Reading Earth Normal-Mode Catalogues Back Into Hertz
Mode catalogues list every singlet in microhertz, to two decimal places, because that is the unit in which the splitting is visible. The moment you overlay one of those lines on a spectrum from a raw seismogram, or feed it to a filter design, you need the same number in hertz — the unit your acquisition, your response file and your Fourier axis all use.
What a Long-Period Station Is Actually Chasing
The Football Mode, 0S2
The Breathing Mode, 0S0
Below the Sensor's Corner
Checking a Catalogue Line Against Your Own Spectrum
Enter the catalogue frequency in microhertz
Type the tabulated value — 309.28, 468.55, 814.31 — exactly as printed. Comma or dot both parse, so a value copied from a European-formatted table needs no editing.
Read the hertz value for your Fourier axis
The second field updates on every keystroke, so stepping through a multiplet shows how far apart the singlets are in hertz. Values below 10-6 appear in exponential form.
Copy the plain number into a filter or a plot
Each field has its own copy button yielding digits alone — ready to paste as a bandpass corner or a vertical marker in a plotting script.
Reverse it to label a peak you just found
Press the swap arrow, or type on the hertz side, to take a peak from your own periodogram into microhertz for comparison with published tables.
Normal-Mode Frequencies, Periods and Overtone Order
The subscript before the letter is the overtone number and the one after it the angular degree; S denotes spheroidal motion, with a vertical component, while T denotes toroidal motion — purely horizontal shear, and therefore invisible to a vertical-component sensor.
| Mode | Catalogue frequency | Frequency in Hz | Period |
|---|---|---|---|
| 0S2 — gravest spheroidal | 309.28 μHz | 0.00030928 Hz | 3 233 s (53.9 min) |
| 0T2 — gravest toroidal | 379.30 μHz | 0.00037930 Hz | 2 636 s (43.9 min) |
| 0S3 | 468.55 μHz | 0.00046855 Hz | 2 134 s (35.6 min) |
| 0S4 | 647.07 μHz | 0.00064707 Hz | 1 545 s (25.8 min) |
| 0S0 — radial | 814.31 μHz | 0.00081431 Hz | 1 228 s (20.5 min) |
| 1S0 — first radial overtone | 1 631.36 μHz | 0.00163136 Hz | 613 s (10.2 min) |
Singlet Spacings Kept Intact
Eight decimals are carried through, so the hundredths of a microhertz separating members of a split multiplet survive the trip onto the hertz axis.
Response-File Units on Tap
Responses quote corners in hertz or seconds while mode tables use microhertz; reading one against the other shows how far below the corner a mode sits.
Record-Length Arithmetic in One Step
Enter the 1/T of your analysis window and read the bin width in microhertz to see which neighbouring modes that record can separate.
Questions From the Long-Period Seismology Bench
What is a normal mode, and how does it differ from a body or surface wave?
Body and surface waves are travelling disturbances: a packet leaves the source and arrives at a station minutes later. A normal mode is the standing-wave description of the same physics — a whole-Earth resonance in which every point moves in phase at one discrete frequency fixed by elastic structure, density and self-gravitation. The pictures are equivalent, since a mode can be built by summing surface-wave orbits that have circled the globe, but the standing-wave view is the useful one below a millihertz, where a wave train laps the planet several times before it decays.
Why does a great earthquake make the Earth ring for days?
Attenuation at these frequencies is extremely weak. Amplitude decays with a time constant of roughly Q·T/π, for quality factor Q and period T. With a Q near 500 and a period of 3 233 seconds, 0S2 takes about six days for one e-folding; 0S0, whose Q runs to several thousand, takes weeks. Only magnitude 8.5 or greater excites the gravest modes clearly above the background — hence the 1960 Chile and 2004 Sumatra textbook cases.
What does a seismometer's corner period mean for microhertz signals?
The corner marks where the sensor stops responding flat to ground velocity and begins rolling off. A 120-second instrument turns over at 8 333 μHz and a 360-second one at 2 778 μHz, so a 309 μHz mode is roughly a decade below even the longest-period corner. The signal is not lost — the response can be deconvolved — but sensitivity falls while self-noise and thermal drift rise, which is why superconducting gravimeters compete with seismometers in this band.
How long a record do I need to separate closely spaced modes?
Resolution is 1/T, with T the span of the record. A one-day window gives bins 11.57 μHz wide — barely enough to tell 0S2 from 0T2. Splitting within one multiplet runs to a few hundredths of a microhertz, and resolving 0.06 μHz needs about 193 days. Analysts trade the ends against each other: a long window buys resolution, but the mode decays throughout it, so signal-to-noise eventually falls faster than resolution improves.
Why do mode catalogues mix microhertz and millihertz?
The catalogue spans three decades and neither unit is comfortable across all of it. The gravest modes sit in the hundreds of microhertz, where two decimals express the splitting neatly. Higher overtones and the persistent hum between earthquakes run from about 2 to 7 millihertz, where microhertz values would need five digits. One line can therefore appear as 1 631.36 μHz in one table and 1.63136 mHz in the next.
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