Correct Static Shift#

This tutorial shows a conservative static-shift correction workflow for EDI surveys. It is written for the common profile-processing case: you have already loaded and inspected a survey, you suspect that some apparent-resistivity curves are shifted vertically, and you want to estimate station-level correction factors before preparing inversion files.

Static-shift correction should be handled carefully. It changes impedance amplitudes and apparent-resistivity levels. It does not fix bad phases, frequency-dependent source effects, wrong station coordinates, incorrect component orientation, or a poorly converted EDI file. Always inspect before and after correction.

What You Will Learn#

After this tutorial you should be able to:

diagnose when static-shift correction is worth trying
estimate station-level correction factors with AMA
inspect the meaning of delta_log10_rho, fac_rho, and fac_z
apply the correction without mutating the original survey
compare before and after correction using static-shift QC plots
export corrected EDI files and a correction manifest
choose between AMA, LOESS, reference-median, and bilateral correction styles
run static-shift correction from a pipeline configuration when needed

Prerequisites#

Run first-pass survey inspection before correcting static shift:

from pycsamt.api import read_edis
from pycsamt.emtools.qc import build_qc_table, station_confidence_table

survey = read_edis(
    "data/AMT/WILLY_DATA/L18PLT",
    recursive=False,
    strict=False,
    progress=False,
)
sites = survey.collection

qc = build_qc_table(sites, api=True)
confidence = station_confidence_table(sites, method="composite", api=True)

print(qc)
print(confidence)

Static-shift correction is usually a second step. If the survey did not pass basic loading, station-order, frequency-coverage, and quality checks, solve those problems first. See Inspect and QC a Survey.

This tutorial uses the bundled WILLY L18PLT line so the printed output and figures are reproducible. Replace the path with your own EDI directory when you repeat the workflow on another survey.

When Static Shift Is a Good Candidate#

Static shift is plausible when:

one station is shifted up or down relative to neighboring stations;
the apparent-resistivity curve shape is similar to neighboring curves;
phase does not show an equivalent anomaly;
the offset is approximately frequency independent over the selected band;
the station belongs to a profile where neighboring stations can define a local spatial trend.

Static-shift correction is risky when:

the anomaly is frequency dependent;
phase changes strongly at the same station;
the station order or coordinates are wrong;
several neighboring stations are shifted together because the geology is genuinely different;
the data contain strong CSAMT source effects or near-field behavior;
the EDI file came from another software package and still needs recomputation or component normalization.

For the scientific background, read Static Shift.

Create a Review Folder#

Keep factors, plots, and corrected files together.

from pathlib import Path

review_dir = Path("static_shift_review")
plot_dir = review_dir / "plots"
corrected_dir = review_dir / "corrected_edis"

plot_dir.mkdir(parents=True, exist_ok=True)
corrected_dir.mkdir(parents=True, exist_ok=True)

Estimate AMA Correction Factors#

The standard interactive correction path uses pycsamt.emtools.ss.estimate_ss_ama(). AMA means adaptive moving average: each station is compared with its neighbors in log apparent-resistivity space.

from pycsamt.emtools.ss import estimate_ss_ama

factors = estimate_ss_ama(
    sites,
    sort_by="lon",
    half_window=3,
    weights="tri",
    pband=None,
    max_skew=6.0,
    robust_freq="median",
    robust_overall="median",
    recursive=False,
    api=True,
)

factor_df = factors.to_pandas(copy=True)
factor_df.to_csv(review_dir / "static_shift_factors_ama.csv", index=False)
print(factors)
print(factor_df)

On L18PLT, the conservative skew filter still returns factors, but only a small number of frequency samples survive at many stations:

station  delta_log10_rho  fac_rho    fac_z  n_used
18-001A         1.026469 0.094087 0.306736       2
18-002U         0.393467 0.404141 0.635721       1
18-003A        -0.473762 2.976881 1.725364       1
18-004A        -0.203818 1.598887 1.264471       2
18-005U         0.317344 0.481566 0.693950       3

count    26.000000
mean      2.538462
min       1.000000
max       7.000000

That is a warning, not a failure. For this line, the first-pass QC tutorial already showed high skew across the profile. A strict skew mask leaves too few samples for a comfortable automatic correction, so the factors above should be treated as review evidence.

The factor table contains:

station: Station identifier used to match the factor back to the EDI object.
delta_log10_rho: Estimated log10 apparent-resistivity offset before correction. Positive values mean the station is high relative to its local trend. Negative values mean it is low.
fac_rho: Apparent-resistivity scale factor. This is the multiplicative correction for apparent resistivity.
fac_z: Impedance scale factor. pyCSAMT applies this to the impedance tensor because apparent resistivity is proportional to impedance amplitude squared.
n_used: Number of frequency samples used to estimate the station factor.

Choose the Spatial Order#

AMA needs the profile order to make physical sense. The sort_by parameter controls that order:

sort_by="lon": Use longitude. This is often reasonable for east-west lines.
sort_by="lat": Use latitude. This is often reasonable for north-south lines.
sort_by="name": Use station name order. This is useful when station names already encode line order and coordinates are missing or unreliable.

If the line is oblique, inspect the coordinates before deciding. A wrong order can make the algorithm compare stations that are not neighbors in the field.

Use a Period Band#

Sometimes only part of the spectrum is appropriate for estimating static shift. Use pband=(min_period, max_period) in seconds to restrict the factor estimate.

factors_mid_band = estimate_ss_ama(
    sites,
    sort_by="name",
    half_window=3,
    weights="tri",
    pband=(0.01, 10.0),
    max_skew=6.0,
    recursive=False,
    api=True,
)

factors_mid_band.to_pandas(copy=True).to_csv(
    review_dir / "static_shift_factors_ama_0p01s_10s.csv",
    index=False,
)

Choose a band where the curves appear shifted but not strongly distorted. Avoid using a band dominated by dead-band noise, transmitter source effects, or obvious phase jumps.

For the remaining figures in this tutorial, we use max_skew=None as an exploratory setting so every frequency contributes to the demonstration. In a production workflow, keep the stricter setting unless your dimensionality review justifies relaxing it.

factors_full_band = estimate_ss_ama(
    sites,
    sort_by="name",
    half_window=3,
    weights="tri",
    pband=None,
    max_skew=None,
    recursive=False,
    api=True,
)

factor_df = factors_full_band.to_pandas(copy=True)
print(factor_df.head(6))

Example output:

station  delta_log10_rho  fac_rho    fac_z  n_used
18-001A         0.672558 0.212541 0.461021      53
18-002U         0.625887 0.236654 0.486471      53
18-003A         0.291283 0.511349 0.715087      53
18-004A         0.432026 0.369806 0.608117      53
18-005U         0.634951 0.231766 0.481421      53
18-006A         0.293025 0.509302 0.713654      53

The tutorial figures are generated by docs/scripts/generate_tutorial_static_shift.py. The first figure shows the estimated station offsets. Blue bars have positive delta_log10_rho and therefore receive a downward resistivity correction; red bars move upward.

AMA static-shift factors estimated for the L18PLT tutorial line.

Inspect Large Corrections#

Large static-shift factors should be reviewed before they are applied.

large = factor_df[
    (factor_df["fac_rho"] < 0.5)
    | (factor_df["fac_rho"] > 2.0)
    | (factor_df["n_used"] < 5)
]

print("stations requiring manual review")
print(large[["station", "delta_log10_rho", "fac_rho", "fac_z", "n_used"]])

Example output from the exploratory full-band estimate:

stations requiring manual review
station  delta_log10_rho  fac_rho    fac_z  n_used
18-001A         0.672558 0.212541 0.461021      53
18-002U         0.625887 0.236654 0.486471      53
18-004A         0.432026 0.369806 0.608117      53
18-005U         0.634951 0.231766 0.481421      53
18-007U         0.602360 0.249827 0.499827      53
18-008U         0.593745 0.254833 0.504810      53
18-009A         0.832611 0.147024 0.383438      53
18-010U         0.696217 0.201272 0.448633      53

A factor outside 0.5 to 2.0 is not automatically wrong, but it should make you ask why the station is so different from its neighbors.

Apply Factors Manually#

The safest workflow is to estimate factors first, inspect them, then apply them to a copy of the site collection with pycsamt.emtools.ss.apply_ss_factors().

from pycsamt.emtools.ss import apply_ss_factors

corrected = apply_ss_factors(
    sites,
    factors_full_band,
    key="fac_z",
    inplace=False,
    recursive=False,
    verbose=1,
)

Because apparent resistivity is proportional to |Z|^2, applying fac_z changes determinant apparent resistivity by approximately -delta_log10_rho in log10 space:

18-001A  -0.672558
18-002U  -0.625887
18-003A  -0.291283
18-004A  -0.432026
18-005U  -0.634951
18-006A  -0.293025

Use inplace=False during exploration. This returns a corrected copy and keeps sites unchanged for comparison. Use inplace=True only inside a controlled pipeline or after you have saved the original state.

Apply AMA in One Step#

For routine processing, pycsamt.emtools.ss.correct_ss_ama() combines factor estimation and application:

from pycsamt.emtools.ss import correct_ss_ama

corrected = correct_ss_ama(
    sites,
    sort_by="name",
    half_window=3,
    weights="tri",
    pband=None,
    max_skew=None,
    robust_freq="median",
    robust_overall="median",
    inplace=False,
    recursive=False,
    verbose=1,
)

The one-step call returns a corrected Sites collection:

one_step_sites_type: Sites

The one-step function is convenient, but the two-step factor workflow is better when you are still learning the dataset.

Compare Before and After#

After correction, compare the original and corrected collections. A good correction should reduce station-level vertical jumps without creating frequency-dependent artifacts.

import matplotlib.pyplot as plt
from pycsamt.emtools.ss import (
    plot_ss_delta_profile,
    plot_ss_delta_psection,
    plot_ss_station_curves,
)

ax = plot_ss_delta_profile(
    sites,
    corrected,
    pband=None,
    robust="median",
)
ax.figure.savefig(plot_dir / "delta_profile.png", dpi=200, bbox_inches="tight")
plt.close(ax.figure)

ax = plot_ss_delta_psection(
    sites,
    corrected,
    axis_y="logperiod",
    pband=None,
)
ax.figure.savefig(plot_dir / "delta_psection.png", dpi=200, bbox_inches="tight")
plt.close(ax.figure)

ax = plot_ss_station_curves(
    sites,
    corrected,
    station=str(factor_df["station"].iloc[0]),
    pband=None,
)
ax.figure.savefig(plot_dir / "station_curve_before_after.png", dpi=200)
plt.close(ax.figure)

The generated determinant-resistivity comparison below is intentionally simple: the top panel reduces the correction to one median value per station, and the bottom panel shows that the applied static-shift factor is period independent.

Static-shift correction by station and by period for the L18PLT line.

Before and after apparent-resistivity curve for the largest corrected station.

The profile plot shows one correction value per station. The pseudo-section shows whether the correction is approximately uniform across period. The station-curve plot is useful for manual review of individual stations.

Use One-Call QC Wrappers#

The ss_qc_* helpers estimate, apply, and plot in one call. They are useful for fast experiments. Use return_sites=True when you want the corrected collection returned with the plot.

from pycsamt.emtools.ss import ss_qc_psection, ss_qc_profile

ax, corrected_preview = ss_qc_profile(
    sites,
    method="ama",
    return_sites=True,
    sort_by="lon",
    half_window=3,
    max_skew=6.0,
)
ax.figure.savefig(plot_dir / "ama_preview_profile.png", dpi=200)
plt.close(ax.figure)

ax = ss_qc_psection(
    sites,
    method="ama",
    sort_by="lon",
    half_window=3,
    max_skew=6.0,
    axis_y="logperiod",
)
ax.figure.savefig(plot_dir / "ama_preview_psection.png", dpi=200)
plt.close(ax.figure)

These wrappers are excellent for exploration. For a formal processing record, also save the factor table produced by estimate_ss_ama.

Try Alternative Estimators#

AMA is the recommended starting point, but pyCSAMT also exposes other factor estimators:

from pycsamt.emtools.ss import (
    estimate_ss_bilateral,
    estimate_ss_loess,
    estimate_ss_refmedian,
)

loess = estimate_ss_loess(
    sites,
    half_window=3,
    poly=1,
    it=2,
    pband=(0.01, 10.0),
    max_skew=6.0,
    api=True,
)

bilateral = estimate_ss_bilateral(
    sites,
    half_window=4,
    pband=(0.01, 10.0),
    max_skew=6.0,
    summary="median",
    api=True,
)

refmedian = estimate_ss_refmedian(
    sites,
    pband=(0.01, 10.0),
    max_skew=6.0,
    api=True,
)

loess.to_pandas(copy=True).to_csv(review_dir / "factors_loess.csv", index=False)
bilateral.to_pandas(copy=True).to_csv(
    review_dir / "factors_bilateral.csv",
    index=False,
)
refmedian.to_pandas(copy=True).to_csv(
    review_dir / "factors_refmedian.csv",
    index=False,
)

For L18PLT, the first rows of the comparison show why method comparison is useful:

station      ama    loess  refmedian  bilateral
18-001A 0.461021 1.438779   0.654036   0.191077
18-002U 0.486471 0.906571   0.909473   0.256785
18-003A 0.715087 1.416089   1.304343   0.322513
18-004A 0.608117 0.829027   0.901936   0.239036
18-005U 0.481421 0.672624   0.840085   0.222722
18-006A 0.713654 1.202319   1.115067   1.147786

Comparison of static-shift factor estimators for the L18PLT tutorial line.

Use the alternatives as checks:

estimate_ss_loess: Useful when you want a local smooth trend rather than a simple moving neighbor median.
estimate_ss_refmedian: Useful when the whole profile can be compared to a survey-wide reference.
estimate_ss_bilateral: Useful when you want spatial weighting that also respects value similarity.

If all methods point to the same shifted stations, confidence in the correction increases. If the methods disagree strongly, inspect the data before applying a large correction.

Export Corrected EDI Files#

Once the correction is accepted, export the corrected collection as new EDI files. Do not overwrite the raw EDI directory during tutorial or exploratory work.

from pycsamt.site.export import write_sites

written = write_sites(
    corrected,
    corrected_dir,
    template="{station}_static_shift_corrected.edi",
    exist_ok=True,
    manifest_csv=review_dir / "corrected_edi_manifest.csv",
)

print(f"wrote {len(written)} corrected EDI files")

The manifest records which station was written to which file. Keep it with the factor table and QC plots.

Run Through a Pipeline#

For repeatable production work, put static-shift correction in a pipeline configuration. SS001 is the AMA correction step.

name: static_shift_review
input: data/AMT/WILLY_DATA/L18PLT
output_dir: results/static_shift_review

steps:
  - name: qc_before
    code: QC001
  - name: static_shift
    code: SS001
    params:
      sort_by: lon
      half_window: 3
      weights: tri
      max_skew: 6.0
  - name: qc_after
    code: QC001

Inspect the registered static-shift steps from the command line:

pycsamt pipe steps --category static_shift

The pipeline registry currently includes:

SS001: AMA correction with pycsamt.emtools.ss.correct_ss_ama().
SS002: LOESS factor estimation followed by factor application.
SS003: Reference-median factor estimation followed by factor application.
SS004: Bilateral factor estimation followed by factor application.

Use the pipeline when the same correction recipe must be shared, reviewed, or re-run on several lines.

Checklist Before Inversion#

Before using corrected data for inversion preparation, confirm that:

the original EDI files are still available;
the factor table has been saved;
large correction factors have been manually reviewed;
phase behavior is still geologically reasonable;
correction plots show station-level offsets, not frequency-dependent distortion;
corrected EDI files were exported into a separate directory;
the inversion input preparation step points to the corrected directory, not the raw directory by accident.

Troubleshooting#

All factors are exactly one: The selected band may not contain usable samples, all stations may already be aligned, or the estimator could not build a neighbor trend.
One station receives an extreme factor: Check whether it has enough frequencies, whether its coordinates are correct, and whether the station is an actual geologic outlier.
The pseudo-section correction is not period independent: The problem may not be static shift. Inspect source effects, dead-band behavior, phase jumps, and frequency-dependent noise.
Corrected curves look worse: Revisit station order, period band, half_window, and skew threshold. Try sort_by="name" if coordinates are unreliable.
Correction changes interpretation too strongly: Treat the correction as provisional. Run one inversion with raw data and one with corrected data, then compare residuals and geologic plausibility.