations in

NE Brazil. For each station pair, multiple correlations

were obtained at one-day intervals and then stacked

by using the time–frequency, phase-weighted meth-

odology of SCHIMMEL and GALLART (2007). Only the

vertical component of the seismic noise recordings

was considered, which led to the emergence of

Rayleigh waves in the reconstructed empirical

Green’s functions. After obtaining the empirical

Green’s functions, group velocities were measured on

the cross-correlated time series by using the multiple

filtering analysis (MFA) of DZIEWONSKI et al. (1969)

for periods between 5 and 20 s. Tomographic maps

of lateral group-velocity variation were developed by

using the fast marching surface tomography (FMST)

inversion procedure of RAWLINSON (2005), which

combines the fast marching method (FMM) of

RAWLINSON and SAMBRIDGE (2005) for forward com-

putation of surface-wave group delays with the

iterative subspace inversion scheme of KENNETT et al.

(1988) to map lateral variations in group velocity.

Geologically, the Borborema Province is a struc-

tural domain located in the northeastern-most corner

of South America (Fig. 1). It is characterized by

complex tectonic evolution that began during Pre-

cambrian times and extended into the Cenozoic

(ALMEIDA et al. 1981, 2000; SANTOS et al. 2000; BRITO

NEVES and CORDANI 1991; TROMPETTE 1994). The

Province is criss-crossed by several east–west and

northeast–southwest trending shear-zones, suggested

as marking the boundaries of smaller tectonic terrains

that amalgamated during the Brasiliano–Pan African

orogeny (BRITO NEVES and CORDANI 1991; JARDIM DE

SA et al. 1992; CORDANI et al. 2003). Some authors,

however, regard them as the surface expression of

supracrustal deformations overlying a mostly coher-

ent Early Proterozoic basement (NEVES 2003; NEVES

et al. 2000, 2006). Because of extension during con-

tinental breakup in Mesozoic times, a number of rift

basins, now aborted, formed in the continental inte-

riors. These include the Potiguar basin to the north, the

Araripe basin to the center-west, and the Tucano, Ja-

toba, and Reconcavo basins to the south, with smaller

rift basins scattered throughout the Province (Fig. 1).

Evolution of the province in the Cenozoic was marked

by episodes of intraplate volcanism and uplift (MIZU-

SAKI et al. 2002; MORAIS NETO et al. 2009), which are

probably related to magmatic upwellings originating

from upper mantle sources (USSAMI et al. 1999;

KNESEL et al. 2011; OLIVEIRA and MEDEIROS 2012;

PINHEIRO and JULIA 2014).

For short periods (5–10 s) our tomographic ima-

ges clearly outline the major intra-continental rift

R. C. Dias et al. Pure Appl. Geophys.

basins with slower-than-average group velocities. For

longer periods (15–20 s) the anomaly associated with

the Potiguar basin fades away, as expected from the

shallow depth-extent of the basin, whereas the

anomaly associated with the Tucano–Reconcavo rift

system remains. The Tucano–Reconcavo rift system

is overlain by a thick layer of slow-velocity sedi-

mentary rocks, and the persistence of the anomaly

probably reflects leaking of the sedimentary structure

into the longer-period dispersion velocities. Perhaps

more interestingly, high-velocity anomalies are also

observed for shorter periods, approximately coincid-

ing with the geologic outlines of the Sao Francisco

craton and the Rio Grande do Norte domain of the

Borborema Province. For longer periods, the high-

velocity anomaly associated with the Sao Francisco

craton is still observable, consistent with the litho-

spheric scale of this terrain at depth. The high-

velocity anomaly associated with the Rio Grande do

Norte domain, on the other hand, fades away com-

pletely, suggesting this domain does not extend into

the deep crust. The fading of this anomaly, with the

overall lack of correlation between surface geology

and group velocity variation for longer periods,

throughout the Province, suggest the Precambrian

domains making up the Borborema Province may not

continue at depth.

2. Geology and Tectonic Setting

The Borborema Province is located in the north-

eastern most corner of the South American continent.

It is limited by the Sao Francisco craton to the south,

the Parnaıba Basin to the west, and several marginal

sedimentary basins to the north and east (ALMEIDA

et al. 1981, 2000; Fig. 1). It is regarded as a complex

orogenic system that was severely affected by

deformational, metamorphic, and magmatic pro-

cesses during the Braziliano/Pan-African orogenic

cycle at 850–500 Ma (SANTOS et al. 2010). The

varying geological and geophysical characteristics of

the crustal blocks that make up the Borborema

Province led to its subdivision into five tectonic

Figure 1Topographic map of the Borborema Province and surrounding physiographic provinces with its Precambrian domains, Mesozoic rift-basins,

and shear-zones superimposed. Cenozoic volcanic features along the Fernando de Noronha-Mecejana alignment (FNMA) and the Macau-

Queimadas alignment (MQA) are also indicated. Adapted from DE CASTRO et al. (2008), OLIVEIRA (2008), and KNESEL et al. (2011)

Group-Velocity Tomography of the Borborema Province

domains, separated by shear zones (JARDIM DE SA

et al. 1992; CAMPELO 1999; SANTOS and MEDEIROS

1999; OLIVEIRA 2008): the External or South Domain,

the Transversal or Central Zone, the Rio Grande do

Norte Domain, the Ceara Domain, and the Medio

Coreau Domain. The boundary between the South

and Central domains is given by the Pernambuco

Lineament, and the Patos Lineament separates the

Central Zone from the Rio Grande do Norte Domain.

The limit between the Ceara Domain and the Medio

Coreau Domain is given by the Transbrasiliano Lin-

eament (locally, Sobral-Pedro II Shear Zone), a

continental-scale lineament that can be traced into

West Africa in paleo-geographic reconstructions. The

Ceara Domain is limited in the east by the Rio

Grande do Norte Domain along the Jaguaribe–Tata-

juba Lineament, and in the west by the

Transbrasiliano Lineament (OLIVEIRA 2008). The

tectonic domains are displayed in Fig. 1.

The Borborema Province had a complex geo-

logical evolution in the Precambrian that resulted

from the Brasiliano/Pan-African orogenic cycle.

During this cycle, amalgamation of different conti-

nents and the closing of paleo-oceans led to the

formation of Gondwanaland at the end of the Neo-

proterozoic and early Paleozoic (*950–450 Ma)

(BRITO NEVES and CORDANI 1991; TROMPETTE 1994).

In particular, West Gondwana was formed by

amalgamation of the Amazonian, West-African, Rio

de La Plata, Congo-Sao Francisco and Kalahari

cratons at *600 Ma. Considering this background,

some authors regard the Borborema Province as the

result of amalgamation of several micro-plates and

oceanic island-arcs that were located between the

West-African craton to the north and the Congo-Sao

Francisco craton to the south (BRITO NEVES and

CORDANI 1991; JARDIM DE SA 1994; CORDANI et al.

2003), with the main shear zones that pervade the

Province marking the boundaries of the accreted

terrains. In contrast with this accretionary model,

some researchers argue that the Borborema Province

was part of a larger tectonic block that remained

consolidated since 2.0 Ga (NEVES 2003; NEVES et al.

2006). In this alternative model, the Borborema

Province would be regarded as a fold belt of the

Archean and Paleoproterozoic basement overlain by

Neoproterozoic sediments that were deformed and

metamorphosed during the Brasiliano orogeny (NE-

VES 2003; NEVES et al. 2006).

In Paleozoic times, with the Gondwana Super-

continent already formed, the Parnaıba Basin

developed in the interior of the continent, and its area

of sedimentation expanded on to the Province (OLI-

VEIRA 2008). In the Mesozoic, continental breakup led

to the shaping of the continental margins of the

Province and the formation of marginal and interior

rift basins (MATOS 1992). A system of rifts in the

Atlantic Ocean gave origin to the marginal basins

along the Equatorial and Eastern margins of the

Province (MATOS 1999), with most of the extensional

events marked by the occurrence of semi-grabens

distributed along three main axes of deformation:

Gabao–Sergipe–Alagoas, Cariri–Potiguar, and Rec-

oncavo–Tucano–Jatoba. The final breakup of the

West African and Sao Luis cratons caused the Rec-

oncavo–Tucano–Jatoba and Cariri–Potiguar rift

systems to abort, and the Gabao–Sergipe–Alagoas

trend to evolve into a phase of continental breakup

(OLIVEIRA 2008).

After continental breakup, the evolution of the

Province in the Cenozoic was marked by episodes of

volcanism (ALMEIDA et al. 1988; MIZUSAKI et al.

2002; KNESEL et al. 2011) and uplift of the Borbor-

ema Plateau (JARDIM DE SA et al. 1999; 2005;

OLIVEIRA 2008; OLIVEIRA and MEDEIROS 2012). Vol-

canism occurs along two mutually orthogonal

alignments: the Fernando de Noronha-Mecejana

alignment (FNMA), mostly off-shore and trending

east–west, and the Macau-Queimadas alignment

(MQA), on-shore and approximately trending north–

south. Cenozoic volcanism and uplift was initially

explained as resulting from passage of the Province

above one or more mantle plumes (ALMEIDA et al.

1988; JARDIM DE SA et al. 1999; JARDIM DE SA 2001;

MIZUSAKI et al. 2002). The orthogonal arrangement

of the alignments, the low-volume and long-lived

character of the volcanism, and their lack of a clear

age progression, however, have led to suggestions

that such magmatism was the result of small-scale

convection at the cratonic edge (KNESEL et al. 2011).

The causes of uplift in the Province have been

associated with magmatic underplates at the base of

the Borborema crust from melts derived from litho-

spheric erosion by the small-scale convection cell

R. C. Dias et al. Pure Appl. Geophys.

Figure 2Illustration of pre-processing steps with ambient seismic noise recordings at station LP05. a Raw data (top), one-bit normalization (middle),

and spectral whitening (bottom) for a 1-day-long time series recorded on the vertical component of station LP05. Left panels display the time

series, and right panels display the corresponding amplitude spectra. The 1-day-long time series was recorded on 01/23/2013. b Comparison

of the original (raw) and pre-processed (one bit ? whitening) ambient noise recording at station LP05. Note how the spurious signals

(earthquakes) in the original waveform disappear after the pre-processing steps

Group-Velocity Tomography of the Borborema Province

(OLIVEIRA and MEDEIROS 2012). Alternative mecha-

nisms for plateau uplift have been proposed,

including thickening of the crust after depth-depen-

dent stretching of the lithosphere (MORAIS NETO et al.

2009) and thermal doming from a low-density body

in the upper mantle (USSAMI et al. 1999).

3. Empirical Green’s Functions

3.1. Data Pre-Processing

The purpose of the data pre-processing step is

removal of unwanted signals, for example earth-

quakes and instrumental artifacts, from the seismic

recordings, to enhance the profile of ambient seismic

noise. First, for each station, continuous data were cut

into 24-h long segments and the corresponding time

series were decimated to 10 samples/s, to reduce data

size and equalize sampling rates among seismic

stations. The decimated, 24-h-long segments were

then demeaned, detrended, and tapered with a 5 %

cosine window. As recording equipment varied

among the stations, instrument responses were

removed from continuous waveform data and then

band-pass filtered in the 0.01–1.0 Hz frequency range

to equalize the time series. Second, time–frequency

normalization (CUPILLARD and CAPDEVILLE 2010) was

applied to remove earthquakes, instrumental irregu-

larities, and other non-stationary noise sources near

the stations that inevitably entered the seismic

recordings. Time-domain normalization consisted of

constructing one-bit normalized signals from the 24-h

long data segments, and the frequency-domain nor-

malization consisted of whitening the amplitude

spectrum of the one-bit normalized time series

(LAROSE et al. 2004; SHAPIRO and CAMPILLO 2004;

BENSEN et al. 2007; CUPILLARD and CAPDEVILLE 2010;

SCHIMMEL et al. 2011).

The one-bit normalization consists in equalizing

all amplitudes in the time series to a unit value, while

keeping the positive or negative polarity of the

originally recorded amplitude (CUPILLARD and CAPDE-

VILLE 2010). Even though BENSEN et al. (2007)

believe one-bit normalization to be the most aggres-

sive of a range of normalization methods, we found it

worked acceptably well with our dataset. One-bit

normalization has been successfully used in seismic

interferometry studies with both coda waves and

ambient seismic noise (CAMPILLO and PAUL 2003;

SHAPIRO and CAMPILLO 2004; SHAPIRO et al. 2005),

and resulted in a clearly apparent increase in signal-

to-noise ratio in acoustic laboratory experiments

(LAROSE et al. 2004). Spectral whitening consists in

normalizing the amplitude spectrum to a unit value

without changing the phase of the signal. The purpose

of spectral whitening is to improve the relative

weight of the low-amplitude frequency components.

Figure 2a shows an example of ambient seismic

noise recorded at station LP05 on January 23, 2013.

The left-hand panels show the raw, one-bit normal-

ized, and spectrum-whitened time series, and the

right-hand panels display the corresponding ampli-

tude spectra for each of the time-series. The effect of

the one-bit normalization is clearly visible in the time

domain, and the effect of spectral normalization

appears in the frequency domain. The spectral

normalization reduces imbalances in the amplitude

spectrum of the cross-correlation that enable the

emergence of an empirical Green’s function with a

broad frequency content. The raw time series and the

time–frequency normalized time series are compared

in Fig. 2b, which reveals removal of the spurious

signals within the 24-h-long time window.

3.2. Cross-Correlation and Stacking

The next step in the data processing is calculation

of the daily cross-correlations for each station pair in

the study area and their stack, to retrieve the

corresponding empirical Green’s functions from the

ambient seismic noise. Cross-correlation integrals

were computed in the frequency domain for each day

and station pair for time lags between -400 and

400 s, which encloses the dispersed surface-wave

train at the longest inter-station distances. All station

pairs had 31-days-long time series of overlapping

ambient seismic noise recordings.

Stacking of the daily cross-correlations was

achieved by use of the time–frequency, phase-

weighted stacking (tf-PWS) procedure of SCHIMMEL

and GALLART (2007). This procedure is an extension

of the phase-weighted stacking (PWS) of SCHIMMEL

and PAULSSEN (1997), in which each sample of a

R. C. Dias et al. Pure Appl. Geophys.

linear stack is weighted by a coherence measure

independent of amplitude. The weights of the PWS

can be expressed as:

cðtÞ ¼ 1

N

XN

j¼1

ei/jðtÞ

�����

�����

m

; ð1Þ

where c(t) is the phase stack, N the number of traces

used, j is an index that enumerates the N traces used,

/(t) the instantaneous phase (BRACEWELL 1965), and mis a variable for tuning the transition between

coherent and less coherent signal summation. The

amplitudes of the weights range between 0 and 1 as a

function of time. If the instantaneous phases of the

signals at a given time are coherent, the amplitude of

the weight is equal to unity, and zero amplitude

means that the signals are incoherent. Stacking is then

realized by use of the non-linear relationship:

pðtÞ ¼ 1

N

XN

k¼1

skðtÞ1

N

XN

j¼1

ei/jðtÞ

�����

�����

m

; ð2Þ

where p(t) is the phase-weighted stack, s(t) the seis-

mic trace, N the number of traces used, j is an index

that enumerates the N traces used, /(t) is the

instantaneous phase (BRACEWELL 1965), and m is a

variable for tuning the transition between coherent

and less coherent signal summation.

By analogy, the extended tf-PWS is expressed as:

ptfðs; f Þ ¼ S1sðs; f Þctfðs; f Þ

¼ S1sðs; f Þ 1

N

XN

J¼1

Sjðs; f Þeipf s

Sjðs; f Þ

�����

�����

m

; ð3Þ

where Sj(s, f) is the S-transform (STOCKWELL et al.

1996; SCHIMMEL and GALLART 2005; SCHIMMEL

et al. 2011) of the jth time-series and S1s(s, f) is

the S-transform of the linear stacking of all the

N time-series (cross-correlograms). The phase

coherence ctf(s, f) is used to downweight the

incoherent portions of the linear stacking in the

time–frequency domain (SCHIMMEL et al. 2011).

Examples of 31-days-long stacks of ambient noise

cross-correlations, with and without the phase-

weighting scheme, are given in Fig. 3. The figure

clearly illustrates the dramatic improvement in the

signal-to-noise ratio of the recovered empirical

Green’s function achieved with the tf-PWS

scheme of SCHIMMEL and GALLART (2007). It also

displays the strong asymmetry of the empirical

Green’s functions, which probably reflects the

predominant direction of propagation of the

microseismic noise from the continental margins

toward the continental interiors (as discussed in

the Sect. 3).

Figure 3Examples of 31-day-long stacks of ambient noise cross-correlations between stations NBPE and NBPS (left) and NBLI and NBPI (right). Note

how the empirical Green’s function emerges on the causal portion of the time-series. The top traces were obtained by use of the extended

phase weight stacking (tf-PWS) procedure of SCHIMMEL and GALLART (2007) whereas the bottom traces correspond to unweighted point-to-

point stacks. Note how the tf-PWS procedure improves the signal-to-noise ratio of the empirical Green’s function

Group-Velocity Tomography of the Borborema Province

Figure 4a Topographic map showing the location of the 34 broadband stations considered in this study. b Ray paths corresponding to the 333 station

pairs for which an empirical Green’s function could be reconstructed. c Symmetric empirical Green’s functions (Rayleigh wave) sorted by

interstation distance. The symmetric empirical Green’s functions were obtained from the causal and acausal portions after stacking of the

forward and time-revered daily cross-correlations by use of the tf-PWS scheme of SCHIMMEL and GALLART (2007). The time series have been

filtered between 0.01 and 1.0 Hz for display purposes

R. C. Dias et al. Pure Appl. Geophys.

3.3. Empirical Green’s Functions

Phase-weighted stacks of daily cross-correlations

have been developed from 34 broadband stations in

Northeast Brazil, resulting in a total of 333 empir-

ical Green’s functions sampling the Borborema

Province and neighboring regions. The broadband

stations are equipped with either RefTek-120A or

Streckheisen STS-2 sensors, with a flat velocity

response between 120 s and 50 Hz, feeding high-

gain digitizers (Reftek RT-130 or Quanterra Q330),

sampling continuously at 100 samples/s and with

GPS timekeeping. The empirical Green’s functions

are displayed in Fig. 4, with the location of the

broadband stations and the interstation ray paths

associated with the empirical Green’s functions. The

cross-correlation stacks were obtained from the

vertical component of the ambient seismic noise

only, and have been band-pass filtered between 0.01

and 1.0 Hz for displaying purposes. Distances range

from approximately 40 km to slightly over

1,287 km. Short-period Rayleigh waves clearly

emerge from the ambient seismic noise, although

the signal is somewhat obscured at long distances

because of attenuation. The dispersive character of

the Rayleigh waves recovered from the cross-

correlation stacks is illustrated in Fig. 5 for the

NBIT–NBPS station pair. The figure shows the

stacked time-series, band-pass filtered in several

frequency bands. Note how the wave trains consis-

tently emerge at all periods and that the emerged

signal is dispersive, as expected.

The cross-correlations displayed in Fig. 4c were

constructed by stacking both the causal and acausal

portions of the daily cross-correlations together

through the extended phase-weighted procedure

described in the Sect. 3.2, after time-reversing the

acausal portion of the daily cross-correlations. In

fact, because of their dependence on the location of

the noise sources, the causal and acausal portions

of the cross-correlation differ in amplitude (Fig. 3).

If the sources of ambient seismic noise were

homogeneously distributed in azimuth, the causal

and acausal parts of the Green’s functions would be

symmetric with respect to the arrival time. If,

however, the density of sources is larger on one of

the sides than on the other, the amount of energy

propagating in both directions will be different. In

this case, the Green’s functions are asymmetric.

According to SABRA et al. (2005), and given the

proximity of our network to the coast, it is

expected that the Green’s functions for station

pairs oriented perpendicular and close to the coast

will emerge more clearly than those for station

pairs oriented parallel and further inland.

Figure 5Empirical Green’s functions for the NBIT–NBPS station pair, filtered at different frequency bands. Note the dispersive character of the

recovered Rayleigh wave trains. The frequency bands are noted to the right of each frame, in Hz

Group-Velocity Tomography of the Borborema Province

4. Measuring Group Velocity

Group velocities for the fundamental mode of the

Rayleigh waves reconstructed in the stacked cross-

correlations were determined by using the MFA of

DZIEWONSKI et al. (1969), as implemented in the

Computer Programs in Seismology package of

HERRMANN and AMMON (2002). The MFA procedure

analyzes variations of signal amplitudes as a function

of velocity and period and it has its theoretical basis

in the use of a Gaussian filter to isolate the wave

package around the central period of the filter. The

width of the Gaussian filter is chosen according to

epicentral distance (or, in our case, inter-station dis-

tance) to minimize the area of the fundamental mode

in the group velocity-period profile surface (AMMON

2001). Consequently, this width parameter controls

the resolution of the group velocity measurement, and

the group velocity for each frequency can be calcu-

lated by dividing the distance between the stations by

the group delay (maximum of the filtered wave-

package envelope).

The group velocity-period profile surface con-

structed by use of the MFA may have contours

contaminated, for example, with the higher modes of

the surface waves. To isolate the fundamental mode a

phase-matched filter is used (HERRIN and GOFORTH

1977). The isolation filter C(x) is constructed in

accordance with the expression:

CðxÞ ¼ expfihðxÞg; ð4Þ

where h(x) is the integral of the group delay given

by:

hðxÞ ¼Zx

0

tgðxÞdx; ð5Þ

and where tg is the group delay.

Group velocities were measured for the 333

stacked cross-correlations obtained from the ambient

seismic noise recorded at 34 broadband stations in the

Borborema Province (discussed in the Sect. 3.3). As

only the vertical component of the recordings was

used, the dispersion measurements correspond to

Rayleigh waves. Period was chosen to range from 1

to 30 s and group velocity between 2 and 5 km/s.

Inter-station distances ranged from 40 to 1,287 km

and the filter width varied between 3 and 50, in

accordance with the linear relationship given in

HERRMANN and AMMON (2002). A first run of

Figure 6Examples of reliable (left) and unreliable (right) multiple-filter analysis (MFA) surfaces for empirical Green’s functions obtained in this study.

Note how the dispersion curve is clearly delineated along the maximum values of the MFA surface in the left panel for periods under 20 s,

whereas no clear maximum can be observed on the MFA surface in the right panel

R. C. Dias et al. Pure Appl. Geophys.

Figure 7Sequential stacks of 10, 20, and 31 daily cross-correlations (left) and corresponding dispersion curves obtained through multiple-filter analysis

(MFA) (right) for short (a), intermediate (b), and long (c) interstation distances. Note the rapid convergence of the cross-correlation stacks

into the empirical Green’s functions, and the stability of the corresponding dispersion curves in the 5–20 s period range

Group-Velocity Tomography of the Borborema Province

measurements was done on the raw empirical Green’s

function waveforms and, using the preliminary fun-

damental-mode, group-delays thus obtained, a phase-

matched filter was constructed. The empirical

Green’s functions were then filtered with the con-

structed phase-match filter to isolate the fundamental

mode and a new run was applied to the filtered

waveforms to obtain the final set of group velocity

measurements.

A strict quality-control procedure was imple-

mented to identify and reject bad group-velocity

measurements. First, dispersion velocities were

measured from the stacked cross-correlations only

along well-defined ridges along the MFA contour

plots (Fig. 6). Second, the period-range of stability

for the measured group velocities was investigated by

stacking daily cross-correlations for progressively

increasing periods of time of 10, 20, and 31 days at

three select station pairs and superimposing the

measured dispersion curves. The investigation is

shown in Fig. 7, and demonstrates that the empirical

Green’s function waveforms stabilize after stacking

20 daily cross-correlations, and that 20 days are

generally enough for consistently measuring disper-

sion velocities up to 20 s for the entire interstation

distance range. Recall that microseismic energy

decays abruptly for periods longer than 20 s (BRO-

MIRSKI 2009), which probably explains why group-

velocity measurements for the longer periods are

more scattered. Thus, group-velocity measurements

for periods longer than 20 s were not considered in

our study.

Third, we adopted a minimum wavelength crite-

rion for group-velocity measurements. Close

inspection of Fig. 7 reveals that the stability of the

period range in the dispersion curves is slightly

dependent on interstation distance. Note that the

period-range of stability seems to grow to 24 s for

LP03–NBAN (597 km) and to 27 s for NBIT–NBPS

(1,188 km). This dependence probably reflects the

increasing separation of the harmonic components

making up the surface-wave train with increasing

interstation distance, which facilitates their isolation

by the narrow-band Gaussian filtering utilized during

the construction of the MFA envelopes. For this

reason, many surface-wave and ambient noise

tomography studies require interstation distances that

are at least three wavelengths long when measuring

dispersion velocities for a given period (FENG et al.

2004; VILLASENOR et al. 2007). Therefore, to ensure

stability of the group-velocity measurements in our

study, we adopted the same minimum wavelength

criterion as in surface-wave tomography studies.

Finally, the stability of the measured dispersion

curves was further tested by producing empirical

Green’s functions at three select station pairs from

ambient seismic noise recorded during three different

Figure 8Dispersion curves measured on 31-day-long cross-correlation

stacks for short (a), intermediate (b), and long (c) inter-station

distances, superimposed for three different months during 2013.

Note the stability of the dispersion curves below 20 s, despite small

differences (\0.1 km/s) depending on the time of the year

R. C. Dias et al. Pure Appl. Geophys.

months of the year. The measured dispersion curves

are superimposed in Fig. 8, which shows that dis-

persion velocities up to 20 s period differ slightly

(\0.1 km/s) with the month of the year. Because such

differences are likely to result from variations in the

location of the noise sources during the year, dis-

persion velocity anomalies that are 0.1 km/s or less in

the tomographic maps may not be reliable.

5. Lateral Variation of Group-Velocity

To obtain tomographic images for fundamental-

mode, Rayleigh-wave, group-velocity variations in

the Borborema Province we used the FMST scheme

of RAWLINSON (2005). The FMST is implemented

iteratively in two steps: (i) prediction of travel-times

(forward problem); and (ii) adjustment of the model

parameters that satisfy the data, with regularization

constraints (inverse problem).

To solve the forward problem, the FMM (SETHIAN

1996; SETHIAN and POPOVICI 1999; RAWLINSON and

SAMBRIDGE 2005) is applied. The method finds the

solution to the eikonal equation using finite differ-

ences within a pre-determined grid, to construct the

wave fronts from the phase delays (RAWLINSON and

SAMBRIDGE 2005). The most important advantage of

this method over more traditional ray-tracing meth-

ods is that travel-times are computed for all the grid

points in the mesh, so there is no need to repeat the

calculations for every single ray path. To solve the

inverse problem, a subspace inversion scheme is used

(KENNETT et al. 1988) that reduces computational

effort during the inversion by expansion of the model

space. Moreover, the inversion strategy follows an

iterative, linear scheme where the ray paths are re-

computed after each model update, effectively

accounting for the non-linearity of the forward

problem. The combination of the two steps provides

stable and robust results, even in heterogeneous,

strongly varying media (RAWLINSON et al. 2010).

More specifically, the inverse problem is formu-

lated as an optimization problem where it is

necessary to minimize the objective function

S(m) given by:

SðmÞ ¼ ðgðmÞ � dobsÞTC�1d ðgðmÞ � dobs

þ eðm�m0ÞTC�1m ðm�m0Þ þ gmTDTDm;

ð6Þ

where m is the unknown vector of model parameters,

dobs the observed travel-time (group-delay) data,

g(m) contains the predicted travel-times, m0 the ini-

tial or reference model, Cd the data covariance

matrix, Cm the model covariance matrix, e the

damping variable, g the smoothing variable, and

D the smoothness matrix. The first term in Eq. (6)

represents a weighted misfit between data and

observations, the second term is a regularization term

Figure 9Trade-off curves between root-mean-square (RMS) misfit and model roughness (a), RMS misfit and model variance (b), and variation of RMS

misfit with iteration number (c). The curves show that the optimum balance between RMS misfit and model roughness, and between RMS

misfit and model variance is achieved for regularization terms of g = 840 (smoothness) and e = 140 (damping), respectively, and that the

tomographic inversions converge after six iterations for the selected regularization terms. All curves are shown for inversions of group-

velocities for periods of 5 and 20 s

Group-Velocity Tomography of the Borborema Province

that penalizes models that differ substantially from

the initial or reference model (RAWLINSON and SAM-

BRIDGE 2005), and the third term is another

regularization term to favor models with smooth

lateral velocity variations against models with more

abrupt variations.

The FMST procedure was applied to the selected

group-velocity measurements in the 5–20 s period

Figure 10Group velocity tomography maps developed for T = 5, 10, 15, and 20 s for the Borborema Province and surrounding areas. Slow-velocity

anomalies correlate with Mesozoic rift basins, while fast-velocity anomalies correlate with the Rio Grande do Norte domain and the sampled

portion of the Sao Francisco craton for short periods (5–10 s). Note how the fast-velocity anomaly corresponding to the Rio Grande do Norte

domain fades away for longer periods (15–20 s), along with the slow-velocity anomalies associated with the rift basins

R. C. Dias et al. Pure Appl. Geophys.

range to produce maps of group velocity variation for

the fundamental-mode Rayleigh wave over a grid of

0.5� 9 0.5� in the Borborema Province and sur-

rounding regions. The model is parameterized with

551 velocity nodes, and 2D group-velocity maps

were produced for periods of 5, 10, 15, and 20 s, with

the damping variable equal to 140 and the smoothing

variable equal to 840. The regularization terms were

Figure 11Noise-contaminated checkerboard tests for tomographic inversions for periods of 5 s (top) and 20 s (bottom). Ray-path coverage, initial

checkerboard models, and recovered models are shown in the left, middle, and right panels, respectively. Note the excellent recovery of the

starting checkerboard cells for 5 s and the degradation of the cells for the longest period. All checkerboard inversions were performed with the

same node spacing as the 0.5� 9 0.5� grid used in the tomographic maps of Fig. 10

Group-Velocity Tomography of the Borborema Province

chosen after careful inspection of trade-off curves

between root-mean-square (RMS) misfit with respect

to model roughness and RMS with respect to model

variance, where model roughness and model variance

are defined as mTDTDm and (m - m0)TCm-1(m -

m0), respectively (Eq. 6). The trade-off curves were

obtained for periods of 5 and 20 s for smoothness

varying between 1 and 9,000 (Fig. 9a) and damping

varying between 0.5 and 380 (Fig. 9b), and show that

the selected values (g = 840, e = 140) provide an

optimum balance between resolution and model

roughness and model variance, respectively. An

investigation of the number of iterations required to

achieve convergence was also performed by

inspecting the reduction in RMS misfit with the

number of iterations. The results are displayed in

Fig. 9c, which shows that the reduction in RMS

misfit starts stabilizing after six iterations. Figure 9b

also shows that model variance decreases to an

average of *0.03 km2/s2 or, equivalently, an aver-

age standard deviation *0.2 km/s for the selected

regularization terms after six iterations. Average

standard deviations in our measured group velocities

are in the 0.1–0.2 km/s velocity range for periods

between 5 and 20 s, demonstrating that the inverted

tomography maps are close to the maximum resolv-

ing power of the dataset.

Tomographic maps of group-velocity variation

are displayed in Fig. 10 for periods of 5, 10, 15, and

20 s. A quick inspection of the maps reveals that the

variation in group-velocity correlates well with sur-

face geology for shorter periods (5–10 s) whereas the

correlation degrades substantially for longer periods

(15–20 s). In more in detail, tomographic maps for

5 s show well-defined slow-velocity anomalies

coinciding with the Potiguar basin in the north and

the Tucano–Reconcavo basins in the south, and well-

developed fast-velocity anomalies coinciding with

the sampled portion of the Sao Francisco craton and

with the Rio Grande do Norte domain, north of the

Patos Lineament. Weak fast-velocity anomalies also

dominate across the Transversal and South domains,

and in the Coreau domain of the northwesternmost

corner of the Borborema Province and in the western

half of the Ceara domain. A similar pattern of slow

and fast velocity anomalies is observed in the tomo-

graphic maps for periods of 10 s. For periods of 15

and 20 s, on the other hand, the well-developed

anomalies in the Potiguar basin and the Rio Grande

do Norte domain completely fade away whereas

those in the Sao Francisco craton and the Reconcavo–

Tucano basin remain, although strongly attenuated. A

faster-than-average velocity anomaly also develops at

20 s under the western half of the Araripe basin.

The robustness of the tomographic maps was

checked by use of a checkerboard test, displayed in

Fig. 11, for periods of 5 and 20 s. The starting

checkerboard models were defined through a grid of

nodes with B-spline cubic interpolation, which pro-

duces a continuous, smooth, and locally controlled

velocity medium. The corresponding synthetic

‘‘dataset’’ for the starting velocity models was pro-

duced using the FMM procedure with the same inter-

station ray-path pattern of the observed dataset

(Fig. 11a, d), with addition of 20 % random noise to

the synthetic data. The recovery of the starting model,

obtained by using the same regularization terms and

the same 0.5� 9 0.5� grid as for the tomographic

images in Fig. 10, is quite satisfactory for 5 s and

indicates overall good resolution for short periods.

The recovery of the starting models for 20 s, on the

other hand, is less satisfactory, especially across the

western and southern portions, despite the increased

cell size. Comparing the ray-path coverage for both

periods, it seems quite clear that the decrease in

resolution can be directly attributed to the sparser

ray-path coverage across the poorly resolved regions

for a period of 20 s.

6. Discussion

The most important result revealed by the tomo-

graphic maps displayed in Fig. 10 is the strong

correlation of the group-velocity variations with

surface geology for short periods and the degradation

of the correlation for longer periods. Part of the

degradation can certainly be attributed to the decrease

in the number of ray paths at 20 s, which probably

explains the strong attenuation of the fast-velocity

anomaly under the Sao Francisco craton and, perhaps,

the development of a fast velocity anomaly under the

western Araripe basin. Close inspection of the

checkerboard tests in Fig. 11 shows, nonetheless, that

R. C. Dias et al. Pure Appl. Geophys.

recovery of the starting model East of the 40�W

longitude is still good for 20 s, so a more geological

explanation must be sought in explain the fading of

the slow-velocity anomalies under the rift basins and

the fast-velocity anomaly under the Rio Grande do

Norte domain.

A possible explanation of the fading of the group-

velocity anomalies at longer periods is that short-

period surface-waves sample shallower depths than

long-period surface-waves. More specifically, sensi-

tivity kernels for fundamental-mode, Rayleigh-wave

group-velocities show that peak sensitivity for 5 s

occurs at approximately 5 km depth whereas peak

sensitivity for 20 s occurs lower—down to 20–25 km

depth (TANIMOTO 1991). Thus, the correlation of the

tomographic maps for 5 s with surface geology is not

surprising, because they are mostly sensitive to

shallow velocity variations; correlation of 15–20 s

tomographic images with surface geology, on the

other hand, would require a continuation of the sur-

face features at upper-to-mid crustal depths. Fading

of the anomalies because of the limited depth-extent

of surface geologic structures is consistent with the

association of the slow-velocity anomalies with the

slow-velocity sediments filling the Potiguar and

Reconcavo–Tucano basins. The Potiguar basin has

maximum depths of approximately 6 km (PEDROSA

et al. 2010) and its signature in the tomographic maps

completely disappears for 15 s; the Reconcavo–Tu-

cano basin is considerably deeper, approximately

12 km in its central portion (DA SILVA et al. 2003),

and therefore its signature leaks slightly into the

longer periods down to 20 s. The fading of the fast-

velocity anomaly associated with the Rio Grande do

Norte domain, on the other hand, is more intriguing

and would suggest the Patos Lineament marks the

border between two supracrustal structures that do

not have a continuation into the deep crust.

To further investigate the robustness of the fast-

velocity anomaly in the Rio Grande do Norte domain

for short periods we performed two additional

tomographic inversions with a perturbed dataset.

Figure 12a shows the tomographic map for 5 s

obtained after removing the group-velocity

Figure 12Tomographic maps of group-velocity variation for periods of 5 s on removal of the dispersion curve associated with the ray path connecting

the stations on each side of the Rio Grande do Norte, fast-velocity anomaly (a), and on removal of all the dispersion curves associated with ray

paths connecting either of the two stations on each side of the Rio Grande do Norte, fast-velocity anomaly (b). Note how the fast-velocity

anomaly in the Rio Grande do Norte domain disappears on removal of the ray paths

Group-Velocity Tomography of the Borborema Province

measurement for the ray path joining the two stations

flanking the fast-velocity anomaly in the Rio Grande

do Norte domain to the East and West, respectively

(PFBR and SLBR). The anomaly disappears, clearly

indicating that the anomaly is constrained by the

empirical Green’s function corresponding to the

medium between those two stations. This suggests

that the fast velocity anomaly might be an artifact

resulting from a timing problem at one of the stations.

This ray path, however, is also included in the group-

velocity maps at 15–20 s, where no fast velocity

anomaly is observed for the Rio Grande do Norte

domain (Fig. 10c, d). Realize that if the fast-velocity

anomaly at 5 s were an artifact because of a timing

problem, it should be actually observed for all peri-

ods; as this is not the case, we must conclude that the

fading of this anomaly for longer periods is not an

artifact. Furthermore, Fig. 12b displays the tomo-

graphic map for 5 s obtained after removing the two

stations that flank the Rio Grande do Norte domain

anomaly. Realize that, in addition to the ray path

connecting the stations, this operation will remove all

ray paths having one of the two stations on one side.

As expected, the fast velocity anomaly disappears,

but the rest of the anomalies in the map remain

basically the same. Once again, if the anomaly were

an artifact, one would expect that removal of all the

ray paths associated with the malfunctioning station

would have a greater effect on the tomographic maps.

These additional tomographic inversions thus dem-

onstrate that the Rio Grande do Norte domain

anomaly is well constrained for short periods and that

it is not the result of a drifting GPS clock or any other

malfunction at the stations flanking the anomaly.

After these additional tests, we conclude that

fading of the fast-velocity anomaly in the Rio Grande

do Norte domain is a well-constrained feature in our

tomographic maps, and that the anomaly is probably

a supracrustal structure that does not extend into the

deep crust. This is an important observation with

regard to the Precambrian evolutionary models that

have been proposed for the Borborema Province (as

discussed in the Sect. 2). On one hand, the accre-

tionary model (BRITO NEVES and CORDANI 1991;

JARDIM DE SA 1994; CORDANI et al. 2003) views the

main shear zones that traverse the Borborema Prov-

ince—including the Patos Lineament—as marking

the boundaries of several continental fragments and

microplates that amalgamated during the Pan Afri-

can–Brasiliano orogenic cycles. In that context, these

shear zones must be regarded as major lithospheric

boundaries that separate tectonic blocks with inde-

pendent tectonic evolution during the Precambrian.

On the other hand, the single-block model (NEVES

2003; NEVES et al. 2006), views the Borborema

Province as a coherent block that has behaved as a

consolidated tectonic unit for the past 2.0 Ga. In that

model, the shear zones are regarded as supracrustal

features that mark the boundaries of Neoproterozoic

metasediments that were deformed and metamor-

phosed during the Pan African–Brasiliano orogeny.

The fading of the fast velocity anomaly in the Rio

Grande do Norte domain would thus be better

understood within the framework provided by the

single-block model.

The lack of substantial anomalies for short periods

across the other major shear zones, and the overall

lack of correlation of the tomographic maps for

longer periods with surface geology may indeed

suggest that the Borborema Province is a single,

coherent tectonic block. We must keep in mind,

however, that the resolution of the tomographic maps

degrades for longer periods, especially in the south-

ern and western portions of the study area. Although

the permanence of the fast-velocity anomaly under

the Sao Francisco craton down to 20 s, which is

located within the poorly resolved southwestern

portion of the study area, may give some confidence

that long-wavelength structures are still resolved,

spatial resolution for long periods remains low, so

interpretation of the Borborema Province as a single,

coherent Precambrian block will still require better

sampling of the western and southern portions of the

Province and the surrounding Parnaıba basin and Sao

Francisco craton.

7. Conclusions

To summarize, cross-correlation of ambient seis-

mic noise in the Borborema Province of NE Brazil

has enabled reconstruction of the Green’s functions

for pairs of stations separated by approximately 40

and 1,287 km. The Green’s functions revealed a clear

R. C. Dias et al. Pure Appl. Geophys.

dispersive signal, which was identified as the funda-

mental mode of Rayleigh waves. Group velocities

were measured with success for periods between 5

and 20 s, and the dispersion measurements were

inverted tomographically to map subsurface struc-

tural features. For short periods, the tomographic

images correlate well with such surface geological

features as Mesozoic rift basins and the Precambrian

Rio Grande do Norte domain. For longer periods,

corresponding to upper-to-mid crustal levels, no clear

correlation is observed between group-velocity

anomalies and surface geology. We conclude that the

lack of correlation for long periods reveals the Rio

Grande do Norte domain is likely to be a supracrustal

structure, as predicted by models of Precambrian

evolution that regard the Borborema Province as a

single, coherent tectonic unit over geologic time.

Confident interpretation of the depth-extent of other

Precambrian domains making up the entire Borbor-

ema Province will, however, require better sampling

of its western and southern portions.

Acknowledgments

This work was supported in part by the Instituto

Nacional de Ciencia e Tecnologia em Estudos

Tectonicos (INCT-ET) of the Brazilian Centro Nac-

ional de Desenvolvimento Cientıfico e Tecnologico

(CNPq, grant number 57.3713/2008-01). RCD was

supported by a two-year scholarship from CNPq to

complete her M.Sc. degree at UFRN. JJ thanks CNPq

for his research fellowship (CNPq, grant number

308171/2012-8) and MS acknowledges support by

the Brazilian Science Without Border Program

(CNPq, grant number 40.2174/2012-7). M. As-

sumpcao and an anonymous reviewer are thanked

for thorough review of the original manuscript. Most

of the figures were produced with the generic

mapping tools of WESSEL and SMITH (1998).

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(Received January 28, 2014, revised November 4, 2014, accepted November 4, 2014)

Group-Velocity Tomography of the Borborema Province