Seismometers, Networks, and Signal Processing

How are mechanical ground motions turned into trustworthy digital observations?

Fictional unit investigation. A fictional broadband station is upgraded during a month of local seismicity; the replacement sensor has different sensitivity, clipping behavior and data gaps. Students must avoid inventing a trend from the hardware change.

Before beginning, distinguish the scientific question, the measured quantity and the latent parameter that the student hopes to infer. Assign physical units, name a plausible alternate hypothesis, and state what data are fictional. For instruments, preserve original digital counts as well as corrected SI motion. Timing drift, channel orientation, response changes, and acquisition gaps can masquerade as evolving seismicity if ignored. The experiments are deliberately simplified so their calculations can be independently checked. They are not validated field instruments, real-time forecasts, or site-specific hazard assessments.

Learning goals. Explain the mechanism, translate the problem into measurable quantities, test an alternative interpretation and defend an uncertainty statement.

Physical foundation. Velocity sensors, accelerometers and broadband systems convert motion into signals with frequency-dependent gain and phase. Digitized counts require instrument metadata to be expressed as physical velocity, displacement or acceleration. In the broader unit, Reliable seismology starts with traceable measurement. Digitized amplitudes, timing systems and instrument calibration are not interchangeable; processing decisions alter the observability of phases and amplitudes. Archive station metadata with the actual waveform interval rather than assuming today’s response applied historically.

Observational method. Compare response-corrected and raw synthetic traces; record the poles, zeros, calibration factor and orientation metadata used. Specify the coordinate frame, observation period, relevant units, acquisition and calibration limitations before interpreting the resulting figure.

Common interpretive trap. The tallest digital count is not necessarily the strongest actual motion when instruments or gains differ. A neat numeric solution does not remove this interpretive ambiguity. Ask which further independent measurement could reveal whether the preferred explanation is incorrect.

Applied investigation. Document a corrected waveform with units and a record of the response-removal procedure. Provide a labeled sketch, a short reproducible table and a paragraph separating observed evidence from inferred process.

Interpretation and quantitative example

Worked case 3.1: Nyquist frequency. Synthetic input: 66.4 samples/s. Apply the explicitly declared relationship x/2 to obtain 33.2 Hz. Restrictions: Useful bandwidth also depends on analog antialias filters and sensor response. For this worked exercise, treat the input as a declared hypothetical value rather than a measurement. Copy the formula into a fresh calculation and check the unit conversion independently. Vary the input by ten percent and decide whether the output changes proportionally or nonlinearly. Explain which real-world conditions violate the assumptions listed. If the numeric result seems implausibly precise, round it appropriately and describe a physically meaningful range instead of inventing calibration. The purpose is transparent reasoning, not an official estimate. Trace all signal processing decisions to an observable consequence. If the spectrum changes after response removal, show the original count spectrum alongside the corrected SI spectrum. If a pick moves after filtering, report both times. If the sensor clipped, do not label amplitude restoration as a measurement unless an independent sensor constrains it.

Evidence design and falsification

Reconstruct the inference backwards. Start with the headline result and locate every conversion, classification and assumption required to obtain it. An estimate based on a chosen velocity, phase pick or site parameter should be labelled conditional on those inputs. Review the same steps after making one intentional mistake in the input metadata; document which output would become misleading and why. Here, the principal source of ambiguity is stated explicitly: The tallest digital count is not necessarily the strongest actual motion when instruments or gains differ. Method A: compute a baseline result using the stated relation, preserving all units. Method B: perturb one relevant input and record the change. Method C: replace the simplest assumption with an alternative that would be plausible at the study scale; if you cannot recalculate it with the available information, state what is missing. Method D: compare with an independent kind of observation, if available. This order avoids hiding assumptions under additional significant figures. End the notebook by explaining how the proposed investigation (Document a corrected waveform with units and a record of the response-removal procedure.) addresses at least one weakness of the primary model.

Knowledge check. (1) Which claim is directly observed and which is inferred? (2) How would an alternate model change the expected observation? (3) Which number must be accompanied by uncertainty? (4) Why is the worked result unsuitable as a real-time safety conclusion?

Learning goals. Explain the mechanism, translate the problem into measurable quantities, test an alternative interpretation and defend an uncertainty statement.

Physical foundation. Sample interval defines the Nyquist frequency, one half the sampling rate. Frequencies above it may alias unless appropriately filtered before sampling, and a high sample rate does not repair a noisy sensor. In the broader unit, Reliable seismology starts with traceable measurement. Digitized amplitudes, timing systems and instrument calibration are not interchangeable; processing decisions alter the observability of phases and amplitudes. Archive station metadata with the actual waveform interval rather than assuming today’s response applied historically.

Observational method. Generate two analytic sinusoids sampled at different rates and compare their discrete waveforms and apparent peaks. Specify the coordinate frame, observation period, relevant units, acquisition and calibration limitations before interpreting the resulting figure.

Common interpretive trap. Interpolating an undersampled waveform can make a smooth but wrong picture; it cannot recover unknown lost frequencies. A neat numeric solution does not remove this interpretive ambiguity. Ask which further independent measurement could reveal whether the preferred explanation is incorrect.

Applied investigation. Choose sampling and anti-alias constraints for distinct local and teleseismic signals. Provide a labeled sketch, a short reproducible table and a paragraph separating observed evidence from inferred process.

Interpretation and quantitative example

Worked case 3.2: Illustrative observed alias of a 16 Hz tone. Synthetic input: 20.16 samples/s. Apply the explicitly declared relationship Math.abs(16-Math.round(16/x)*x) to obtain 4.16 Hz. Restrictions: Sampling ideal single sinusoid; analog anti-alias filters are deliberately omitted. For this worked exercise, treat the input as a declared hypothetical value rather than a measurement. Copy the formula into a fresh calculation and check the unit conversion independently. Vary the input by ten percent and decide whether the output changes proportionally or nonlinearly. Explain which real-world conditions violate the assumptions listed. If the numeric result seems implausibly precise, round it appropriately and describe a physically meaningful range instead of inventing calibration. The purpose is transparent reasoning, not an official estimate. Trace all signal processing decisions to an observable consequence. If the spectrum changes after response removal, show the original count spectrum alongside the corrected SI spectrum. If a pick moves after filtering, report both times. If the sensor clipped, do not label amplitude restoration as a measurement unless an independent sensor constrains it.

Evidence design and falsification

A strong evidence chain identifies what the observer physically controls. Specify waveform or map provenance, the acquisition time standard, the instrument or field method, the adopted calibration, and an independent comparison. Is the observed pattern repeatable across genuinely separate records or did it arise after multiple views of the same data? Where an observation is transformed into a calculated quantity, retain its original units and values. Write an audit note on which data would be decisive and which are merely compatible. Here, the principal source of ambiguity is stated explicitly: Interpolating an undersampled waveform can make a smooth but wrong picture; it cannot recover unknown lost frequencies. Create a four-row evidence matrix: observed quantity, inferred physical quantity, principal confounder, and proposed falsifying observation. Mark an entry as measured only when acquisition metadata is known. Repeat the matrix for a second hypothesis instead of dismissing it without calculation. This discipline prevents a tidy narrative from substituting for testable physical interpretation. End the notebook by explaining how the proposed investigation (Choose sampling and anti-alias constraints for distinct local and teleseismic signals.) addresses at least one weakness of the primary model.

Knowledge check. (1) Which claim is directly observed and which is inferred? (2) How would an alternate model change the expected observation? (3) Which number must be accompanied by uncertainty? (4) Why is the worked result unsuitable as a real-time safety conclusion?

Learning goals. Explain the mechanism, translate the problem into measurable quantities, test an alternative interpretation and defend an uncertainty statement.

Physical foundation. Bandpass filtering can improve visibility of selected phases but also distort amplitude, timing and apparent onset, especially with sharp corners or short records. Integration of acceleration magnifies baseline offsets. In the broader unit, Reliable seismology starts with traceable measurement. Digitized amplitudes, timing systems and instrument calibration are not interchangeable; processing decisions alter the observability of phases and amplitudes. Archive station metadata with the actual waveform interval rather than assuming today’s response applied historically.

Observational method. Record raw and filtered synthetic traces together, specify filter order and corner frequencies, and inspect transients around gaps. Specify the coordinate frame, observation period, relevant units, acquisition and calibration limitations before interpreting the resulting figure.

Common interpretive trap. A cleaner picture is not proof of a cleaner measurement; phase shifts and ringing may create false arrivals. A neat numeric solution does not remove this interpretive ambiguity. Ask which further independent measurement could reveal whether the preferred explanation is incorrect.

Applied investigation. Explain how zero-phase and causal filters differ when timing must be interpreted. Provide a labeled sketch, a short reproducible table and a paragraph separating observed evidence from inferred process.

Interpretation and quantitative example

Worked case 3.3: Nyquist frequency. Synthetic input: 126.4 samples/s. Apply the explicitly declared relationship x/2 to obtain 63.2 Hz. Restrictions: Useful bandwidth also depends on analog antialias filters and sensor response. For this worked exercise, treat the input as a declared hypothetical value rather than a measurement. Copy the formula into a fresh calculation and check the unit conversion independently. Vary the input by ten percent and decide whether the output changes proportionally or nonlinearly. Explain which real-world conditions violate the assumptions listed. If the numeric result seems implausibly precise, round it appropriately and describe a physically meaningful range instead of inventing calibration. The purpose is transparent reasoning, not an official estimate. Trace all signal processing decisions to an observable consequence. If the spectrum changes after response removal, show the original count spectrum alongside the corrected SI spectrum. If a pick moves after filtering, report both times. If the sensor clipped, do not label amplitude restoration as a measurement unless an independent sensor constrains it.

Evidence design and falsification

When comparing scenarios, preserve the same measurement geometry if possible. A change in a source parameter may look like a path effect when stations or filters differ. Design a sensitivity table with columns for adopted value, plausible range, reason for uncertainty and effect on inference. Distinguish an instrumental limitation from a physical ambiguity: improving sampling can solve the former while the latter may need an entirely different experiment. Here, the principal source of ambiguity is stated explicitly: A cleaner picture is not proof of a cleaner measurement; phase shifts and ringing may create false arrivals. Build the result graph only after labelling its axes and quantities. Include a plausible range of inputs rather than a single favorable selection. Annotate any discontinuity, threshold or saturated measurement. Next, state whether the curve demonstrates a general law, a restricted approximation or merely the numerical behavior of an arbitrary toy formula. The caption should not promise resolution that the data cannot support. End the notebook by explaining how the proposed investigation (Explain how zero-phase and causal filters differ when timing must be interpreted.) addresses at least one weakness of the primary model.

Knowledge check. (1) Which claim is directly observed and which is inferred? (2) How would an alternate model change the expected observation? (3) Which number must be accompanied by uncertainty? (4) Why is the worked result unsuitable as a real-time safety conclusion?

Learning goals. Explain the mechanism, translate the problem into measurable quantities, test an alternative interpretation and defend an uncertainty statement.

Physical foundation. Absolute station clocks and known coordinates make phase arrival comparisons meaningful. Clock error, telemetry latency and incorrect component orientations can propagate directly into hypocenter error. In the broader unit, Reliable seismology starts with traceable measurement. Digitized amplitudes, timing systems and instrument calibration are not interchangeable; processing decisions alter the observability of phases and amplitudes. Archive station metadata with the actual waveform interval rather than assuming today’s response applied historically.

Observational method. Insert a known clock offset into a synthetic four-station pick table and inspect the residual pattern after inversion. Specify the coordinate frame, observation period, relevant units, acquisition and calibration limitations before interpreting the resulting figure.

Common interpretive trap. An excellent fit after freely adjusting station clocks is not independent validation of the estimated event location. A neat numeric solution does not remove this interpretive ambiguity. Ask which further independent measurement could reveal whether the preferred explanation is incorrect.

Applied investigation. Estimate how a stated timing uncertainty influences a first-order distance uncertainty. Provide a labeled sketch, a short reproducible table and a paragraph separating observed evidence from inferred process.

Interpretation and quantitative example

Worked case 3.4: Illustrative observed alias of a 16 Hz tone. Synthetic input: 27.91 samples/s. Apply the explicitly declared relationship Math.abs(16-Math.round(16/x)*x) to obtain 11.91 Hz. Restrictions: Sampling ideal single sinusoid; analog anti-alias filters are deliberately omitted. For this worked exercise, treat the input as a declared hypothetical value rather than a measurement. Copy the formula into a fresh calculation and check the unit conversion independently. Vary the input by ten percent and decide whether the output changes proportionally or nonlinearly. Explain which real-world conditions violate the assumptions listed. If the numeric result seems implausibly precise, round it appropriately and describe a physically meaningful range instead of inventing calibration. The purpose is transparent reasoning, not an official estimate. Trace all signal processing decisions to an observable consequence. If the spectrum changes after response removal, show the original count spectrum alongside the corrected SI spectrum. If a pick moves after filtering, report both times. If the sensor clipped, do not label amplitude restoration as a measurement unless an independent sensor constrains it.

Evidence design and falsification

Choose one prediction that would differ under a competing mechanism. A useful prediction has a measurable sign, timing, spectral or spatial signature rather than an undefined expectation that a map should look different. Explain how the predicted quantity would be calculated before looking at the fictional test record. If both explanations remain consistent with the evidence, report the unresolved alternatives and the next practical observation needed. Here, the principal source of ambiguity is stated explicitly: An excellent fit after freely adjusting station clocks is not independent validation of the estimated event location. Keep a processing log with coordinate reference, UTC times, units, processing order and exclusion rules. Compare pre- and post-processing records and explain discrepancies. In the conclusion, identify which claim survives the most consequential alternative parameterization. Reproducibility means another researcher could regenerate the result and find the same limitations, not simply the same decimal answer. End the notebook by explaining how the proposed investigation (Estimate how a stated timing uncertainty influences a first-order distance uncertainty.) addresses at least one weakness of the primary model.

Knowledge check. (1) Which claim is directly observed and which is inferred? (2) How would an alternate model change the expected observation? (3) Which number must be accompanied by uncertainty? (4) Why is the worked result unsuitable as a real-time safety conclusion?

Learning goals. Explain the mechanism, translate the problem into measurable quantities, test an alternative interpretation and defend an uncertainty statement.

Physical foundation. Gap codes, saturation, spikes, response changes and repeated packets belong in the provenance record. Waveform identifiers describe networks, stations, locations and channels; periods of validity matter. In the broader unit, Reliable seismology starts with traceable measurement. Digitized amplitudes, timing systems and instrument calibration are not interchangeable; processing decisions alter the observability of phases and amplitudes. Archive station metadata with the actual waveform interval rather than assuming today’s response applied historically.

Observational method. Audit a synthetic waveform manifest for overlapping samples, changes in gain and inconsistent UTC timestamps. Specify the coordinate frame, observation period, relevant units, acquisition and calibration limitations before interpreting the resulting figure.

Common interpretive trap. A data file without metadata is not self-explanatory even if it loads successfully in a plotting program. A neat numeric solution does not remove this interpretive ambiguity. Ask which further independent measurement could reveal whether the preferred explanation is incorrect.

Applied investigation. Write a station-quality summary with explicit exclusion and retention criteria. Provide a labeled sketch, a short reproducible table and a paragraph separating observed evidence from inferred process.

Interpretation and quantitative example

Worked case 3.5: Nyquist frequency. Synthetic input: 186.4 samples/s. Apply the explicitly declared relationship x/2 to obtain 93.2 Hz. Restrictions: Useful bandwidth also depends on analog antialias filters and sensor response. For this worked exercise, treat the input as a declared hypothetical value rather than a measurement. Copy the formula into a fresh calculation and check the unit conversion independently. Vary the input by ten percent and decide whether the output changes proportionally or nonlinearly. Explain which real-world conditions violate the assumptions listed. If the numeric result seems implausibly precise, round it appropriately and describe a physically meaningful range instead of inventing calibration. The purpose is transparent reasoning, not an official estimate. Trace all signal processing decisions to an observable consequence. If the spectrum changes after response removal, show the original count spectrum alongside the corrected SI spectrum. If a pick moves after filtering, report both times. If the sensor clipped, do not label amplitude restoration as a measurement unless an independent sensor constrains it.

Evidence design and falsification

Reconstruct the inference backwards. Start with the headline result and locate every conversion, classification and assumption required to obtain it. An estimate based on a chosen velocity, phase pick or site parameter should be labelled conditional on those inputs. Review the same steps after making one intentional mistake in the input metadata; document which output would become misleading and why. Here, the principal source of ambiguity is stated explicitly: A data file without metadata is not self-explanatory even if it loads successfully in a plotting program. Method A: compute a baseline result using the stated relation, preserving all units. Method B: perturb one relevant input and record the change. Method C: replace the simplest assumption with an alternative that would be plausible at the study scale; if you cannot recalculate it with the available information, state what is missing. Method D: compare with an independent kind of observation, if available. This order avoids hiding assumptions under additional significant figures. End the notebook by explaining how the proposed investigation (Write a station-quality summary with explicit exclusion and retention criteria.) addresses at least one weakness of the primary model.

Knowledge check. (1) Which claim is directly observed and which is inferred? (2) How would an alternate model change the expected observation? (3) Which number must be accompanied by uncertainty? (4) Why is the worked result unsuitable as a real-time safety conclusion?

Research scenario: A fictional broadband station is upgraded during a month of local seismicity; the replacement sensor has different sensitivity, clipping behavior and data gaps. Students must avoid inventing a trend from the hardware change. The goal is to produce a reasoned comparison of at least two defensible models, not to reverse-engineer a predetermined answer. Start by recording each input variable with units, a confidence grade and a plausible range. Name the forward calculation associated with each inference and outline how the inputs enter the formula. Preserve the fabricated dataset in its supplied CSV form and cite its generation method; these records do not correspond to real earthquakes or real sensor networks.

Procedure. First, draw a map or schematic that makes geometric assumptions visible. Second, check station or sample identifiers and the relationship of the observation period to the question. Third, compute baseline statistics and at least one worked relation by hand before using the browser model. Fourth, investigate a competing hypothesis using an independently chosen measurement or a perturbation of a consequential parameter. Fifth, repeat after withholding one doubtful observation. Compare whether the scientific conclusion survives that choice. Trace all signal processing decisions to an observable consequence. If the spectrum changes after response removal, show the original count spectrum alongside the corrected SI spectrum. If a pick moves after filtering, report both times. If the sensor clipped, do not label amplitude restoration as a measurement unless an independent sensor constrains it.

Required outputs. Submit a two-page technical brief with a hypothesis table, raw and corrected values, an equation inventory, an uncertainty budget, a labelled graphic and a short limitations section. Include all model parameters. Do not omit unsuccessful tests and do not represent computer-generated data as measured field observations. Students should record their own explanations rather than copying one another's interpretation. Discuss how different station distributions or sampling choices could cause an apparently significant spatial pattern without a corresponding physical change.

Extensions. Reliable seismology starts with traceable measurement. Digitized amplitudes, timing systems and instrument calibration are not interchangeable; processing decisions alter the observability of phases and amplitudes. Archive station metadata with the actual waveform interval rather than assuming today’s response applied historically. Write an explicit counterfactual: what observation would undermine the main hypothesis? Consider what a larger dataset could resolve and what it would leave uncertain. Finally, design an accessible presentation of the result with a descriptive figure caption, a plain-language explanation of each symbol, and a table of numerical values for readers who cannot interpret a colored graph. Re-evaluate the result against professional source and public-safety boundaries before suggesting a consequential application.

Peer-review rubric. Assign 0–4 points each for correctness of units, explicit assumptions, data provenance, comparison with alternatives, uncertainty treatment, computational reproducibility and ethical communication. A polished figure without units, or a convincing narrative without a falsifiable test, should not receive full credit. Explain in prose why the least certain input affects confidence, and identify at least one result that could change with additional observations.