Agroseismology: Monitoring Soil Hydromechanics

• Agroseismology is a technique that employs DAS and hydromechanical modeling to continuously monitor soil water fluxes and structural changes in agricultural landscapes.
• It leverages high-resolution seismic observables and water-balance models to correlate rainfall, drainage, and evapotranspiration with dynamic soil stiffness and pore connectivity.
• The method facilitates real-time soil condition assessments and informs best practices for reducing water loss and mitigating compaction impacts in managed fields.

Searching arXiv for the specified paper to ground the article and citation. Agroseismology is the use of distributed acoustic sensing (DAS) and physics-based hydromechanical modeling to continuously monitor, interpret, and invert near-surface seismic property changes caused by water fluxes in managed agricultural soils. As defined in "Agroseismology: unraveling the impact of farming practices on soil hydrodynamics" (Shi et al., 11 Sep 2025), the field treats farmed landscapes as a natural laboratory in which replicated plots, controlled tillage depths and compaction histories, and strong meteorological forcing make it possible to test how disturbance reshapes pore connectivity, capillarity, and transient stiffness at minute-to-hour timescales and meter-scale spatial resolution. The framework links seismic velocity perturbations, rainfall forcing, storage changes, drainage, and evapotranspiration (ET), and uses these relationships to characterize how management alters flux partitioning, moisture redistribution, and the hydromechanical state of disturbed soils.

1. Conceptual basis

Soil structure governs water storage and movement, and management in the form of tillage and machinery compaction reorganizes porosity, pore-size distribution, and macropore connectivity. This reorganization changes how precipitation infiltrates, how capillary forces act during wetting and drying, and how evapotranspiration depletes near-surface water (Shi et al., 11 Sep 2025). In the agroseismological formulation, these structural modifications are not treated as secondary complications; they are the primary mechanism by which agricultural disturbance modulates hydrodynamics.

The central physical premise is that seismic wave speeds in the top tens of centimeters depend on the stiffness of the granular soil frame, which in turn depends on effective stress. In unsaturated soils, effective stress includes dynamic capillary suction that is sensitive to the rate of wetting and drying. Seismic velocities therefore encode information about the hydromechanical state of soil. This coupling allows DAS-derived seismic observables to be interpreted not merely as proxies for water content, but as signatures of effective stress, capillary state, and transient stiffness (Shi et al., 11 Sep 2025).

Farmed experimental fields are particularly suitable because they provide replicated conditions with known disturbance gradients. In the reported field setting, 27 plots, each approximately 4 m wide by 85 m long, had received one of three tillage regimes and one of three traffic regimes since 2011, producing stable contrasts in porosity and connectivity. This suggests that agroseismology is most informative where management histories are controlled well enough to support process attribution rather than purely descriptive monitoring.

2. Observational architecture and seismic observables

The observational design in agroseismology relies on shallow, continuous DAS acquisition across managed plots. A standard fiber-optic cable was trenched finger-wide into bare soil at approximately 2 cm depth, perpendicular to plot boundaries at Harper Adams University in the United Kingdom (Lat. 52.782, Long. −2.428). A Sintela Onyx 1.0 interrogator recorded continuously for 40 hours at 2 kHz sampling with 3.19 m channel spacing, and 51 well-coupled channels were used in the analysis (Shi et al., 11 Sep 2025).

The system provides meter-scale spatial sampling and minute-scale temporal sampling. The seismic products are organized around three observables: strain-rate-derived ambient noise auto-correlation functions (ACFs) used with coda stretching to estimate seismic velocity perturbations $\Delta v / v$; a rainfall proxy constructed from high-frequency DAS power spectral density (PSD) integrated over 80–140 Hz; and resonance peaks, with a 15–25 Hz fundamental and a 25–50 Hz overtone, indicating soft topsoil over stiffer subsoil and corroborating shallow stiffness changes (Shi et al., 11 Sep 2025).

The following table summarizes the principal observables.

Observable	Frequency range or cadence	Role
$\Delta v/v$ from ACFs and coda stretching	15–60 Hz; 5-minute cadence through stacking	Tracks seismic velocity perturbations, predominantly sensitive to shear-wave speed changes
Rainfall proxy from DAS PSD	80–140 Hz; 1-minute resolution	Tracks rainfall intensity and provides precipitation rate $R(t)$
Resonance peaks	15–25 Hz fundamental; 25–50 Hz overtone	Corroborates shallow stiffness changes

These observables jointly enable a closed interpretive chain from meteorological forcing to hydromechanical response. The rainfall proxy constrains precipitation input, $\Delta v/v$ measures the transient stiffness response, and the resonance behavior provides an independent consistency check on shallow structural changes. A plausible implication is that the method is especially powerful because each signal type constrains a different stage of the near-surface water balance rather than all quantities being inferred from a single seismic feature.

3. Signal processing and inversion workflow

The derivation of $\Delta v / v$ follows coda interferometry. For a diffuse ambient field, relative velocity change is inferred from coda time dilation. If $\mathrm{ACF}_{\mathrm{cur}}(t)$ is the current ACF and $\mathrm{ACF}_{\mathrm{ref}}(t)$ the reference, the stretching factor $\varepsilon$ maximizes

$CC(\varepsilon) = \frac{\int_{t_1}^{t_2} \mathrm{ACF}_{\mathrm{cur}\big(t(1+\varepsilon)\big)\,\mathrm{ACF}_{\mathrm{ref}(t)\,dt}} {\sqrt{\int [\mathrm{ACF}_{\mathrm{cur}]^2 dt}}\,\sqrt{\int [\mathrm{ACF}_{\mathrm{ref}]^2 dt}} .$

The velocity perturbation is $\Delta v/v = \varepsilon$ (Shi et al., 11 Sep 2025). The processing sequence uses bandpass filtering from 15–60 Hz, one-bit normalization, smoothing, stacking of four 15 s subwindows per minute, and a three-pass denoising routine to stabilize $\Delta v/v$0 during rapid transients. ACFs are computed over lag −5 s to +5 s and downsampled to 500 Hz, while the stretching grid search spans $\Delta v/v$1.

The rainfall proxy is computed separately. For each 1-minute file, the PSD is calculated and integrated over the 80–140 Hz band. Hourly sums of the band-limited energy are regressed against onsite rain-gauge hourly rainfall, and the scaled 1-minute PSD then gives precipitation rate $\Delta v/v$2 in mm/min. Strong broadband energy above 80 Hz coincides with rainfall, whereas weaker bursts with high spatial variability are flagged as non-rain sources, including wind, thunder, and anthropogenic activity (Shi et al., 11 Sep 2025).

The inversion algorithm uses the following sequence: estimate $\Delta v/v$3 per channel by coda stretching with three-pass denoising and piecewise polynomial smoothing to avoid cycle-skipping; use the lithological model to find $\Delta v/v$4 that best reproduces $\Delta v/v$5 over time by least-squares fitting; compute $\Delta v/v$6 and $\Delta v/v$7; and, with calibrated $\Delta v/v$8 and closed-form $\Delta v/v$9, infer $R(t)$0 as the residual of the water balance. The procedure can optionally regularize $R(t)$1 toward $R(t)$2 using the disturbance index, with uncertainty propagated from rainfall calibration errors, model mismatch, and noise in $R(t)$3 (Shi et al., 11 Sep 2025).

4. Hydromechanical formulation

The physical model connects water saturation, effective stress, granular contact mechanics, and seismic velocity. Standard wave-speed relations are written as

$R(t)$4

where $R(t)$5 is the drained bulk modulus, $R(t)$6 the shear modulus of the soil frame, and $R(t)$7 the bulk density. In the agroseismological formulation, the operative seismic observable is $R(t)$8, modeled as

$R(t)$9

with effective shear modulus $\Delta v/v$0 computed from Hertz–Mindlin contact theory and saturation-dependent bulk density

$\Delta v/v$1

Effective stress in unsaturated soils combines overburden minus fluid pressure plus suction stress,

$\Delta v/v$2

although the implementation adopts an equivalent formulation embedding suction into an effective confining pressure $\Delta v/v$3 (Shi et al., 11 Sep 2025).

Dynamic capillary effects are central. Capillary pressure departs from quasi-equilibrium under finite drainage and wetting rates according to

$\Delta v/v$4

where $\Delta v/v$5 is a dynamic capillarity coefficient that differs between wetting and drying. Rate-dependent suction stresses create hysteresis: rapid wetting produces transient softening, while rapid drying produces transient stiffening, even at fixed $\Delta v/v$6. This is the mechanistic basis for interpreting post-rain velocity drops and evapotranspiration-driven rebounds (Shi et al., 11 Sep 2025).

The soil frame is idealized as a random packing with average contact number $\Delta v/v$7 and non-slipping fraction $\Delta v/v$8, explored over $\Delta v/v$9–$\Delta v / v$0 and allowed to vary with $\Delta v / v$1. Given grain properties, Hertz–Mindlin contact theory yields

$\Delta v / v$2

and

$\Delta v / v$3

where $\Delta v / v$4 is a geometric/contact factor and $\Delta v / v$5 is the effective confining pressure. The latter aggregates gravitational loading, phase contributions, and dynamic suction:

$\Delta v / v$6

with effective saturation

$\Delta v / v$7

Residual saturation is $\Delta v / v$8 for clay and $\Delta v / v$9 for sand. Distinct dynamic capillarity coefficients are adopted for wetting and drying:

$\mathrm{ACF}_{\mathrm{cur}}(t)$0

These choices produce pronounced hysteresis in the $\mathrm{ACF}_{\mathrm{cur}}(t)$1–$\mathrm{ACF}_{\mathrm{cur}}(t)$2 trajectories, with larger and faster rebounds under drying and sharper drops under wetting (Shi et al., 11 Sep 2025).

5. Water-balance model, disturbance index, and evapotranspiration inversion

Rather than solving a full Richards equation, the framework uses a vertically averaged control-volume water budget for the upper approximately 10 cm:

$\mathrm{ACF}_{\mathrm{cur}}(t)$3

where $\mathrm{ACF}_{\mathrm{cur}}(t)$4 is precipitation rate from the DAS rainfall proxy, $\mathrm{ACF}_{\mathrm{cur}}(t)$5 is vertical drainage, and $\mathrm{ACF}_{\mathrm{cur}}(t)$6 is bare-soil evaporation modulated by a disturbance index $\mathrm{ACF}_{\mathrm{cur}}(t)$7 (Shi et al., 11 Sep 2025).

The evapotranspiration parameterization is

$\mathrm{ACF}_{\mathrm{cur}}(t)$8

with $\mathrm{ACF}_{\mathrm{cur}}(t)$9 for bare soil and reference evapotranspiration

$\mathrm{ACF}_{\mathrm{ref}}(t)$0

Here $\mathrm{ACF}_{\mathrm{ref}}(t)$1 is net radiation, $\mathrm{ACF}_{\mathrm{ref}}(t)$2 soil heat flux, $\mathrm{ACF}_{\mathrm{ref}}(t)$3 air temperature, $\mathrm{ACF}_{\mathrm{ref}}(t)$4 wind speed, $\mathrm{ACF}_{\mathrm{ref}}(t)$5 saturation vapor pressure, $\mathrm{ACF}_{\mathrm{ref}}(t)$6 actual vapor pressure, $\mathrm{ACF}_{\mathrm{ref}}(t)$7 the slope of the vapor pressure curve, and $\mathrm{ACF}_{\mathrm{ref}}(t)$8 the psychrometric constant. $\mathrm{ACF}_{\mathrm{ref}}(t)$9 is computed at 1-minute cadence from onsite or regional weather (Shi et al., 11 Sep 2025).

Drainage is represented by a convolution of rainfall with an exponential kernel:

$\varepsilon$0

where $\varepsilon$1 is the drainage timescale, approximately 70 h, consistent with nominal infiltration depths of approximately 0.7–1 m and hydraulic conductivity of approximately 10 mm/h. The disturbance index is parameterized by tillage depth $\varepsilon$2 and compaction $\varepsilon$3 as $\varepsilon$4 normalized to $\varepsilon$5. Grid search across plots yields $\varepsilon$6 and $\varepsilon$7, demonstrating compaction’s dominant control with secondary tillage influence (Shi et al., 11 Sep 2025).

This yields a forward chain from rainfall to saturation, from saturation to effective confining pressure, from confining pressure to frame stiffness and density, and from those quantities to seismic velocity. Observed velocities are expressed as

$\varepsilon$8

with $\varepsilon$9 set just after a reference rainfall event. The water-balance form used in inversion,

$CC(\varepsilon) = \frac{\int_{t_1}^{t_2} \mathrm{ACF}_{\mathrm{cur}\big(t(1+\varepsilon)\big)\,\mathrm{ACF}_{\mathrm{ref}(t)\,dt}} {\sqrt{\int [\mathrm{ACF}_{\mathrm{cur}]^2 dt}}\,\sqrt{\int [\mathrm{ACF}_{\mathrm{ref}]^2 dt}} .$0

makes ET a residual constrained jointly by DAS-derived rainfall, inferred storage change, and drainage closure (Shi et al., 11 Sep 2025).

6. Empirical findings and mechanistic interpretation

The principal empirical result is that rainfall triggers immediate negative $CC(\varepsilon) = \frac{\int_{t_1}^{t_2} \mathrm{ACF}_{\mathrm{cur}\big(t(1+\varepsilon)\big)\,\mathrm{ACF}_{\mathrm{ref}(t)\,dt}} {\sqrt{\int [\mathrm{ACF}_{\mathrm{cur}]^2 dt}}\,\sqrt{\int [\mathrm{ACF}_{\mathrm{ref}]^2 dt}} .$1 excursions across plots. Daily totals of 5–10 mm produce broadband DAS energy above 80 Hz and sharp post-rain velocity drops. Near-surface saturation produces sharp softening, and channels over high-disturbance plots show large negative $CC(\varepsilon) = \frac{\int_{t_1}^{t_2} \mathrm{ACF}_{\mathrm{cur}\big(t(1+\varepsilon)\big)\,\mathrm{ACF}_{\mathrm{ref}(t)\,dt}} {\sqrt{\int [\mathrm{ACF}_{\mathrm{cur}]^2 dt}}\,\sqrt{\int [\mathrm{ACF}_{\mathrm{ref}]^2 dt}} .$2 immediately after storms, consistent with rapid reduction of $CC(\varepsilon) = \frac{\int_{t_1}^{t_2} \mathrm{ACF}_{\mathrm{cur}\big(t(1+\varepsilon)\big)\,\mathrm{ACF}_{\mathrm{ref}(t)\,dt}} {\sqrt{\int [\mathrm{ACF}_{\mathrm{cur}]^2 dt}}\,\sqrt{\int [\mathrm{ACF}_{\mathrm{ref}]^2 dt}} .$3 by wetting. These transients occur within minutes and persist over multi-hour drainage windows (Shi et al., 11 Sep 2025).

A second result is the presence of large hysteretic velocity rebounds driven by ET. Under sunny, dry conditions, high-disturbance plots exhibit rapid drying, with $CC(\varepsilon) = \frac{\int_{t_1}^{t_2} \mathrm{ACF}_{\mathrm{cur}\big(t(1+\varepsilon)\big)\,\mathrm{ACF}_{\mathrm{ref}(t)\,dt}} {\sqrt{\int [\mathrm{ACF}_{\mathrm{cur}]^2 dt}}\,\sqrt{\int [\mathrm{ACF}_{\mathrm{ref}]^2 dt}} .$4 reductions up to approximately 50% within a single afternoon and $CC(\varepsilon) = \frac{\int_{t_1}^{t_2} \mathrm{ACF}_{\mathrm{cur}\big(t(1+\varepsilon)\big)\,\mathrm{ACF}_{\mathrm{ref}(t)\,dt}} {\sqrt{\int [\mathrm{ACF}_{\mathrm{cur}]^2 dt}}\,\sqrt{\int [\mathrm{ACF}_{\mathrm{ref}]^2 dt}} .$5 increases up to approximately 60%. The $CC(\varepsilon) = \frac{\int_{t_1}^{t_2} \mathrm{ACF}_{\mathrm{cur}\big(t(1+\varepsilon)\big)\,\mathrm{ACF}_{\mathrm{ref}(t)\,dt}} {\sqrt{\int [\mathrm{ACF}_{\mathrm{cur}]^2 dt}}\,\sqrt{\int [\mathrm{ACF}_{\mathrm{ref}]^2 dt}} .$6 traces define pronounced hysteresis loops in $CC(\varepsilon) = \frac{\int_{t_1}^{t_2} \mathrm{ACF}_{\mathrm{cur}\big(t(1+\varepsilon)\big)\,\mathrm{ACF}_{\mathrm{ref}(t)\,dt}} {\sqrt{\int [\mathrm{ACF}_{\mathrm{cur}]^2 dt}}\,\sqrt{\int [\mathrm{ACF}_{\mathrm{ref}]^2 dt}} .$7–$CC(\varepsilon) = \frac{\int_{t_1}^{t_2} \mathrm{ACF}_{\mathrm{cur}\big(t(1+\varepsilon)\big)\,\mathrm{ACF}_{\mathrm{ref}(t)\,dt}} {\sqrt{\int [\mathrm{ACF}_{\mathrm{cur}]^2 dt}}\,\sqrt{\int [\mathrm{ACF}_{\mathrm{ref}]^2 dt}} .$8 or $CC(\varepsilon) = \frac{\int_{t_1}^{t_2} \mathrm{ACF}_{\mathrm{cur}\big(t(1+\varepsilon)\big)\,\mathrm{ACF}_{\mathrm{ref}(t)\,dt}} {\sqrt{\int [\mathrm{ACF}_{\mathrm{cur}]^2 dt}}\,\sqrt{\int [\mathrm{ACF}_{\mathrm{ref}]^2 dt}} .$9–$\Delta v/v = \varepsilon$0 space: during drying, dynamic suction adds to effective stress faster than saturation alone would predict, yielding steep $\Delta v/v = \varepsilon$1 rebounds; during wetting, dynamic capillary effects suppress stiffness, leading to sharp drops. Morning-to-midday ET peaks produce fast rebound, whereas evening cooling slows ET and hysteresis relaxes (Shi et al., 11 Sep 2025).

Flux partitioning differs strongly across treatments. Low-disturbance plots, characterized by no or shallow tillage and low compaction, show minimal near-surface saturation perturbations over approximately 2 days, rapid infiltration into the vadose zone, muted $\Delta v/v = \varepsilon$2 excursions, and buffered ET response. High-disturbance plots, by contrast, exhibit near-surface saturation, prolonged drainage over several hours to days, and enhanced evaporation. Under shallow tillage plus high compaction, micropores dominate flow, enabling capillary rise and prolonged Stage I evaporation. Under deep tillage plus low compaction, disrupted macropore networks produce less efficient Stage II evaporation and shorter drainage tails. The disturbance-index fit explains the spatial trend of cumulative drainage-induced $\Delta v/v = \varepsilon$3 and its amplitudes along the cable (Shi et al., 11 Sep 2025).

The proposed mechanistic explanation is that repeated tillage and heavy machinery compaction reduce effective porosity and close macropores, including plow-pan formation at tillage depth and aggregate collapse. This impedes vertical connectivity, traps water near the surface, and shifts flow toward micropores. Smaller pores raise static suction, while limited connectivity increases redistribution time and amplifies dynamic suction. Hydrologically, near-surface saturation increases runoff and evaporation losses and decreases infiltration to the root zone; seismically, the same mechanisms produce larger $\Delta v/v = \varepsilon$4 swings and stronger hysteresis in high-disturbance plots (Shi et al., 11 Sep 2025).

7. Relation to other methods, implications, and limitations

Agroseismology is positioned relative to several established approaches to soil-moisture and hydrodynamics monitoring. Time-domain reflectometry and capacitance or impedance probes provide high accuracy but are point-scale and sparse, making scaling difficult under heterogeneity. Ground-penetrating radar provides high spatial resolution but limited temporal continuity and is sensitive to surface roughness and vegetation. Electrical resistivity, gamma-ray, and GNSS reflectometry are non-invasive but have varying sensitivity to moisture and may be limited by spatial coverage or temporal resolution. Cosmic-ray neutron sensing provides a hectare-scale footprint and continuous monitoring of near-surface water content but has limited vertical resolution and can be confounded by biomass or wet canopy (Shi et al., 11 Sep 2025).

Within that landscape, the reported advantages of agroseismology are that it is non-invasive, leverages existing fiber assets, offers meter-scale spatial continuity over tens of kilometers and minute-scale temporal resolution, and is directly sensitive to hydromechanical state rather than moisture alone. The principal limitations are that it requires good fiber–soil coupling, careful separation of hydrologic signals from anthropogenic and wind noise, and physics-based inversion to interpret $\Delta v/v = \varepsilon$5; parameters such as $\Delta v/v = \varepsilon$6 and contact properties must also be constrained (Shi et al., 11 Sep 2025).

The broader implications are threefold. For Earth system modeling, the method provides constraints on dynamic capillarity, hysteresis, and disturbance-evolving structural state, with the stated aim of improving parameterizations of land–atmosphere coupling, ET, runoff, and recharge. For land management, real-time spatially continuous tracking of near-surface storage and flux partitioning can guide low-disturbance practices that preserve macroporosity, buffer moisture volatility, and reduce evaporative losses. For hazards and infrastructure, time-variable near-surface $\Delta v/v = \varepsilon$7 challenges assumptions of stationary site conditions, and dynamic saturation and suction alter liquefaction susceptibility; partially saturated soils can liquefy once $\Delta v/v = \varepsilon$8 (Shi et al., 11 Sep 2025).

The framework also carries explicit assumptions and uncertainties. Hydrologically, it uses a first-order water balance with a drainage closure rather than explicitly solving

$\Delta v/v = \varepsilon$9

and retention functions such as van Genuchten are not explicitly solved. Mechanically, Hertz–Mindlin effective-medium assumptions and constant mineral properties introduce uncertainty, while $\Delta v/v$00 and $\Delta v/v$01 are simplified. The mapping from $\Delta v/v$02 to $\Delta v/v$03 depends on $\Delta v/v$04, $\Delta v/v$05, $\Delta v/v$06, $\Delta v/v$07, and $\Delta v/v$08, and requires regularization and prior bounds. The DAS footprint samples a quasi-1D transect, neglecting upslope and lateral flows and microtopography, and parameter robustness may vary under extreme compaction or under biological and chemical treatments (Shi et al., 11 Sep 2025).

Best practices identified for the method include shallow deployment at approximately 2 cm depth and perpendicular to treatment boundaries, use of two-band seismic products with low-frequency coda for $\Delta v/v$09 and high-frequency PSD for rainfall, application of multi-pass denoising and piecewise polynomial smoothing during rapid transients, and coupling of DAS observations with a physics-based hydromechanical model that explicitly includes dynamic capillarity and a disturbance index (Shi et al., 11 Sep 2025). Taken together, these elements define agroseismology as an integrated observational and inversion framework for resolving how agricultural disturbance reorganizes near-surface hydrodynamics through its effects on pore structure, capillarity, storage, drainage, and transient stiffness.