CSAMT axial-anisotropy diagnostics (pycsamt.emtools.anisotropy)

pycsamt.emtools.anisotropy implements the axial-anisotropy metrics from Wang & Tan (2017, J. Appl. Geophys. 146): the two independent Cagniard apparent resistivities

\[\rho_{xy} = \frac{|Z_{xy}|^2}{\omega \mu_0} \qquad \rho_{yx} = \frac{|Z_{yx}|^2}{\omega \mu_0}\]

their log-ratio \(\Lambda = \log_{10}(\rho_{xy}/\rho_{yx})\) (zero for a perfectly isotropic 1-D earth), plus the classic Swift (1967) skew and strike computed from the full impedance tensor. Three functions cover this: analyze_anisotropy() (per-frequency detail), anisotropy_table() (per-station summary with an anisotropy_flag), and plot_anisotropy() (station x period pseudo-section, parameterised by metric).

This is a CSAMT-band method, so it needs a controlled-source-style frequency sweep rather than long-period natural-source MT — this example therefore uses L18PLT (and, for the comparison at the end, L22PLT) from data/AMT/WILLY_DATA/ (see its README.md): a real AMT/CSAMT field line spanning 1 Hz-10.4 kHz over 53 frequencies, with a full, energetic Z tensor (unlike KAP03’s long-period natural-source band used in the tf example).

Load the L18PLT line and compute both tables

_datasets.py is the shared loader introduced in the tf example. analyze_anisotropy() returns one row per (station, frequency); anisotropy_table() collapses that to one row per station.

import matplotlib.pyplot as plt
from _datasets import load_survey

from pycsamt.emtools import (
    ANISO_RATIO_THRESH,
    SWIFT_SKEW_THRESH,
    analyze_anisotropy,
    anisotropy_table,
    plot_anisotropy,
)

survey = load_survey("amt_l18plt")
detail = analyze_anisotropy(survey)
table = anisotropy_table(survey)

print(f"{len(table)} stations, {len(detail)} station-frequency rows")
print(
    f"flagged at defaults (|ratio|>{ANISO_RATIO_THRESH} or skew>{SWIFT_SKEW_THRESH}): "
    f"{int(table['anisotropy_flag'].sum())}/{len(table)}"
)

28 stations, 1484 station-frequency rows
flagged at defaults (|ratio|>0.1 or skew>0.2): 28/28

1. One station’s raw metrics vs. period

Before the multi-station views, it helps to see what analyze_anisotropy() actually returns for a single station: the log-ratio \(\Lambda\) and the Swift skew, both as plain functions of period. 18-009A is used here because its profile is well-behaved — some stations in this line have a handful of extreme skew spikes (see step 3b) that would make a first introduction confusing.

station = "18-009A"
d = detail[detail["station"] == station].sort_values("period_s")

fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(7, 6), sharex=True)
ax1.semilogx(d["period_s"], d["ratio_log10"], "o-", ms=3, color="#1f77b4")
ax1.axhline(ANISO_RATIO_THRESH, color="0.4", ls="--", lw=1)
ax1.axhline(-ANISO_RATIO_THRESH, color="0.4", ls="--", lw=1)
ax1.set_ylabel(r"$\log_{10}(\rho_{xy}/\rho_{yx})$")
ax1.set_title(f"{station} — anisotropy ratio and Swift skew vs. period")
ax1.grid(alpha=0.3)

ax2.semilogx(d["period_s"], d["swift_skew"], "o-", ms=3, color="#d62728")
ax2.axhline(
    SWIFT_SKEW_THRESH, color="0.4", ls="--", lw=1, label="flag threshold"
)
ax2.set_ylabel("Swift skew S")
ax2.set_xlabel("Period (s)")
ax2.legend(fontsize=8, loc="upper left")
ax2.grid(alpha=0.3)
fig.tight_layout()

Reading this figure. The ratio (top) stays mostly positive and grows toward longer periods, crossing the +0.1 flag line for most of the band. The skew (bottom) sits above its 0.2 flag threshold at essentially every period, reaching 1-2.5 — a genuinely 3-D-looking response by both independent indicators, not a marginal, one-metric call.

2. Per-station ranking

anisotropy_table() collapses the whole band into one row per station. With the module’s default thresholds, every one of this line’s 28 stations gets anisotropy_flag=True — unsurprising for real, non-ideal field data, and a reminder that the binary flag is less useful here than the relative ranking between stations.

t = table.copy()
t["abs_ratio"] = t["mean_ratio_log10"].abs()
by_ratio = t.sort_values("abs_ratio")
by_skew = t.sort_values("mean_swift_skew")

fig, (axr, axs) = plt.subplots(1, 2, figsize=(10, 6), sharey=False)
axr.barh(by_ratio["station"], by_ratio["abs_ratio"], color="#1f77b4")
axr.axvline(ANISO_RATIO_THRESH, color="0.3", ls="--", lw=1)
axr.set_xlabel(r"$|\overline{\log_{10}(\rho_{xy}/\rho_{yx})}|$")
axr.set_title("Ranked by mean ratio")
axr.tick_params(axis="y", labelsize=6)

axs.barh(by_skew["station"], by_skew["mean_swift_skew"], color="#d62728")
axs.axvline(SWIFT_SKEW_THRESH, color="0.3", ls="--", lw=1)
axs.set_xlabel("mean Swift skew")
axs.set_title("Ranked by mean skew")
axs.tick_params(axis="y", labelsize=6)
fig.tight_layout()

Reading this figure. The two rankings do not agree on a “most anisotropic” station: 18-016A tops the ratio ranking (\(|\Lambda|\) ≈ 1.9) but is unremarkable in skew, while 18-007U tops the skew ranking (≈5.1) yet has one of the smallest mean ratios (≈0.06). Step 5 below quantifies this across the whole survey — the two metrics are picking up genuinely different aspects of non-1-D structure.

3. Ratio pseudo-section

plot_anisotropy() grids a chosen metric onto a station x period pseudo-section — the module’s core view, and the multi-station counterpart to step 1’s single-station line plot.

plot_anisotropy(survey, metric="ratio_log10")

<Axes: title={'center': 'Anisotropy: log₁₀(ρ_xy/ρ_yx) (wang2017)'}, xlabel='Station', ylabel='Period (s)'>

Reading this figure. Colour warms (ratio increases) toward the bottom of the section for most stations — the same long-period growth seen for 18-009A in step 1 turns out to be a profile-wide pattern, not a one-station quirk. 18-016A-18-018A (the top of the step-2 ratio ranking) stand out as a sustained warm block rather than an isolated spike, which is a good sign it reflects real structure rather than a processing artefact.

3b. Swift-skew pseudo-section — and a numerical caution

The same function, metric="swift_skew".

plot_anisotropy(survey, metric="swift_skew")

<Axes: title={'center': 'Anisotropy: Swift skew S (wang2017)'}, xlabel='Station', ylabel='Period (s)'>

Reading this figure. Unlike the ratio section, this one has sharp, narrow, very intense pixels rather than broad warm regions — most strikingly at 18-007U, whose per-frequency values include a single spike above 44 (its neighbours in period sit around 1-2). Swift skew is defined as \(|Z_{xx}-Z_{yy}| / |Z_{xy}+Z_{yx}|\): whenever the denominator happens to pass near zero at one frequency, the ratio blows up without any corresponding physical anomaly. Treat isolated single-pixel extremes in a skew section with suspicion — the broad, multi-frequency patterns (as for 18-016A-18-018A here too) are the trustworthy signal.

3c. Strike pseudo-section

metric="strike_deg" — the Swift-decomposition strike angle, with the usual 90 degree ambiguity of any EM strike estimate.

plot_anisotropy(survey, metric="strike_deg")

<Axes: title={'center': 'Anisotropy: Strike angle θ (°) (wang2017)'}, xlabel='Station', ylabel='Period (s)'>

Reading this figure. plot_anisotropy also accepts metric="phase_diff_deg" (φ_xy − φ_yx) the same way, not shown here to keep this gallery page from repeating the same figure type a fourth time — its API reference entry covers it.

4. Advanced: comparing two lines of the same survey

plot_anisotropy accepts an ax so two lines can be placed side by side on one figure — here L18PLT against its neighbour L22PLT.

survey22 = load_survey("amt_l22plt")
table22 = anisotropy_table(survey22)

fig, (axa, axb) = plt.subplots(1, 2, figsize=(12, 5), sharey=True)
plot_anisotropy(survey, metric="ratio_log10", ax=axa)
axa.set_title("L18PLT")
plot_anisotropy(survey22, metric="ratio_log10", ax=axb)
axb.set_title("L22PLT")
fig.tight_layout()

print(
    f"L18PLT: mean|ratio|={table['mean_ratio_log10'].abs().mean():.2f}, "
    f"mean skew={table['mean_swift_skew'].mean():.2f}, "
    f"median strike={table['median_strike_deg'].median():.1f} deg"
)
print(
    f"L22PLT: mean|ratio|={table22['mean_ratio_log10'].abs().mean():.2f}, "
    f"mean skew={table22['mean_swift_skew'].mean():.2f}, "
    f"median strike={table22['median_strike_deg'].median():.1f} deg"
)

L18PLT: mean|ratio|=0.58, mean skew=1.95, median strike=24.4 deg
L22PLT: mean|ratio|=0.52, mean skew=1.76, median strike=17.7 deg

Reading this figure. Both lines show the same qualitative long-period warming, and their summary numbers are close (mean |ratio| 0.58 vs 0.52, mean skew 1.95 vs 1.76, median strike 24 deg vs 18 deg) — reasonable agreement for two neighbouring lines from the same survey, and a useful sanity check: a line whose numbers were wildly different from its neighbour would be worth re-inspecting for a processing problem before trusting its anisotropy result.

5. Advanced: do the two metrics actually agree?

Step 2 showed two rankings that disagreed at the extremes. Pooling both lines’ per-station summaries makes it precise: is |ratio| and skew correlated across the whole survey, or genuinely independent?

import pandas as pd  # noqa: E402

both = pd.concat([table.assign(line="L18PLT"), table22.assign(line="L22PLT")])
corr = both["mean_ratio_log10"].abs().corr(both["mean_swift_skew"])

fig, ax = plt.subplots(figsize=(6, 5))
for line, marker in [("L18PLT", "o"), ("L22PLT", "^")]:
    sub = both[both["line"] == line]
    ax.scatter(
        sub["mean_swift_skew"],
        sub["mean_ratio_log10"].abs(),
        label=line,
        marker=marker,
        alpha=0.8,
    )
ax.set_xlabel("mean Swift skew")
ax.set_ylabel(r"$|\overline{\log_{10}(\rho_{xy}/\rho_{yx})}|$")
ax.set_title(f"Ratio vs. skew across both lines  (Pearson r = {corr:.2f})")
ax.legend()
ax.grid(alpha=0.3)

Reading this figure. Across all 53 stations from both lines, mean |ratio| and mean skew are negatively correlated (Pearson r ≈ -0.5) — stations with a strong ρ_xy/ρ_yx contrast tend to have comparatively modest Swift skew, and vice versa, echoing 18-016A vs 18-007U in step 2. That is the practical conclusion of this whole page: the two indicators are not redundant. A site could pass as “isotropic” on one and still be clearly non-1-D on the other, so a real assessment should check both rather than either alone.