Application of Seismic Noise Interferometry to Extract High-Resolution P-Wave Reflectivity and Near-Surface Velocity Structure from Hydraulic Fracturing Data

Abstract

This study demonstrates the application of passive seismic interferometry, specifically through single-station autocorrelation, to extract high-resolution P-wave reflections from seismic data acquired during hydraulic fracturing. Using 10 h of continuous passive records from the Potiguar Basin, NE Brazil, we applied a processing sequence comprising a Gaussian smoothing filter and spectral whitening to eliminate source distortions and recover the empirical Green’s function. The resulting zero-offset seismic sections, constructed in 2D and projected into 3D, reveal continuous, coherent reflectors down to 2 s two-way travel time. While deeper reflectors correlate closely with legacy active-source profiles and regional geology, direct validation of the shallowest interfaces (<500 m, corresponding to Cenozoic cover and the upper Jandaíra Formation) remains interpretive due to the lack of local borehole or high-resolution shallow geophysical control in the uppermost 300 m. Additionally, Rayleigh-wave dispersion analysis from cross-correlations yielded an S-wave velocity model for the shallowest 180 m (V_s ≈ 1350 m/s), constrained by the maximum available array offset of 1450 m. These results highlight the efficacy of hydraulic fracturing-induced noise as a high-frequency source for exploration-scale reflectivity imaging, providing a non-invasive, potentially cost-effective tool to complement active seismic campaigns.

1. Introduction

The term ”interferometry” refers to the study of interference phenomena between pairs of signals to acquire information from their differences and similarities [1,2]. According to the definition above, in ambient seismic noise interferometry (ANSI), the empirical Green’s function (EGF) between two receivers can be retrieved: one receiver acts as a virtual source and the other as a receiver. In practice, this method requires computing cross-correlations and subsequently stacking the resulting waveforms [1,3,4]. Over the past two decades, seismic interferometry has established itself as a method applicable in various areas of geophysics [5,6,7,8]. In single-station applications, computing the autocorrelation function (ACF) of continuous passive records yields an empirical trace that serves as a proxy for the zero-offset reflection response beneath a receiver. Stacking each station’s autocorrelogram provides a proxy image of the subsurface [9]. Seismic interferometry (SI) is a well-established method for imaging subsurface structures [10,11,12]. Typically, ambient noise is used as input data in the autocorrelation function to determine crustal structures and Moho reflections [9,13]. Cross-correlation has also been widely applied to extract valuable information in the study of the Earth’s crust [14]. Its application at exploration scales has increased recently, particularly at local scales, where the properties of surface waves can be used to obtain velocity models and S-wave tomography [15,16,17], as well as high-resolution seismic imaging from ACF at the exploration scale [18]. In this context, passive seismic interferometry can be used for geophysical exploration and other applications such as engineering. Many studies have used cross-correlations to estimate S-wave velocity model parameters. Recent studies have examined applications in mapping important exploration areas in mining [16,19] and advanced monitoring of tailings dams [20]. It also has applications in the oil and gas industries, typically as a complement to active seismic events [21]. Additionally, it has been used in geotechnical applications integrated with surface methods, such as MASW [22] and variations in the seismic interferometry method [15], extending into the continuous condition monitoring and property quantification of unconsolidated infrastructure layers [23].

While seismic interferometry using autocorrelation functions (ACF) has traditionally focused on deep crustal and Moho investigations using low-frequency signals ($<5$ Hz) [9,13,24,25,26], recent studies have successfully applied ACF in higher-frequency bands ($>20$ Hz) for near-surface geotechnical engineering and blast-mining exploration [15,16,18]. However, harnessing high-frequency passive interferometry within hydrocarbon sedimentary basins remains challenging due to the scarcity of energetic, broadband high-frequency sources in conventional ambient noise environments.

This study addresses this challenge by demonstrating the efficacy of hydraulic fracturing-induced seismic noise as a transient, high-energy source to extract high-resolution P-wave reflectivity across an expanded frequency range (up to 30 Hz) at exploration scales. Using continuous records from a hydraulic fracturing treatment in the Potiguar Basin, NE Brazil (Figure 1A), we adapt established interferometric workflows through optimized Gaussian spectral smoothing and whitening. Our primary novelty lies in demonstrating that hydraulic fracturing noise—historically used solely for passive microseismic hypocenter tracking—can be effectively repurposed to retrieve continuous, zero-offset reflection profiles that delineate sedimentary stratigraphy and reservoir-scale lithological contacts. Accurately resolving formation layer thickness and petrophysical properties from field datasets is a critical focus in modern subsurface characterization, increasingly enhanced by advanced computational and physically constrained frameworks [27].

Figure 1. Survey data localization, Potiguar Basin, Brazil. (A) Regional map displaying the location of the Potiguar Basin in Northeast Brazil, South America. (B) Detailed layout of the survey area, illustrating the acquisition geometry across the intersecting receiver lines (lines 01, 02, 03, and 04). An active 2D seismic line available in the area is represented here as a pink NE-SW striking line. The wellhead point (CAM1436D) is also indicated. The receiver network is superimposed on a simplified geological map featuring local lithologies: unconsolidated sediments, Cenozoic deposits, clastic-carbonate sequences, and Jandaíra Formation limestones.

The vertical seismic resolution limit ($R_v$) is evaluated using the Rayleigh quarter-wavelength criterion ($R_v=\lambda /4$). Assuming an average compressional wave velocity of $V_p\approx 2400$ m/s for the post-rift sedimentary sequence (Jandaíra and upper Açu formations) [28], the dominant wavelength ($\lambda$) at the maximum evaluated frequency cutoff of $f_{\max }=30$ Hz is

$$\lambda ={\displaystyle \frac{V_p}{f_{\max }}}={\displaystyle \frac{2400\mathrm{m}/\mathrm{s}}{30\mathrm{Hz}}}=80\mathrm{m}$$

(1)

which yields an idealized vertical resolution limit of

$$R_v={\displaystyle \frac{\lambda }{4}}={\displaystyle \frac{80\mathrm{m}}{4}}=20\mathrm{m}$$

(2)

It should be noted that this estimate represents an idealized, best-case theoretical limit; in practice, subsurface propagation effects—principally intrinsic anelastic attenuation and wavefield scattering across heterogeneous interfaces—broaden the wavelet and degrade the effective achievable resolution in the subsurface.

We evaluated these results using available geological and geophysical data, which validated the shallow lithologies in the northern zone of the Potiguar Basin. This approach provides high-resolution reflectors associated with the three main lithological bodies of the area: the Jandaira Formation, the Açu Formation, and the top of the basement. In contrast, we estimated the maximum possible cross-correlation calculations and S-wave velocity models for the same data. A secondary objective is to determine whether the available acquisition geometry permits integration of autocorrelation-derived reflectivity profiles with cross-correlation-derived S-wave velocity models. Specifically, we test whether the maximum offset (1450 m) provides sufficient wavelength penetration to generate velocity models that overlap in depth with the autocorrelation reflectivity sections.

2. Survey Area and Data

Noise records were obtained near two wells in the northern part of the Potiguar Basin, specifically in the Canto do Amaro field in Northeast Brazil (Figure 1).

Fifteen gigabytes of data were recorded from 183 seismic vertical sensors (Sercel L4-A geophones) with a natural frequency of 2 Hz, as depicted in Figure 1B and Table 1. These sensors used a RefTek 125-A acquisition system (Texan). Each sensor location was surveyed using a high-precision geodetic GNSS receiver. To enhance ground coupling and minimize wind-induced ambient noise, the sensors were sealed in protective plastic bags and buried in cylindrical pits excavated to a depth of approximately 30 cm. Throughout the 10 h acquisition window, prevailing meteorological conditions were consistently warm and dry, with no recorded precipitation. The data were recorded continuously at a sampling frequency of 200 Hz for ten hours. The raw noise data from this monitoring experiment are presented in Figure S1 of the Supplementary Material.

Table 1. Geophone acquisition parameters and array geometry. Detailed breakdown of receiver line layouts, indicating total active sensor counts and station intervals (m) used during the passive monitoring survey. Numbers in parentheses indicate the count of non-functional or inactive sensors omitted from the final interferometric processing workflow.

Line Number	Number of Receivers	Spacing (m)
Line 01	33 (2)	15
Line 02	59 (1)	10
Line 03	67 (3)	10
Line 04	24 (2)	10

Well-defined linear receiver lines characterize the acquisition geometry of the data. Although this deployment was not originally optimized for passive interferometry—resulting in limited azimuthal coverage and sparse lateral sampling in some areas—the geographic intersection of lines 1, 2, and 3 enabled cross-validation of zero-offset reflection profiles directly over the source zone. Future deployments should incorporate denser 2D or 3D arrays to improve lateral resolution and reduce spatial aliasing. This intersection is located approximately above the point where fracturing was performed and enables the evaluation and comparison of the results for each corresponding seismic section. Furthermore, the linear arrangement of all receivers allows for a higher lateral resolution. The data were continuously recorded for five hours each day for two days. The recordings included both ambient noise and noise induced by hydraulic fracturing. These data were used in previous studies by [29,30], and their results served as the basis for the present study.

The hydraulic fracturing operation was carried out in a directional well drilled from east to west (wellhead CAM1436D shown in Figure 1). As documented by well logs in Silva et al. [30], the contact between the overlying Jandaíra carbonates and the target oil-bearing Açu Formation siliciclastics is encountered at a true vertical depth (TVD) of 412 m. The deviated well enters the Açu reservoir at 412 m TVD and extends laterally westward for approximately 450 m (reaching a terminal TVD of ≈620 m). Fluid injection and proppant stimulation were executed at a target depth of 453 m TVD, approximately 475 m west of the surface wellhead and ≈100 m from the center of the seismic array [30].

3. Geological Setting

The Potiguar Basin is located at the extreme northeastern tip of Brazil on the equatorial margin of South America (Figure 1A). It is positioned at the intersection of the eastern and equatorial Atlantic margins, representing a key tectonic feature formed during the Mesozoic breakup of Pangaea and the subsequent separation of the South American and African plates [31,32]. The basin encompasses both onshore and offshore domains, covering an area of approximately 48,000 km², and its origin is linked to dextral transform shearing along the equatorial margin [32,33]. The study area is situated in the northern onshore sector of the basin, specifically within the Canto do Amaro oil field, where a relatively simple and undeformed shallow stratigraphic framework prevails (Figure 1B). The tectono-sedimentary evolution of the Potiguar Basin comprises three major depositional sequences: rift, transitional, and post-rift (drift) phases [34,35]. The rift sequence, which is deeply buried in the central grabens and does not crop out in the study area, developed during the Neocomian to Early Barremian under a predominantly extensional-to-transtensional regime [31,34]. This was followed by an Aptian transitional marine sequence, which marked the first marine incursion. Finally, the post-rift sequence was deposited from the Albian to the Campanian, characterized by broad thermal subsidence that covered the entire basin and extended beyond the rift boundaries [34,35]. The subsurface and outcropping geology in the northern onshore sector of the basin is dominated by post-rift successions, specifically the Açu and Jandaíra formations, which are capped by younger Cenozoic deposits (Figure 1B). The Açu Formation, of Albian to Cenomanian age, primarily consists of siliciclastic rocks deposited in fluvial to shallow marine environments. The lower section of this formation is composed of thick reddish conglomerates and sandstones with thin intercalations of shales and siltstones, whereas the upper section comprises sandstones interbedded with greenish shales [34,36]. This formation constitutes the primary oil reservoir in the Canto do Amaro field and is the main target of the hydraulic fracturing operations monitored in this study [30]. Overlying the Açu Formation with a gradational contact is the Jandaíra Formation, a widespread carbonate platform of Turonian to Campanian age [34,37,38]. This unit consists of marine-derived carbonates, mainly calcilutites and calcarenites, deposited in tidal and shallow shelf environments [35,36]. In the study area, the Jandaíra Formation is exposed at the surface as limestone (Figure 1B) and constitutes the uppermost continuous lithological layer before the unconsolidated Cenozoic cover, which includes the siliciclastic Barreiras Formation and recent alluvial sediments [30]. From a structural and geophysical perspective, the geological characteristics of the northern Potiguar Basin provide a highly favorable setting for passive seismic interferometry. The post-rift strata in this region, including the Açu and Jandaíra formations, exhibit sub-horizontal dips and remarkable lateral continuity [39]. Consequently, the subsurface can be accurately modeled as a sequence of homogeneous, well-defined lithological layers, specifically the Cenozoic cover, Jandaíra carbonates, Açu siliciclastics, and the underlying crystalline basement. The lack of significant lateral velocity variations and the absence of complex structural deformation in the shallow subsurface enhance the reliability of the zero-offset reflections retrieved from autocorrelation functions.

4. Methodology

Passive seismic interferometry using single-station autocorrelation is theoretically grounded in acoustic reciprocity and the one-dimensional synthesis principle established by [10] and generalized by [4]. In a stratified medium excited by subsurface noise or microseismic energy, the autocorrelation of the transmission response $T\left(\omega \right)$ recorded at the surface recovers the medium’s zero-offset reflection response $R\left(\omega \right)$ via the fundamental spectral relationship:

$${\left|T\left(\omega \right)\right|}^2=1-[R\left(\omega \right)+R^{*}\left(\omega \right)]$$

(3)

where $R^{*}\left(\omega \right)$ denotes the complex conjugate of the reflection response.

In the time domain, when upgoing body waves generated at depth (e.g., induced fracturing activity and fluid-flow noise) travel through the subsurface, they undergo partial reflection and reverberation at acoustic impedance boundaries. Autocorrelating the continuous record of a single vertical-component station computes the correlation lag between the direct upgoing transmission and subsequent reflected phases. These lag times correspond qualitatively to the two-way travel time (TWT) of normally incident P-waves reverberating between the surface and subsurface reflectors. As a result, each surface receiver acts simultaneously as a co-located virtual source and virtual receiver, yielding an empirical zero-offset reflection trace directly beneath the station. Stacking these autocorrelation traces across a linear geophone array reconstructs a coherent subsurface reflection profile without requiring active explosive/vibroseis sources or precise knowledge of subsurface event origin times ($t_0$). Unlike active-source seismic exploration, where discrete shot locations, origin times ($t_0$), and source wavelets are precisely controlled, hydraulic fracturing generates a continuous, semi-stochastic wavefield composed of fluid injection turbulence, machinery vibrations, and thousands of overlapping micro-ruptures without individual temporal triggers. Consequently, deterministic kinematic ray tracing and classical shot-domain processing cannot be directly applied to the raw continuous records; the zero-offset impulse response must first be retrieved through interferometric autocorrelation.

In this study, we used two methodologies to calculate the autocorrelation function (ACF) and retrieve the S-wave velocity from the cross-correlations between seismic stations. The background seismic noise characterization for this asset was previously established by [30], and the main features were considered for the frequency analysis. The amplitude spectrum of the entire record for the first station in Lines 02 and 04 is presented in Figure S2 of the Supplementary Material. The spectrum shows intervals of mini-fracturing and fracturing processes and several discrete resonant frequencies that contribute to the total power spectral density.

4.1. Autocorrelation Function

While continuous recording spanned 5 h each day, the actual hydraulic fracturing treatment occurred exclusively during the final hour of acquisition. We isolated this specific high-energy window for autocorrelation analysis. Preprocessing began by slicing the raw records into one-hour blocks, followed by mean and trend removal and a 10% cosine taper. A Fourier transform was then applied, as depicted in the workflow diagram in Figure 2.

Figure 2. Processing workflow for the extraction of P-wave reflectivity from autocorrelation functions. The flowchart outlines the sequential data processing stages applied to continuous passive seismic records. The architecture is divided into three core phases: time-domain preprocessing (raw data ingestion, segment windowing, linear/mean detrending, and data tapering); frequency-domain conditioning via Fast Fourier Transform (FFT) for Gaussian smoothing and spectral whitening; and the return to the time domain via Inverse Fast Fourier Transform (IFFT) for discrete autocorrelation calculation and final linear trace stacking.

We calculated the amplitude spectrum and applied a smoothing Gaussian filter. We obtained a whitened spectrum by dividing the raw spectrum by the smoothed spectrum [13,18,40]. The Gaussian smoothing filtering process and spectral whitening are shown in Figure S3 of the Supplementary Material. The whitening process is essential for reducing the effects of microseismic peaks because it controls the correlation results. After the whitening process, it was necessary to reduce the frequency range to the desired spectrum, which was achieved by applying a zero-phase bandpass filter. We tested multiple high-frequency cutoffs, specifically 16, 20, and 30 Hz, to evaluate the impact of higher frequencies on image resolution. Because the local stratigraphic boundaries are well established from legacy geological data, varying these bandpass filters allowed us to pinpoint the exact frequency range required to clearly resolve the known lithological contacts. Higher frequencies were required to achieve the necessary resolution to discriminate lithologic layers in the study area. Applying a Gaussian filter aims to achieve a broader filter response and smoother filtering. For this purpose, larger standard deviations were used, and the smoothing bandwidth was set to 15 Hz. We also evaluated a 1-bit filter, which is widely used in the processing flow for surface wave retrieval and in the processing of the autocorrelation function [13,15,16,19]. However, the 1-bit filter yielded results of varying quality, likely due to its strong nonlinearity, which can distort amplitude information crucial for reflectivity studies, and ultimately required an AGC filter for amplitude balancing. In contrast, the Gaussian smoothing filter provided superior results, effectively smoothing the spectrum while better preserving the relative amplitudes that are essential for accurate P-wave reflectivity imaging. This methodological distinction arises because phase-only extraction remains sufficient for retrieving kinematic dispersion curves and phase velocity models of surface waves, whereas zero-offset reflectivity imaging depends strictly on preserving relative amplitude contrasts across subsurface acoustic impedance interfaces.

Another important factor in the processing sequence is the size of the correlation window [40]. We started with a window of 60 s and then reduced it to 30 and 15 s. The 15 s window provided the best results. From a theoretical perspective, segmenting the 1 h injection record into shorter (15 s) sub-windows provides a higher number of independent realizations ($N=240$) for stacking, which suppresses non-stationary transient spikes and satisfies the statistical condition for noise cross-term cancellation [41,42]. Autocorrelation wiggles for different frequency ranges are presented in Figure S4 of the Supplementary Material, which shows the autocorrelation functions calculated for all stations of Line 02. The figure illustrates the continuity of amplitudes across different depths, the effects of frequency cuts in each section, and the changes in the definition of each reflector after the seismic image is completed.

Applying an Inverse Fast Fourier Transform (IFFT) converts the conditioned spectra back to the time domain, yielding individual station autocorrelation traces. As a final step in the calculation, we linearly stacked all the windows obtained from the autocorrelation process.

A foundational theoretical assumption of passive seismic interferometry is that the ambient wavefield is diffuse, equipartitioned, and isotropically distributed. Transient signals generated during hydraulic fracturing (e.g., fluid injection pulses, casing/pump vibrations, and localized micro-ruptures) deviate from this condition by acting as non-diffuse, directional energy sources. In theory, non-diffuse illumination can cause incomplete cancellation of cross-terms, introduce spurious events, or bias the apparent reflection amplitudes and arrival times.

In this study, several geometrical and data-processing factors mitigate these directional biases:

• Single-station zero-offset geometry: Single-station autocorrelation retrieves zero-offset reflections dominated by near-vertically propagating upgoing P-waves reverberating between the free surface and subsurface interfaces. Because the reflection travel time is primarily governed by normal incidence beneath the station, single-station autocorrelation is substantially less sensitive to lateral azimuthal imbalances than inter-station cross-correlation.
• Spectral whitening and Gaussian smoothing: Dividing the raw amplitude spectrum by its Gaussian-smoothed envelope flattens the power spectrum across the target frequency band (2–30 Hz). This operation effectively equalizes dominant directional frequencies and suppresses high-amplitude harmonic resonances emitted by surface pumping equipment.
• Windowed averaging and coda stacking: Segmenting the continuous high-energy record into short (15 s) windows and stacking them over the 1 h injection period incorporates multiple overlapping coda waves and scattered arrivals from numerous micro-fracturing loci, which assists in randomizing the phase and approximating a distributed wavefield.
• Sub-horizontal structural framework: The post-rift stratigraphic layers of the Potiguar Basin (Jandaíra and Açu formations) exhibit flat, sub-horizontal bedding with negligible structural dip in the Canto do Amaro field, minimizing out-of-plane scattering artifacts and non-vertical raypath distortions.

4.2. Passive Seismic Interferometry

Given the current acquisition geometry, the objective of cross-correlation-based wave-velocity extraction was to determine the maximum possible penetration depth for a 1D S-wave velocity model. We considered two configuration options for the procedure. First, all stations on Line 3 were used as receptors, with the easternmost station on line 4 as the virtual source. This was done to use the largest offset available to extract the longest wavelength possible. Second, only line 03 was used, with the easternmost station near the well as the virtual source and the remaining stations as the receptors. The workflow used is shown in Figure 3 and is based on [40]. The raw data were evaluated to determine the optimal S-wave retrieval lengths. For this purpose, the cross-correlation was evaluated with lengths of 1, 2, 3, and 5 h. The results are presented in Figure S5 of the Supplementary Material, indicating that 1 h is sufficient to robustly extract surface waves.

Figure 3. Processing workflow for surface-wave retrieval and empirical Green’s function extraction via cross-correlation. The schematic shows the sequential stages optimized for processing continuous passive seismic data based on the method of Bensen et al. [40] The processing sequence moves from raw data evaluation and linear detrending through targeted bandpass filtering. Signal conditioning is achieved by applying 1-bit temporal normalization and spectral whitening to eliminate high-amplitude transient noise and balance the frequency spectrum. The workflow concludes with classical cross-correlation computation between receiver pairs, followed by phase-weighted stacking (PWS) to optimize the retrieval of coherent Rayleigh wave trains.

We executed the standard processing workflow through six consecutive stages: (1) conducting frequency analysis to determine the optimal retrieval window; (2) applying a linear detrending operator; (3) implementing a zero-phase bandpass filter based on the spectrum; (4) normalizing the datasets using 1-bit temporal and spectral whitening; (5) computing classical cross-correlations followed by phase-weighted stacking (PWS) [43]; and (6) Dispersion curve inversions were performed to resolve the local shear-wave velocity profile. This choice, consistent with the findings of [30] and confirmed in our study, effectively enhances coherent signals while suppressing the incoherent noise inherent to our dataset.

Conventionally, linear stacking combines processed cross-correlation data windows directly over given time intervals. This basic approach often struggles in a complex noise environment, where sources are not isotropically distributed across the oil field. Phase-weighted stacking (PWS) addresses this issue by using phase coherence to weight the data. Instead of relying strictly on standard amplitude sums, the algorithm uses phase consistency to downweight inconsistent portions of the linear stack. This specific mechanism targets the incoherent noise inherent in the records while actively enhancing the underlying coherent wavefield. In our cross-correlation analysis, the performance gap between the two methods was evident, as illustrated in Figure S6 of the Supplementary Material. Linear stacking retains a higher degree of incoherent noise, which can obscure weaker features, whereas PWS provides a significantly improved signal-to-noise ratio. This phase-based enhancement suppresses background noise artifacts, enabling the easier and cleaner identification of the retrieved Rayleigh waves along the channels. The selection of a phase-weighted scheme over a standard linear stack directly aligns with the effective processing strategies established by Silva et al. [30] for this acquisition geometry.

The processing flow for this project was implemented using ObsPy [44], a software that allows data plotting and the application of several seismological processing algorithms. The dispersion curve and inversion process were determined using Geopsy [45], an open-source software package. Among its capabilities is the application of the Multichannel Analysis of Surface Waves (MASW) method [46] for dispersion curve calculation, as well as the Dinver inversion module, which uses the neighborhood algorithm for velocity curve inversion. The complete set of inversion parameter ranges, search boundaries, layer parameterizations, and geometric constraints applied in Dinver is summarized in Table 2. The frequency range used to calculate the dispersion curves was 2–16 Hz. Within this range, there was constant noise with a relatively constant amplitude, as shown in the frequency spectrum in Supplementary Figure S2. We selected the lowest available frequency window (2–16 Hz) and leveraged the maximum source–receiver offsets to capture the longest possible surface wavelengths, thereby maximizing structural depth penetration during inversion. The S-wave velocity model results were validated by comparing them with the ground-roll values commonly used in the area. In contrast, the P-wave velocity was validated using the information published by [28]. These values were obtained from seismic acquisitions in the same area and validated using consolidated geological information.

Table 2. Parameters and search bounds used for the surface-wave dispersion inversion in Dinver (Geopsy).

Group	Parameter	Value/Range
Input data	Method	Passive MASW from cross-correlations
	Dispersion software	Geopsy 3.4.2
	Inversion software	Dinver 1.1.3
	Algorithm	Neighborhood Algorithm
	Wave type	Rayleigh
	Velocity type	Phase velocity
	Mode	Fundamental
	Frequency band	2–16 Hz
	Data duration	1 h
Cross01 geometry	Virtual source	Easternmost station of Line 04
	Receivers	Line 03
	Offset range	750–1450 m
Cross02 geometry	Virtual source	Eastern station of Line 03
	Receivers	Remaining stations of Line 03
	Offset range	10–660 m
Central model	$H_1$	∼50 m
	$V_{s1}$	∼1300 m/s
	$V_{p1}$	∼2350 m/s
	${\rho }_1$	∼2050 kg/m3
	$V_{s2}$	∼1550 m/s
	$V_{p2}$	∼2800 m/s
	${\rho }_2$	∼2250 kg/m3
Inversion ranges	$H_1$	30–70 m
	$V_{s1}$	1100–1500 m/s
	$V_{s2}$	1400–1900 m/s
	$V_{p1}$	2000–2600 m/s
	$V_{p2}$	2500–3200 m/s
	${\rho }_1$	1900–2200 kg/m3
	${\rho }_2$	2100–2500 kg/m3
	Poisson’s ratio ($\nu$)	0.25–0.32
	$V_s$ constraint	$V_{s2}>V_{s1}$
Dispersion target	Phase velocity	∼1200–1700 m/s
	Slowness	∼0.00059–0.00083 m/s
	Initial error	∼5% of $V_{ph}$
Inversion model	Number of layers	1 layer + half-space
	Maximum depth	∼180–200 m

5. Results and Interpretations

5.1. Seismic Section, and Autocorrelation Functions

We calculated the autocorrelations for the final hour of acquisition, during which hydraulic fracturing occurred. After processing the data according to the scheme shown in Figure 2, each station was plotted to create the corresponding seismic sections. The results obtained for Line 03 are shown in Figure 4 for the three frequency ranges of 2–16, 2–20, and 2–30 Hz. Each seismic line in the figure clearly identifies several reflectors and their positions. It is important to note that the applied processing prioritizes the extraction of the low-frequency body waves. The resulting processing pipeline achieved a coherent imaging depth corresponding to a two-way travel time of 2 s.

Figure 4. Seismic imaging section of line 03. Figure (a) displays the results for a frequency range between 2 and 16 Hz, while figures (b) and (c) show the seismic sections for frequency ranges between 2–20 Hz and 2–30 Hz, respectively.

We obtained equally consistent and well-defined reflectors along the remaining lines, with reflectors at similar depths and very consistent lithology. Figure 5 and Figure 6 show the results for Lines 01 and 02, respectively. We observed an improvement in resolution with the application of a broader frequency range. Each reflector improves its definition and maintains continuity, even at frequencies of up to 30 Hz. One plausible reason for the obtained resolution is the acquisition geometry at the hydraulic fracturing point. The controlling influence of source and receiver distributions on interferometric reflection images has been examined by Beckel and Juhlin [47], who showed that uneven illumination degrades the imaging of dipping interfaces most severely. A comparable autocorrelation scheme for retrieving P-wave reflectivity, validated against independent structural constraints, has been applied at the lithospheric scale by Gómez-García et al. [48]; the present study extends this principle to the exploration scale. The sub-horizontal bedding of the post-rift sequence in the Canto do Amaro field therefore represents a comparatively favourable case for the geometry available here. A detailed comparison between ambient noise and fracturing intervals is shown in Supplementary Figure S7 of the Supplementary Material, which compares an hour of processed data obtained only when ambient noise prevails with the result of processing during the interval when fracturing occurred. Visual comparison suggests that records captured during active fluid injection yield higher-quality imaging than those from background ambient noise alone, as evidenced by improved reflector continuity and definition in Supplementary Figure S7. However, quantitative signal-to-noise ratio analysis was not performed to confirm this observation. Background noise alone successfully maps the primary structural horizons, as shown in Supplementary Figure S7, but completely misses the weaker or deeper interfaces. This resolution gap becomes even more pronounced as the bandpass filter is widened to include higher frequencies.

Figure 5. Seismic imaging section of Line 01. Figure (a) displays the results for a frequency range between 2 and 16 Hz, while figures (b) and (c) show the seismic sections for frequency ranges between 2–20 Hz and 2–30 Hz, respectively.

Figure 6. Seismic section of Line 02. Figure (a) displays the results for a frequency range between 2 and 16 Hz, while figures (b) and (c) show the seismic sections for frequency ranges between 2–20 Hz and 2–30 Hz, respectively.

In contrast, Figure 7c displays a legacy active-source seismic profile acquired in the immediate vicinity of the survey area. The active seismic line features a conventional exploration bandwidth (≈15–40 Hz), which overlaps well with the high-frequency bandpass filter (2–30 Hz) applied to our passive autocorrelation section. While differences in source wavelet signature, spatial sampling, and near-surface mute preclude an exact trace-to-trace wavelet match, the frequency content is sufficiently consistent to enable robust structural correlation.

Figure 7. Comparison between the zero-offset seismic section obtained from single-station autocorrelation (2–30 Hz) and a legacy active-source seismic profile (≈15–40 Hz) located near the survey area, as shown in Figure 1. (a) Reproduction of Figure 4c. Uninterpreted Line 03 autocorrelation section (2–30 Hz). (b) Structural interpretation of Line 03 highlighting primary reflectors AP, BP, and CP (green horizontal lines). (c) Uninterpreted active-source seismic line. (d) Active-source profile highlighting legacy regional horizons AA and BA (green horizontal lines). Both sections exhibit consistent frequency content and close two-way travel time alignment for the top Jandaíra and basement markers.

Considering the regional geological context, the primary reflectors obtained through autocorrelation data reflect subsurface geometry. As demonstrated in Figure 7b and Figure 7d, key two-way travel time (TWT) markers exhibit close alignment: reflectors AP and CP in the passive autocorrelation section correlate directly with legacy active horizons AA (top of the Jandaíra Formation) and BA (acoustic basement), respectively. Reflector BP likely corresponds to the top of the Açu Formation, though this assignment remains interpretive given the limited direct validation data at this depth (Figure 7b). Additionally, reflector DP, located at a greater depth, lacks legacy information for direct comparison. While a rigorous, well-calibrated quantitative velocity model and depth conversion remain beyond the scope of the present study, this regional time-domain framework provides a consistent structural baseline for interpreting the primary seismic architecture.

To illustrate the consistency of the results and form an interpretable high-resolution seismic model, a 3D representation of the three seismic sections is shown in Figure S8 of the Supplementary Material for each frequency cutoff used in the study: 2–16 Hz, 2–20 Hz, and 2–30 Hz. The consistency and continuity of each reflector can be observed at the intersection point of the three seismic sections, even in the highest frequency range.

5.2. S-Wave Velocity Model and Cross-Correlation Functions

We obtained another key result: the cross-correlations between stations determined the surface wave velocity. This calculation aimed to determine the maximum achievable penetration with the current acquisition geometry.

We evaluated two separate cross-correlation configurations. The first involved using the largest offset among all acquisition geometries. In this configuration, the receiver located furthest east on Line 04 was used as the virtual source, and all stations on Line 03 were used as receivers (Figure 1B). The largest and shortest offsets were 1450 m and 750 m, respectively. This cross-correlation configuration will be referred to as “Cross01”.

A seismogram of the surface wave retrieval is shown in Figure S9 of the Supplementary Material. A frequency range of 2–16 Hz was used for this calculation. We chose the lowest frequency range to maximize penetration, and, given the relative geological homogeneity of the study area, a higher-resolution capacity was unnecessary. The result had a lower signal-to-noise ratio and greater interference, mainly towards the end of the line. However, the wave train could be extracted completely for this offset. The other configuration considered only line 3 for the cross-correlation calculations. The station furthest to the east, near the well, served as the virtual source, and the remaining stations served as receivers. The offset between the virtual source and the first receiver was 10 m, and the last receiver was located 660 m from the virtual source. This cross-correlation is referred to as Cross02 in this study. A frequency cutoff of 2–16 Hz. The resulting seismogram with the extracted surface waves is shown in Figure S10 of the Supplementary Material and displays a good signal-to-noise ratio. Notably, the surface wave train could not be extracted in the first 200 m of the line, where the start of each trace was not observable.

Figures S11 and S12 show the dispersion curves and velocity models obtained for the two studied cases, Cross01 and Cross02, respectively, inverted using the model parameter bounds defined in Table 2. The S-wave velocities in both cases were similar to the commonly reported ground-roll values in the area, at approximately 1350 m/s. In addition, the weathered layer was approximately 50 m thick. We estimated a maximum penetration depth of approximately 180 m, with a wavelength of approximately 540 m. The short distance of 10 m between the virtual source and the first receiver in Cross02, relative to the 540 m wavelength, explains why it was not possible to obtain complete traces along the first 200 m of the Cross02 seismogram. In our case, the offset between the virtual source and the first receiver should have been at least one-third of the wavelength, as confirmed by Cross01.

A significant limitation of our S-wave velocity models is their limited penetration depth of the data. This is primarily attributable to the relatively short maximum offset available within our acquisition geometry, which inherently limits the longest wavelengths that can be robustly extracted from the cross-correlation. While lower-frequency filtering (e.g., <2 Hz) might theoretically extend penetration, the available noise spectrum (Figure S2) lacks sufficient energy below 2 Hz to enable robust extraction. Recent work on low-frequency signal reconstruction from land nodal passive-source recordings [49] indicates that dedicated low-frequency processing, combined with node-based acquisition, may partially compensate for this deficiency, which is a promising direction for extending the usable depth range of future deployments in this setting.

Consequently, the derived S-wave models provide detailed information only for the shallowest approximately 180 m, precluding their direct integration with the deeper P-wave reflectivity sections obtained from autocorrelation and highlighting a geometric limitation inherent to legacy arrays. This constraint demonstrates that securing expanded aperture offsets is a prerequisite for generating deep velocity models that can be seamlessly and structurally tied to autocorrelation-derived reflectivity profiles. This baseline parameterization provides a predictive framework for designing optimized sensor layouts for future passive surveys.

Resolving the shallow shear-wave velocity structure ($V_s$) provides essential constraints for the construction and interpretation of zero-offset P-wave reflectivity profiles:

• Near-surface weathered layer characterization: The retrieved S-wave model identifies an unconsolidated weathered layer (≈50 m thick with $V_s\approx 1350$ m/s). Constraining the thickness and velocity of this shallow low-velocity zone is critical for evaluating near-surface statics and travel time delays that directly affect the vertical positioning of shallow P-wave reflection events.
• Identification of wavefield conversion and multiples: A well-defined shallow S-wave velocity helps distinguish true primary normal-incidence P-wave reflections from potential surface-wave coda, converted S-wave phases (P-to-S or S-to-P), and shallow reverberating multiples that occupy the early lag times ($t<0.25$ s) of the autocorrelogram.
• Assessment of array depth sensitivity: Comparing the depth penetration of the cross-correlation-derived S-wave model (≈180 m, limited by the 1450 m maximum array aperture) with the autocorrelation P-wave imaging depth (>1000 m) establishes the geometric boundaries required for future integrated joint inversions.

6. Conclusions

Auto- and cross-correlations derived from ambient noise have proven useful for many applications at various scales. In our study, we aimed to assess the effects of hydraulic fracturing and ambient noise on the results of seismic sections and velocity models derived from autocorrelations, as well as on the extraction of surface waves using cross-correlation. This integrated approach yielded high-resolution P-wave reflectivity, accurately reproduced known lithological information, and provided practical S-wave velocity values for the shallow strata. These findings suggest that hydraulic fracturing-induced seismic noise may serve as a viable supplementary source for detailed subsurface characterization in settings where such operations are already planned, potentially reducing the need for dedicated active-source surveys. However, formal cost–benefit analyses and broader validation in diverse geological settings are required to establish its practical advantages. The quantity and location of the recording stations enabled achieving the required information density to create high-resolution seismic sections with depths exceeding 1000 m. Passive interferometry eliminates the need for active sources (e.g., vibroseis trucks, explosive charges), potentially reducing acquisition costs and permitting requirements. However, its operational feasibility depends on the availability of energetic noise sources—such as the hydraulic fracturing operations used here—which are not universally present. Comparable repurposing of industrial activity as an interferometric source has been reported in underground mining, where excavation noise is used for seismic-while-tunneling imaging ahead of coal-mine roadways [50], supporting the more general view that routine operational noise can be exploited for imaging wherever such activity is already ongoing. Further economic analysis is needed to quantify cost savings relative to conventional active surveys. However, this method is not without operational challenges. Success depends on the availability of an energetic broadband source. Furthermore, transient events such as hydraulic fracturing often violate the theoretical assumption of a perfectly diffuse wavefield, potentially introducing directional biases in the retrieved reflectivity and incomplete Green’s function reconstruction. While our results show good reflector continuity, the extent to which non-diffuse illumination affects amplitude fidelity or introduces artifacts remains unquantified and warrants further investigation. Our maximum offset of 1450 m limits S-wave velocity modeling to ≈180 m depth (approximately one-third of the longest wavelength, 540 m at 2.5 Hz). To achieve 500 m of penetration, offsets exceeding 4 km would be required (assuming $V_s$ = 1350 m/s and a minimum frequency of 1 Hz). Such large arrays are logistically challenging and costly. The mismatch between autocorrelation imaging depth (1000 m) and velocity model depth (≈180 m) precludes direct integration of these results. Future surveys targeting deep velocity models should prioritize long-offset receiver lines or deploy dedicated ambient-noise arrays over extended time periods.