Stanford University · Visiting Student Researcher · 2025 – 2026

New Methods for Ice-Penetrating Radar

Radar sees almost nothing in the lowest few hundred metres of Antarctic ice, so motion there is usually extrapolated. A year of radar data above a subglacial lake shows this zone still carries coherent phase, and two new estimators turn it into velocity down to the bed.

SiteMercer Subglacial Lake, West Antarctica
Record312 days · 1,878 radar bursts
InstrumentApRES FMCW radar, 200–400 MHz
Ice thickness1,094 m

Based on Evidence for Coherent Phase Signal in the Antarctic Echo-Free Zone by H. M. Stählin, D. M. Schroeder and M. R. Siegfried.

01

The measurement

A radar on the ice surface repeats the same measurement for almost a year. Everything here comes from how its echoes change.

moves with the ice · 226 m/yr ApRES 0 m 600 m 1,094 m Internal layers bright, continuous echoes Echo-Free Zone 20–30 dB weaker, no continuous layers Subglacial lake bright flat reflector
  1. 01

    One radar burst every four hours

    A 200 to 400 MHz sweep goes down into the ice. Echo delay gives depth in 5 cm steps, down to the lake at 1,094 m.

  2. 02

    Amplitude and phase at every depth

    Each depth returns an amplitude (echo strength) and a phase (position in the wave cycle). 1 mm of motion shifts the phase by 1.3°.

  3. 03

    312 days of repeats

    1,878 bursts side by side form the echogram. Downward motion makes the phase drift; sideways motion slowly scrambles the echo pattern.

Layers are easy to follow. The Echo-Free Zone has only weak echoes from small scatterers. Does their phase still record the motion?

02

The ice column

312 days of echoes and three profiles computed from them, on a shared depth axis. Hover to read one depth.

Echogram

Contrast equalized by depth. Weak echoes stay visible.

Coherence |γ|

Burst-to-burst phase stability, 0 to 1

Vertical velocity

CW-MLPRplug flow

Horizontal decorrelation

MDI P(v)median

Depth-
Zone-
Coherence-
Vertical (CW-MLPR)-
Plug-flow model-
Horizontal (MDI median)-

The EFZ is 20 to 30 dB weaker than the layers, so at true scale it looks empty. Equalized, its speckled echoes appear. In amplitude they resemble noise; the phase tells them apart.

Velocity is positive downward. The plug-flow line is fitted above 600 m only, so its match in the EFZ is an independent check. Diamonds: conventional layer tracking. Horizontal values are relative to the instrument, so ratios between depths are more reliable than absolute values.

03

Signal in the Echo-Free Zone

Is the EFZ phase more than noise? Step through the two corrections, with the noise below the bed as reference.

Depth window
Amplitude Amplitude of the selected depth window over 312 days
day 0day 312
Phase Phase of the selected depth window over 312 days
day 0day 312

04

Two estimators

Both work on the complex signal without tracking peaks, and apply every nonlinear step only after averaging over time, so noise cancels first.

CW-MLPR · vertical velocity

Coherence-Weighted Multi-Lag Phase Regression

Each depth is correlated with itself at lags of 1 to 8 bursts. The phase grows linearly with lag, at a rate set by the velocity, so a weighted line through the origin gives the velocity without phase unwrapping. With one lag it is the standard ApRES estimator.

v̂ = (λ/4π) · Σ |R(ℓ)| Φ(ℓ) τℓ / Σ |R(ℓ)| τℓ²
phase of each lag (size = weight) CW-MLPR fit true velocity
True-m/yr
CW-MLPR-RMSE -
Unwrap and fit-RMSE -

Simulated 1,878-burst record. Unwrap-and-fit is precise on clean data but fails below an SNR of about 2. RMSE over 40 runs.

MDI · horizontal velocity distribution

Multi-band Decorrelation Inversion

Scatterers drifting sideways through the beam lose coherence at a rate set by their speed. MDI measures this in three sub-bands and inverts them together for the full velocity distribution.

|γ(τ; λ)| = ∫ P(v) · exp(−4π²σθ² v² τ² / λ²) dv
Coherence by sub-band
Recovered distribution
low full high band true populations MDI

Forward model with the real-data settings (σθ = 0.22 rad, three sub-bands, lags to 104 days), inverted with non-negative least squares. A single-velocity fit (red) lands between the populations.