Seismic data for this study were obtained at 75 seismic stations in northeastern Brazil. These stations belong to a variety of seismic networks, both permanent and temporary. The Rede Sismográfica do Nordeste (RSISNE) consists of 19 broadband stations equipped with RefTek 151-120 sensors feeding RT-130 digitizers (24-bit) sampling at 100 Hz, with an interstation spacing of about 250 km and a network aperture of ∼800 km. The RSISNE network has been in operation since 2011 and was initially funded by the national oil company Petrobras. The Instituto Nacional de Ciência e Tecnologia em Estudos Tectônicos (INCT-ET) network, consists of 7 broadband stations and 22 short-period stations. The broadband stations were arranged along an approximately 1000 km long line with interstation spacing of about 100 km. They were equipped with STS-2.5 Streckeisen sensors and Q330 data loggers (24-bit) sampling at 100 Hz. The 22 short-period stations were equipped with L4A-3D Sercel sensors (2 Hz cutoff frequency) and 24-bit RT-130 digitizers sampling at 100 Hz. They were in operations between 2011 and 2012 and recorded continuously for between 6 months and 1.5 years. The INCT-ET network was funded by the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq). Up to six broadband stations operated during the period from 2007 to 2009 under the “Institutos do Milênio” project. These stations were equipped with KS-2000 Geotech sensors and Geotech digitizers sampling continuously at 100 Hz. They recorded continuously for periods ranging from 6 months to 2 years, with two of them still currently in operation. This network was also funded by CNPq. Station RCBR belongs to the Global Seismographic Network (GSN). This station has been recording since March 1999 using a Guralp CMG-3T sensor (replaced in July 2004 by a STS-2 Streckeisen sensor), which always feeds a Q330 data logger and samples continuously at 40 Hz. Seven broadband stations belonging to the broader Brazilian Lithosphere Seismic Project (BLSP) operated for 1.5 to 3.0 years in northeastern Brazil. They were equipped with either Guralp CMG-3T or STS-2 Streckeisen sensors and 24-bit RT-130 digitizers sampling at 100 Hz. Finally, 11 broadband stations deployed during the Borborema Deep Electromagnetic and Seismic (BODES) experiment were installed along an approximately north–south line crossing the Araripe Basin. They were equipped with RefTek 151-120 sensors and RT-130 digitizers. The stations were in operation between 2015 and 2017 and recorded continuously for ∼2 years at 100 Hz. Further details regarding the 75 seismic stations are given in the Table S1, and their geographical location is displayed in Fig. .

Receiver functions were computed for the 75 stations comprising the combined network for northeast Brazil. Most of the receiver function estimates were developed by in order to investigate lateral variations in crustal thickness and the bulk Vp / Vs ratio across the Borborema Province. This dataset was later utilized by to study the crustal architecture of the region from receiver function common conversion point (CCP) stacks. We developed 1400 new receiver function estimates at 11 temporary stations from the BODES network, following the same procedure as . The receiver function approach aims at retrieving P-to-S converted phases within the coda of teleseismic P waves that result from the interaction of the teleseismic P-wave-front with crustal and upper mantle discontinuities under the recording station in order to produce estimates of the depth of the discontinuities. The converted phases are detected by deconvolving the radial and tangential components of the teleseismic waveforms by the corresponding vertical component . This operation removes the effects of the source time function, near source propagation and instrumental response from the seismograms, leaving the signature of propagation local to the receiver.

The main processing steps involved in the development of the receiver function estimates are summarized below, and further details regarding computational and quality control procedures can be found in . First, we selected seismic sources with magnitude greater than 5.0 Mb and occurring at epicentral distances between 30 and 90∘ from the selected stations (see Fig. ). The corresponding waveforms were then windowed 10 s before and 110 s after the P-wave arrival time, demeaned, detrended, tapered with a 5 % cosine taper, and high-pass filtered above 0.05 Hz to remove low-frequency noise. All waveforms were resampled to 20 Hz, after low-pass filtering below 8 Hz to avoid aliasing. Before deconvolution, the waveforms were additionally low-pass filtered below 1.25 Hz with an acausal Gaussian filter (Gaussian width 2.5). The deconvolution procedure of the vertical component from the radial and transverse components was implemented using the iterative, time-domain procedure of , with 500 iterations. The deconvolved time series were again filtered with the same Gaussian filter (width 2.5). Percent recoveries of the observed radial component under 85 % were automatically rejected, and the remaining receiver functions were visually inspected for each station to identify and remove outliers.

Prior to implementing the anisotropy analysis, each radial and tangential receiver function was migrated to depth after P to S ray-tracing through the global velocity model ak135-f . The purpose of the migration is to correct the phase move-out introduced by varying incidence angles among the incoming teleseismic P-wave-fronts, effectively equalizing the receiver function waveforms in the depth domain . Migration before harmonic stripping at individual stations has previously been utilized by , and . Similarly, , and applied harmonic decomposition on depth-migrated cross sections obtained through CCP stacking of receiver functions. Next, the migrated radial and transverse receiver functions for each station were grouped by back azimuth in 36 nonoverlapping, 10∘ wide bins, and averaged within each bin. A given station was then selected if it presented two averaged receiver functions (one radial and one tangential) in at least nine bins. This selection criterion ensured a sampling of at least 90∘ in back azimuth, either continuously or discontinuously, around the station. A back-azimuthal coverage from at least nine bins (each 10∘ wide) allows the mapping of either half the period for a two-lobed pattern (anisotropy with plunging fast axis of symmetry) or a full period for a four-lobed pattern (anisotropy with horizontal fast axis of symmetry). A total of 39 stations were thus selected for anisotropy analysis. An example of stacked and migrated receiver functions is displayed in Fig. .

In order to map deformation within the lithosphere, we estimate seismic anisotropy from the harmonic decomposition of receiver functions. The harmonic stripping method is described in , and . The method assumes that, at every depth, an ensemble of receiver functions can be expressed as a linear combination of cos⁡(kϕ) and sin⁡(kϕ) terms, where k is the harmonic degree or order, and ϕ is the back azimuth. show that, for anisotropic media, radial and tangential receiver functions display a π/2k shift for both k=1 and k=2 harmonic degrees; the tangential receiver functions can thus be added to the radial component after applying a phase shift of +π/2k and naturally improve the azimuthal coverage around the station. After the harmonic decomposition is performed, up to five coefficient functions, corresponding to the first three harmonics, are obtained (k=0,1,2). The first harmonic (k=0) represents the isotropic variations from flat interfaces in an equivalent isotropic medium; for this harmonic, the signal is only present in the radial component. If anisotropic structures are present at depth, the second and third harmonics (k=1 and k=2) contain energy with periodicity of 2π/k. For k=1, a two-lobed periodicity of 2π is either related to the presence of a dipping interface or to an anisotropic layer with a plunging symmetry axis . Two coefficient functions express the projection of this harmonic along the north–south and east–west directions, which correspond to the coefficients multiplying the cos⁡(ϕ) and sin⁡(ϕ) terms, respectively. For k=2, a four-lobed periodicity of π is related to the presence of an anisotropic layer with a horizontal symmetry axis . As for the second degree harmonic, two coefficient functions express the projection of this harmonic degree along the north–south and 45∘ N directions, corresponding to the coefficients multiplying the cos⁡(2ϕ) and sin⁡(2ϕ) terms, respectively. The harmonic decomposition can be expressed in matrix form (Eq. ) and solved for the five coefficients for the three harmonic degrees (k=0,1,2) through a singular value decomposition. These harmonics are calculated for every depth within a selected depth-window.

The matrix equation that implements the harmonic decomposition is given by R1(z)⋮Rn(z)T1(z)⋮Tn(z)=1cos⁡(ϕ1)sin⁡(ϕ1)cos⁡(2ϕ1)sin⁡(2ϕ1)⋮⋮⋮⋮⋮1cos⁡(ϕn)sin⁡(ϕn)cos⁡(2ϕn)sin⁡(2ϕn)0cos⁡(ϕ1+π/2)sin⁡(ϕ1+π/2)cos⁡(2(ϕ1+π/4))sin⁡(2(ϕ1+π/4))⋮⋮⋮⋮⋮0cos⁡(ϕn+π/2)sin⁡(ϕn+π/2)cos⁡(2(ϕn+π/4))sin⁡(2(ϕn+π/4))1×A(z)B(z)C(z)D(z)E(z), where ϕi is the back azimuth of the i-th R (radial) and T (tangential) receiver function doublet, A(z) represents the first harmonic coefficient (k=0), B(z) and C(z) are the coefficient functions of the second harmonic (k=1), and D(z) and E(z) are the coefficient functions of the third (k=2) harmonic.

After solving the matrix Eq. () within a specific depth-window and calculating the five harmonic coefficients, we search for the presence of anisotropy by inspecting the B(z), C(z), D(z) and/or E(z) terms. If at least one of these component displays nonzero amplitudes, we calculate the energy of the second (k=1) and the third (k=2) harmonic degrees as proposed by : 2Ek=1=∑z=1nB(z)2+C(z)2 and 3Ek=2=∑z=1nD(z)2+E(z)2.

These energy functions allow for discrimination between dipping interfaces or anisotropy with a plunging axis of symmetry and anisotropy with an horizontal axis of symmetry. If Ek=1>Ek=2, the dominant anisotropy is either a dipping interface or an anisotropic layer with a plunging axis of symmetry. In that case, we rotate B(z) and C(z) in discrete back-azimuth increments α (where α∈[0,2π]) and search for the value of α that maximizes B(z), and therefore minimizes C(z). This value of α can be directly interpreted as either the trend of the dip, in the case of dipping interface, or as the trend of the fast axis of symmetry in the case of plunging axis of symmetry. If Ek=2>Ek=1, the dominant anisotropy is an anisotropic layer with a horizontal axis of symmetry. In that case, we rotate D(z) and E(z) for each angle increment α (where α∈[0,2π]) and search for the value of α that maximizes D(z), and therefore minimizes E(z). This value of α can be directly interpreted as the trend of either the fast or the slow axis of symmetry.

An example of harmonic decomposition is shown for station PFBR in Fig. . In order to estimate uncertainties, we applied a bootstrap statistical approach by randomly resampling our receiver functions with replacement. We performed the analyses with 200 replications at each of the selected stations. From these 200 values, we estimated the standard error (2σ), which corresponds to the uncertainty in the direction of the fast axis of symmetry. A measurement is considered as unreliable, and then rejected, if the estimated uncertainties are larger than 20∘.

As described is Sect. , we observe a dominance of 2π-periodicity (k=1) anisotropy in the lithospheric mantle in northeast Brazil, which represents either a dipping interface or anisotropy with a plunging axis of symmetry. However, a close inspection of the energy of the k=2 harmonics also suggests an important contribution from anisotropy with a horizontal axis of symmetry. We were able to replicate this pattern with synthetic receiver functions by assuming anisotropy with a slightly (10 to 15∘) dipping axis of symmetry (see Supplement, Fig. S2). Note that, in that case, both k=1 and k=2 harmonics display consistent orientations. This is, the orientation inferred from the k=1 harmonic degree is always parallel to one of the two orientations inferred from the k=2 harmonic degree.

Moreover, we noticed that the anisotropic fast axes of symmetry throughout the crust are consistent with those throughout the lithosphere for most of the stations, suggesting a prolongation of crustal structures within the lithospheric mantle. Within the continental interior, the anisotropic orientations are parallel or subparallel to the main east–west to northeast–southwest shear zone directions (stations ar02, nbli or lp06, for example). The consistency of the fast-axis direction of lithospheric anisotropy with large structures observed at the surface suggest a continuation of the main shear zones into the lithospheric mantle, as suggested by . Nonetheless, a few exceptions are observed, for example, at stations sabr, sbbr and nbpb. Such discrepancies in the anisotropy orientations could be related to more local features such as fluid content, presence of cracks or plutonic bodies along the shear zones, fractures or mineral assemblages .

Inspection of stations located along the eastern and equatorial margins reveals that anisotropy exhibits – on average – directions either perpendicular or oblique to the coast in the lithospheric mantle. This observation is in agreement with SKS-splitting measurements in this area performed by and . These authors concluded that the anisotropy reported from SKS splitting along the northeastern Brazilian margins must be related to fossil anisotropy inherited from the opening of the South Atlantic Ocean. This interpretation is based on the relatively small time delay measured along the coast.

We compare the independent SKS-splitting measurements with our results from harmonic stripping of receiver functions in Fig. . For a better comparison we chose to represent the k=2 harmonics at stations where SKS splitting was measured because: (i) we expect only horizontal (recorded on the k=2 harmonics) or slightly dipping anisotropy in such geodynamical context; (ii) we observe in our data that k=1 and k=2 harmonics display energy within the same order of magnitude, suggesting slightly dipping to horizontal anisotropy beneath most stations; and (iii) SKS waves are mainly sensitive to (sub)horizontal anisotropy . Figure  shows a good agreement between anisotropic orientations recorded by receiver functions and SKS splitting along the eastern and equatorial margins, confirming that the recorded anisotropy beneath coastal stations is mainly located in the lithospheric mantle. The oblique to parallel orientation of anisotropy along the east and equatorial coasts, respectively, is consistent with the opening trend of the margin .

At a number of stations (ar05, nbma, pfbr, nbpa and cs6b), uncertainties regarding the direction of the fast axis of anisotropy are larger than 20∘. These stations, however, display similar energy than stations with smaller uncertainties (see Fig.  and Fig. S3 in the Supplement). Interestingly, those stations seem to form a remarkable line trending northeast–southwest that approximately coincides with the location of the Cariri–Potiguar trend. Stations nbta and pcse also seem to align along the same direction more to the east.

This northeast–southwest oriented line is located above a northeast–southwest trending channel of thin lithosphere imaged by the tomographic study of . We suggest that deformation from thermomechanical erosion by horizontal, sublithospheric flow along the channel – also postulated by – must be ongoing above this northeast–southwest channel. Furthermore, as initial thinning of the lithosphere along the channel was triggered by Mesozoic extension along the Cariri–Potiguar trend, alterations to the original Precambrian anisotropic fabric by Mesozoic extension might still be present. Additionally, we note that the location of the Cariri–Potiguar trend also marks the boundary between the east–west striking shear zones in the southern province from the northeast–southwest striking shear zones in the western province (Fig. ). This suggests the Cariri–Potiguar trend also marks the location of a former paleo-suture that later acted as a zone of weakness along which the Mesozoic rift (now aborted) could develop. Thus, we believe the non-azimuthal anisotropy recorded at stations located along this trend is likely related to complex fossil anisotropic fabrics resulting from a combination of deformation along the ancient collision between Precambrian blocks, Mesozoic extension and thermomechanical erosion/mantle dragging by sublithospheric flow.