Low Vp/Vs Values as an Indicator for Fractures in the Critical Zone

Poisson's ratio for earth materials is usually assumed to be positive (Vp/Vs > 1.4). However, this assumption may not be valid in the critical zone because near Earth's surface effective pressures are low (<1 MPa), porosity has a wide range (0%–60%), there are significant texture changes (e.g., unconsolidated vs. fractured media), and saturation ranges from 0% to 100%. We present P‐wave (Vp) and S‐wave (Vs) velocities from seismic refraction profiles collected in weathered crystalline environments in South Carolina and Wyoming. Our data show that ∼20% of the subsurface has negative Poisson's ratios (Vp/Vs values < 1.4), a conclusion supported by borehole sonic logs. The low Vp/Vs values are confined to the fractured bedrock and saprolite. Our data support the hypothesis that weathering‐generated microcracks can produce a negative Poisson's ratio and that Vp/Vs values can thus provide insight into important critical zone weathering processes.

ratio in elastic isotropic material (Flinchum et al., 2020;Pasquet et al., 2016).Unlike the other elastic moduli, Poisson's ratio (   ) does not require the density only the shear (G) and bulk (K) moduli (Equation 1): Keifer et al., 2019;Wang et al., 2019), and surface and borehole nuclear magnetic resonance data (Flinchum et al., 2019;Ren et al., 2019).The rocks underlying the BW site are not foliated, but the saprolite shows a seismic anisotropy within the saprolite, interpreted as an inherited fracture fabric (Novitsky et al., 2018).There are nine boreholes at BW, and four at the SCP site (Figure 1).

Seismic Refraction
We collected V p and V s velocities using a sledgehammer source and 96 geophones.For V p, we used a small aluminum plate as the source.We acquired V s velocities using shear-wave refraction surveys (Hunter et al., 2022;  Pasquet et al., 2015b;Uhlemann et al., 2016) by inverting shear body wave travel times.We planted horizontal geophones (4.5 Hz) so that they would record ground motion perpendicular to the profile.We generated a horizontally polarized S-wave using a modified I-Beam source, striking each side of the I-beam.The subtraction of the two directional swings enhances shear arrivals and weakens P-wave arrivals (Figures 1c-1h).Shear wave refraction surveys exploit the decoupling of the SH wave from the P-SV system (Stein & Wysession, 2003).A description of the decoupling of SH waves from P-SV waves, information about the source, survey geometry, and analysis showing that our shear-wave refraction survey satisfies these conditions is provided in Supporting Information S1.
We trace-normalized the data and manually picked the first arrivals (Figures 1c-1h).P-wave arrivals were picked first and were plotted on the horizontal records to ensure accurate picking of the S-wave arrival (see Figure 1f).To invert the arrival times, we used the open-source Python Geophysical Inversion and Modeling Library (PyGIMLi) (Rücker et al., 2017), which is based on the shortest path algorithm (Moser, 1991;Rücker et al., 2017).The inversion uses a deterministic Gauss-Newton scheme to minimize χ 2 , which requires a data weight for each pick.We assigned weights using a linear function of offset.We evaluated uncertainty by running the V p and V s inversion 200 times, randomly removing 20% of the travel time picks for each inversion to account for picking uncertainty.We quantified model uncertainty by starting each inversion with different starting velocity gradients and presenting the average of all 200 inversions.We used the inverted velocity models to compute synthetic seismograms using finite difference schemes that applied the elastic and acoustic wave equations (Juhlin, 1995;Stockwell, 1999).The Supporting Information S1 details data collection, picking, modeling, and uncertainty analysis.

Sonic Velocities
We acquired full waveform sonic data using a three-receiver, 2SAF-3R tool manufactured by Mount Sopris Instruments.We logged ∼340 vertical meters at nine boreholes at the BW site and ∼100 m at four boreholes at the SCP site.A subset of V p sonic velocities at BW was reported in previous studies (Flinchum et al., 2018a(Flinchum et al., , 2022)).P-and S-wave velocities were determined from the three-receiver offsets using semblance, computed by summing the amplitudes along 15 different velocities over a 50 us window in WellCAD software version.5.2 (ALT, https://www.alt.lu/).The highest semblance value was automatically picked across the entire log for both P-waves and the first shear phase.We inspected all semblance picks and manually adjusted sporadic picks.S-wave velocities in the sonic logs result from a converted wave caused by the strong elastic contrast between the surrounding rock and fluid (Haldorsen et al., 2006;Hornby & Murphy, 1987).Data were inverted using industry standards provided in WellCad.

Seismic Refraction
The RMS error for all V p and V s models was under 2 ms (Figure 2).All picked travel times were fit within 7 ms, and the mean of the misfit was around zero (Figures S6-S8 in Supporting Information S1).We show contours for 1,200 ± 100 m/s and 4,000 ± 500 m/s as proxies for the boundary dividing saprolite and fractured rock and for the depth to bedrock in crystalline based on data presented in Flinchum et al. (2018b) and Holbrook et al. (2014).
For the following analysis of the V p /V s models, we considered only the cells with at least one ray path from the V p and V s models.
General and consistent patterns emerge from the V p /V s values in the refraction profiles (Figure 2).The mean V p / V s value along SCP L2 is higher than SCP L1 (SCP L1 = 1.66 ± 0.004; SCP L2 = 1.71 ± 0.007; p = 0.0), but differences in the V p /V s value between SCP L2 and BW are negligible (1.66 ± 0.004 at SCP and 1.67 ± 0.006 at BW; p = 0.64).All three V p /V s models show a thin and consistent 1-2 m layer of higher V p /V s values at the surface that is required to fit the near-offset arrival times and is associated with low model uncertainty (Figure S5 in Supporting Information S1), which is likely caused by a change in pore shape.Beneath this layer, low V p /V s values can extend up to 40 m into the subsurface.In all three profiles, the low V p /V s values (<1.4) occur only in the saprolite or weathered/fractured bedrock (Figures 2c-2f and 2i), above the 4,000 m/s V p contour (Figure 2).We observe V p /V s values less than 1.4 at SCP L1 and BW when incorporating the uncertainty from the bootstrapping inversion scheme (Supporting Information S1).This suggests that V p /V s values less than 1.4 are resolvable and required to fit the data (Figures S9 and S10 in Supporting Information S1).At SCP L2, the probability of being less than 1.4 is reduced, suggesting that the V p /V s values on that profile might be low but not negative (Figure S11 in Supporting Information S1) Thus, low V p /V s (<1.4), or at least very close to 1.4 values, must be present to explain our travel time observations.

Sonic Velocities
Sonic velocities from the wells at both sites show similar V s ranges (Figure 3c), while at BW, V p spans a wider range (∼2,200-6,500 m/s).The distribution of V s at both sites shows bimodal distributions, where the BW site has lower V s velocities (Figure 3c).The larger variability in the distributions at BW results from including eight different wells.SCP only includes four wells.Despite the variability, there is a relatively linear relationship between V p and V s at both sites (Figure 3a).Most of the data at BW have V p /V s values of ∼1.8 (   = 0.28), while the SCP appears to fall along a line closer to ∼1.5 (   = 0.10) (Figure 3c).Probability density functions (PDF) of V p /V s values of the sonic logs from BW show a large peak (1.90 ± 0.002, mean ± standard error) and show only 2% of the data have negative Poisson's ratios (V p /V s < 1.4) (Figure 3d).The V p /V s PDF of the sonic velocities at SCP shows a much narrower peak with a mean and standard deviation of 1.49 ± 0.001, with 19% of the sonic V p / V s values falling below 1.4 (Figure 3d).The sonic velocities at BW have a much larger range of observed V p /V s values, suggesting more velocity heterogeneity at the BW site.SCP L2 crosses a borehole at 95 m (Figure 1).The water level was 17.5 m bgs (Figures 2a-2c), and the casing depth is 8.8 m bgs.SCP L2 allows comparing the refraction V p /V s values to the sonic V p /V s values (Figures 3a  and 3b).The sonic velocities are only available in fractured or fresh bedrock below the water table.The V p and V s profiles from SCP L2 are slower than the sonic velocities at almost all depths, but at greater depths (∼25 m), the V p and V s velocities match the sonic velocities within uncertainty (Figure 3a).The mismatch between sonic and surface is common near the surface and could be caused by frequency differences which results in different averaging volumes (see Flinchum et al., 2022).

Discussion
The V p /V s values less than 1.4 observed in the surface refraction (Figure 2) and sonic logs (Figure 3) required additional scrutiny.Additional analysis described in Supporting Information S1 demonstrates that these values are not artifacts.First, we showed that the picked S-wave arrivals are refracted arrivals, not mode-converted waves.Our acquisition geometry satisfies the conditions that allow SH waves to be decoupled from P-SV waves (Figures S1 and S2 in Supporting Information S1).Out-of-plane effects that create SH-P-SV coupling are unlikely because of the high amplitude and coherency of the SH arrivals (Figure S3 in Supporting Information S1).Because mode-converted waves might also have slow apparent velocities similar to those of the SH arrivals (Figure S4 in Supporting Information S1), we used a finite-difference code (Juhlin, 1995;Stockwell, 1999) to compute the elastic response of the BW profile (Figure 1b) to conclusively show that the picked arrivals are SH waves, not mode-converted waves (Mi et al., 2015), which arrive earlier (Figure S13 in Supporting Information S1).
Second, we tested our ability to resolve V p /V s values less than 1.4 by conducting uncertainty analysis (Figures S9-S11 in Supporting Information S1) and estimating the probabilities of V p /V s values less than 1.4 (Figure S9-S11 in Supporting Information S1).At SCP L1 and BW low V p /V s values over large regions are required to fit the observed data.At SCP L2, the probability is lower, and low V p /V s values are focused around a boundary at the valley bottom (Figure 2a).To determine if a higher V p /V s value of 1.5 would fit the data, we constructed S-wave velocity models by dividing the V p models by 1.5 and tracing the rays (Figure S6-S8 in Supporting Information S1), which also shows that V p /V s values less than 1.4 must occur to fit our picked travel times (Figures S6-S8 in Supporting Information S1).The following discussion sections address the question: is there an underlying mechanism that can create large regions of negative Poisson's ratios, and what implications do these values have concerning our understanding of deep CZ architecture?

Figure 3. (a)
A comparison of SCP L2 and the sonic velocity logs.The thin black line is the sonic V p .The thin gray line is the sonic V s .The dashed blue line and corresponding envelope are the extracted V p ± 1σ (Figure S5 in Supporting Information S1).The dashed orange line and corresponding envelope are the extracted V s ± 1σ.The surface profiles only show where at least one ray passes through the V p and V s models.(b) The black curve is the V p /V s profile computed from the sonic logs.The dashed purple line is the V p /V s value extracted from the tomography model.The envelope is the uncertainty associated by taking the ratio using (V p + 1σ)/ (V s − 1σ) and (V p − 1σ)/(V s + 1σ).(c) Sonic velocities, where V s is plotted as a function of V p for all available sonic logs.The yellow color is for SCP, and the brown color is for BW.Normalized Gaussian PDFs for V s are shown on the right of the plot and V p are plotted on top.Dashed lines are constant V p /V s values.(d) Normalized Gaussian PDFs of the distributions of V p /V s .Poisson's ratios are plotted on the top using Equation 1.The means and standard errors are reported in each plot.V p /V s values less than 1.4 (   < 0) are marked by a gray box.
We propose that a combination of low effective pressures in the CZ and biotite expansion can produce auxetic behavior similar to thermally cracked granites.Biotite expansion generates new fractures, providing more mineral surface area for geochemical reactions (Bazilevskaya et al., 2013;Buss et al., 2008;Tian et al., 2019) and sufficient energy density to fracture rock over cm length scales in granites (Goodfellow et al., 2016;Goodfellow & Hilley, 2022).The stresses created by biotite expansion can impact the state of stress on the hillslope scales (Shen et al., 2019;Xu et al., 2022).The low effective pressures in the CZ (<1 MPa) allow fractures created by biotite to remain open.Scanning electron microscope (SEM) sections show that weathering cracks resemble auxetic thermally cracked granite (Figures 4a and 4b) (Griffiths et al., 2018).The velocity changes caused by heat treatment are similar to the contrasts between unweathered and fractured bedrock in our survey, with initial granite velocities (V p = 4,890 m/s; V s = 2,700 m/s) showing more rapid reduction in V p than V s (V p = 2,710 m/s; V s = 2,200 m/s), producing an auxetic response (Figure 4a).The auxetic behavior is restricted to structures above bedrock (V p < 4,000 m/s) (Figure 4c).Probability density functions (PDF) of all model parameters with V p /V s values less than 1.4 show that the probability is less than 3% when V p is greater than 4,000 m/s (Figure 4c).The notable exception is the sonic velocities at SCP, where the probability is higher (20%).However, if the bedrock velocity at SCP is 4,500 m/s, the probability of auxetic behavior is reduced to zero (Figure 4d).Based on the mineralogy at SCP, the bedrock velocity should be 4,480 m/s (Table S3 in Supporting Information S1).
Our data suggest that the auxetic behavior extends into the saprolite (V p < 1,200 m/s) (Figure 4c).This is possible because the saprolite retains the original fabric of the underlying bedrock (Dixon et al., 2009;Graham et al., 2010).The preserved fractures and fabrics in saprolite, even at depths less than a few meters, have caused seismic anisotropy (Eppinger et al., 2021;Novitsky et al., 2018).Furthermore, the volumetric strain of saprolite at seven crystalline rock sites has been associated with positive volumetric expansion (Riebe et al., 2021), which suggests an underlying physical weathering mechanism that creates additional porosity.We speculate that the fractures created by biotite expansion remain open in saprolite.We expect V p /V s values less than 1.4 will occur in locations with positive volumetric strains, like the hillslope in the Southern Sierras, where strains over hundreds of meters exceeded 100% (Hayes et al., 2019).
Finally, we expect a more rapid decrease in the V p /V s value for bedrock with higher biotite concentration, again consistent with our data.The SCP site is on a biotite gneiss with ∼4% biotite (Holbrook et al., 2019).In contrast, the BW site has ∼7.5% biotite (Edwards & Frost, 2000;Flinchum et al., 2018a;Frost et al., 1999).Similarly, previous work in the Southern Sierras showed that small differences in biotite concentration (2%-3%) can strongly impact CZ architecture (Callahan et al., 2022).Our data show a rapid decrease in the V p /V s value from bedrock to fractured rock (∼1.7 to ∼1.2) at BW (Figure 4d) but a smaller at SCP (Figure 4d), consistent with biotite cracking as an important mechanism of porosity creation (Figure 4d).
Our interpretation suggests that V p is more sensitive to fracturing than V s .This is illustrated in the thermally treated sample, which showed the auxetic behavior was created by a faster drop in V p relative to V s (Figure 4a).Our data required significant additional analysis because our V s were suspiciously high.The V p sensitivity is consistent with challenges associated with using existing rock physics models to estimate porosity in weathered and crystalline rocks at the BW site (Flinchum et al., 2018a).At BW, a porous media rock physics model had to be used for the saprolite (V p < 1,200 m/s), and a differential effective medium (DEM) mode had to be used in the fractured bedrock (see Figure 2 from Flinchum et al., 2018a).Porous media models assume the matrix is supported by individual grains (Dvorkin et al., 1999;Dvorkin & Nur, 1996;Hashin & Shtrikman, 1963;Mindlin, 1949), while differential effective media (DEM) models a solid material with penny-shaped inclusions (Berryman et al., 2002).Both models show that velocity decreases with increasing porosity.However, the porous media model requires higher porosities to reduce the velocity than the DEM model (see Figure 2 in Flinchum et al., 2018a).In other words, the faster reduction of V p in the fractured bedrock is consistent with differences between DEM and porous media models for the mineralogy at the BW site.

Anisotropy, Water Saturation and Scaling Effects
P-wave velocities collected in saprolite over weathering crystalline bedrock can be anisotropic due to aligned fracture fabric or inherited foliation at field scales (Eppinger et al., 2021;Leone et al., 2020;Novitsky et al., 2018).The impact of anisotropy on V p /V s has been shown in laboratory studies (Wang et al., 2012).Therefore, depending on fracturing and foliation, measuring V p along a slow axis and V s along a fast axis could produce the low V p / V s values we observe.SCP L1 has much lower V p /V s values than SCP L2 (Figures 3d and 2).While we cannot rule out anisotropy as a contributing factor, we note that explaining the consistently low V p /V s values across the landscape with anisotropy alone would require near-vertical foliation with rather fortuitous alignment of strike directions perpendicular to the direction of each seismic transect.The could be tested with future seismic surveys to measure V p /V s values as a function of azimuth (Eppinger et al., 2021;Leone et al., 2020).
Seismic refraction velocities are averages over large volumes as a function of seismic wavelength (Flinchum et al., 2022).Because V s is slower than V p , S-waves have smaller wavelengths and therefore better resolution.Travel time tomography does not account for this difference in wavelength, but we did apply the same regularization and inverted the data on the same mesh for V p and V s .The contrasting wavelengths will cause the P-and S-waves to travel along slightly different paths and might cause the inversion to place boundaries in slightly different locations.If resolution and inversion regularization were the underlying cause of the low V p /V s values, we would expect the low V p /V s values to be isolated along major boundaries in the V p and V s models, contrary to what is observed (Figure 2).Future work could use joint inversion to structurally couple the V p and V s models to reduce the ambiguity around major V p and V s boundaries.The V p /V s response is sensitive to changes in saturation (Brantut & David, 2018;Hamada, 2004), since fluid-filled pores increase the bulk modulus and density of a porous material but not the shear modulus.This effect can be frequency-dependent (Biot, 1956a(Biot, , 1956b)), resulting in squirt flow (Markova et al., 2014).The V p increase can be dramatic in unconsolidated sands, where V p can rise rapidly from 100s of m/s to ∼1,500 m/s as full saturation is approached (Bachrach & Nur, 1998;Gregory, 1976;Liu & Zhao, 2015;Nur & Simmons, 1969).However, because water does not impact the shear modulus G, V s decreases slightly with increasing saturation as density increases.This phenomenon is why V p /V s values have been used to map the water table (Flinchum et al., 2020;Grelle & Guadagno, 2009;Mota & Santos, 2010;Pasquet et al., 2015a).There isn't a clear increase in V p /V s value that would indicate the water table in our data (Figure 2).

Conclusions
The results presented in this study show anomalously low V p /V s values from both seismic refraction and downhole sonic log data in weathered granites with different histories, lithologies, and climates.We argue that fractures generated by the expansion of biotite are a plausible mechanism to explain the low V p /V s values observed in the CZ.Observations that support our interpretation are that the low V p /V s values (<1.4) occur only in the fractured rock and saprolite, and that SEM images of an auxetic granite appear similar to weathered rock at our sites and have similar V p , V s , and V p /V s values to those observed in our data.Given the line configurations, we cannot rule out the impacts of seismic anisotropy, scaling, and water saturation.Nevertheless, in near-surface environments, the assumption that materials have a positive Poisson's ratio might not always be justified, especially weathered and fractured materials at low effective pressures.We are grateful to the many undergraduate researchers who helped collect the seismic refraction data for the Blair Wallis line as part of the Wyoming Center for Environmental Hydrology and Geophysics (WyCEHG) team.We are also grateful to the Bedrock Critical Zone Network team: Wynnie Avent, Alexa Dodson, Dillon Romero, Charles Lallatin, Kaycee Lallatin, Sky Bensel, Aran Lovato, Wade Renard, Annalee Chiaviello, and many others involved in logistics and project planning.This study was supported by the National Science Foundation award "Collaborative Research: Network Cluster: Bedrock controls on the deep critical zone, landscapes, and ecosystems" (NSFEAR 2012357, NSFEAR 2012227, NSFEAR 2012353) and "Water in a Changing West: The Wyoming Center for Environmental Hydrology and Geophysics" (NSFEPS 1208909).

Figure 1 .
Figure 1.(a) Hillshade LiDAR map showing the two profiles and borehole locations for the South Carolina Piedmont (SCP) site.(b) Hillshade LIDAR map showing the BW profile and borehole locations.Shot gathers and traces in panels c-h are from BW. (c)-(h) Examples of our P-wave and S-wave picks and data from vertical and horizontal shots.The red symbols are the P-wave travel time picks, and the cyan symbols are the S h -wave travel time picks.(c) Stacked shot gather using vertical geophones and vertical source.(d) Traces are from 10 m.The left trace is from the vertical shot gather (panel c) and the right trace is from the horizontal shot gather (panel f).(e) Pre-stacked traces from 10 m in the horizontal gather.The black trace represents the recording when swinging in direction 1 and the gray trace represents swinging in direction 2. The first arrival polarity is swapped indicating the S-wave arrival.When these two traces are subtracted it produces the second trace in panel d.(f) Stacked (by subtracting opposite direction swings) shot gather using horizontal geophones and the horizontal source.(g) Same as panel d but the traces are extracted from 130 m.The left trace is from the vertical shot gather (panel c) and the right trace is from the horizontal shot gather (panel f).(h) Same as panel e but for the trace at 130 m.

Figure 2 .
Figure 2. Seismic refraction results.The left column (a)-(c) are from SCP L2, the middle column (d)-(f) are from SCP L1, and the right column (g)-(i) are from BW.The top row (a, d, and g) are final V p models masked by ray coverage with the RMS fits shown in the lower right-hand corner.The solid black contour is 1,200 m/s, and the dashed black contours are 1,100 and 1,300 m/s.The solid gray contour is 4,000 m/s while the dashed gray contours are 3,500 and 4,500 m/s.The V s model results are the middle row (b, e, and h).The colormap has been rescaled, assuming a constant V p /V s value of 1.5.The velocity contours are from the V p model.The bottom row is the V p /V s values.The colormap was chosen so that values with V p /V s values less than 1.4 (   < 0) are shown as cooler colors and V p /V s values greater than 1.4 (   > 0) are shown in warmer colors.Poisson's ratios are shown in the color scale using Equation 1.

Figure 4 .
Figure 4. (a) SEM sections from a borehole ∼3 km Southwest of our location (Holbrook et al., 2019).The top panel shows an unweathered bedrock sample from 50 m depth and the bottom shows a weathered bedrock from 32 m depth.(b) SEM sections from a thermally treated granite from Griffiths et al. (2018).The top is the untreated sample, and the bottom plot is an SEM section after being heat treated to 450 C to induce microcracks.The samples' V p , V s , V p /V s values, and Poisson's ratios are reported on the panels.(c) Probability density functions of V p for all data with V p /V s values less than 1.4 (   < 0).The percentage data with values less than 1.4 are shown in each plot.Background colors are CZ structure based on V p .White is saprolite (V p ≤ 1,200 m/s), gray is fractured bedrock (1,200 m/s < V p ≤ 4,000 m/s), and dark gray is unfractured bedrock (V p > 4,000 m/s).(d) V p /V s values plotted as a function of V p and colored by V s .Gray shaded regions are the same as panel d with an additional gray rectangle to highlight V p /V s values less than 1.4.The top panel is for BW.The bottom panel is for SCP, which includes both SCP L1 and SCP L2.Squares are data from seismic refraction surveys, and circles are from sonic logs.The dashed black line is the theoretical V p /V s values assuming no porosity based on the mineralogic compositions from Flinchum et al. (2018a) and Flinchum et al. (2018b) for BW and Holbrook et al. (2019) for SCP (Supporting Information S1).The solid black line is the V p /V s value from the thermally treated granite shown in panel c.The dashed white line is our interpretation of the V p /V s value behavior as physical and chemical weathering creates porosity.The vertical white lines are approximate boundaries of change.The line at the highest P-wave velocities marks the onset of weathering, and the line around 1,200 m/s marks the location where V p /V s values increase.
experiments are required to rule out the impacts of anisotropy caused by fabric and foliation, the role of water saturation, and scaling effects.Low V p /V s values at two sites in two different climates, in both foliated and unfoliated bedrock, suggests a deeper underlying mechanism worth investigating.CZ geophysicists working in the low effective pressures near Earth's surface should remain open-minded to a much wider range of V p /V s values than usually expected at higher pressures because small cracks and fractures will remain open.