Ground Motion, Site Effects, and Engineering Interfaces

Why do different sites shake differently during the same earthquake?

Fictional unit investigation. A synthetic urban transect crosses bedrock, alluvium and a sedimentary basin. Stations recorded the same distant event but display different frequency content, durations and amplitudes.

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 ground motion, source, travel path, near-surface stratigraphy and structural response all matter. An average amplification ratio has frequency and motion-level dependence; do not apply simplified models as design coefficients. 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. Ground motion records may be expressed as acceleration, velocity or displacement and converted by differentiation or integration with careful baseline treatment. Peak values refer to different physical measures. In the broader unit, Source, path, site and engineered system each contribute to observed impact. A magnitude is not a direct measure of local shaking or expected losses. Teaching oscillators are valuable for reasoning about resonance but cannot certify real structures or replace seismic design standards.

Observational method. Compare toy acceleration pulses with different durations; numerically integrate after removing an explicitly defined offset. Specify the coordinate frame, observation period, relevant units, acquisition and calibration limitations before interpreting the resulting figure.

Common interpretive trap. High PGA does not guarantee the greatest permanent damage; duration and structural response change the outcome. 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. Present a table of PGA, PGV and period content with units and preprocessing notes. Provide a labeled sketch, a short reproducible table and a paragraph separating observed evidence from inferred process.

Interpretation and quantitative example

Worked case 5.1: Quarter-wavelength fundamental site frequency. Synthetic input: 54.65 m. Apply the explicitly declared relationship 350/(4*x) to obtain 1.6011 Hz. Restrictions: One-dimensional uniform low-velocity layer Vs=350 m/s above rigid base. 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. The shaking at a point contains contributions from rupture direction, travel distance, attenuation and local stratigraphy. Compare frequency content and duration as well as one peak amplitude. Explain why a field observation of damage needs construction and vulnerability information before the physical motion can be converted into a loss statement.

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: High PGA does not guarantee the greatest permanent damage; duration and structural response change the outcome. 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 (Present a table of PGA, PGV and period content with units and preprocessing notes.) 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. Soft sediments and basins can amplify or prolong motion at some frequencies through impedance contrast, trapped waves and resonance. Local conditions matter alongside event magnitude and distance. In the broader unit, Source, path, site and engineered system each contribute to observed impact. A magnitude is not a direct measure of local shaking or expected losses. Teaching oscillators are valuable for reasoning about resonance but cannot certify real structures or replace seismic design standards.

Observational method. Compare transfer functions from two fictional sites and estimate quarter-wavelength resonance for a uniform surface layer. Specify the coordinate frame, observation period, relevant units, acquisition and calibration limitations before interpreting the resulting figure.

Common interpretive trap. Every soft soil site does not amplify every frequency, and a one-dimensional resonance model can miss basin edges. 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 fundamental frequency for a stated layer thickness and shear-wave speed. Provide a labeled sketch, a short reproducible table and a paragraph separating observed evidence from inferred process.

Interpretation and quantitative example

Worked case 5.2: Intrinsic attenuation amplitude ratio. Synthetic input: 168.4 km. Apply the explicitly declared relationship Math.exp(-Math.PI2x/(150*3.5)) to obtain 0.133266 ratio. Restrictions: f=2 Hz, Q=150, v=3.5 km/s; geometric spreading and scattering excluded. 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. The shaking at a point contains contributions from rupture direction, travel distance, attenuation and local stratigraphy. Compare frequency content and duration as well as one peak amplitude. Explain why a field observation of damage needs construction and vulnerability information before the physical motion can be converted into a loss statement.

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: Every soft soil site does not amplify every frequency, and a one-dimensional resonance model can miss basin edges. 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 fundamental frequency for a stated layer thickness and shear-wave speed.) 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. Ground-motion prediction equations relate motion to magnitude, distance, faulting and site parameters using empirically calibrated models. Their uncertainties include natural variability as well as parameter estimation. In the broader unit, Source, path, site and engineered system each contribute to observed impact. A magnitude is not a direct measure of local shaking or expected losses. Teaching oscillators are valuable for reasoning about resonance but cannot certify real structures or replace seismic design standards.

Observational method. Use a toy attenuation curve for a fixed scenario and compare it with invented station observations at multiple distances. Specify the coordinate frame, observation period, relevant units, acquisition and calibration limitations before interpreting the resulting figure.

Common interpretive trap. A classroom curve is not a building code map or a substitute for local ground-motion models and engineering review. 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. Calculate a simple amplitude attenuation factor and examine how the assumed Q changes predictions. Provide a labeled sketch, a short reproducible table and a paragraph separating observed evidence from inferred process.

Interpretation and quantitative example

Worked case 5.3: Quarter-wavelength fundamental site frequency. Synthetic input: 102.15 m. Apply the explicitly declared relationship 350/(4*x) to obtain 0.856583 Hz. Restrictions: One-dimensional uniform low-velocity layer Vs=350 m/s above rigid base. 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. The shaking at a point contains contributions from rupture direction, travel distance, attenuation and local stratigraphy. Compare frequency content and duration as well as one peak amplitude. Explain why a field observation of damage needs construction and vulnerability information before the physical motion can be converted into a loss statement.

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 classroom curve is not a building code map or a substitute for local ground-motion models and engineering review. 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 (Calculate a simple amplitude attenuation factor and examine how the assumed Q changes predictions.) 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. A response spectrum summarizes the peak response of idealized oscillators at varying natural periods and damping ratios. It is not an earthquake forecast or a unique waveform description. In the broader unit, Source, path, site and engineered system each contribute to observed impact. A magnitude is not a direct measure of local shaking or expected losses. Teaching oscillators are valuable for reasoning about resonance but cannot certify real structures or replace seismic design standards.

Observational method. Compute the natural period of a toy spring-mass system and interpret how changing stiffness shifts the oscillator response. Specify the coordinate frame, observation period, relevant units, acquisition and calibration limitations before interpreting the resulting figure.

Common interpretive trap. A response spectrum does not directly identify damage without structural capacity, ductility and configuration. 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. Sketch why a short-period building and long-period bridge can respond differently to identical input motion. Provide a labeled sketch, a short reproducible table and a paragraph separating observed evidence from inferred process.

Interpretation and quantitative example

Worked case 5.4: Intrinsic attenuation amplitude ratio. Synthetic input: 278.4 km. Apply the explicitly declared relationship Math.exp(-Math.PI2x/(150*3.5)) to obtain 0.0357258 ratio. Restrictions: f=2 Hz, Q=150, v=3.5 km/s; geometric spreading and scattering excluded. 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. The shaking at a point contains contributions from rupture direction, travel distance, attenuation and local stratigraphy. Compare frequency content and duration as well as one peak amplitude. Explain why a field observation of damage needs construction and vulnerability information before the physical motion can be converted into a loss statement.

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: A response spectrum does not directly identify damage without structural capacity, ductility and configuration. 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 (Sketch why a short-period building and long-period bridge can respond differently to identical input motion.) 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. Macroseismic intensity summarizes observed effects at a location while instrumental ground-motion measures quantify selected features of the shaking. Damage also depends on vulnerability and exposure. In the broader unit, Source, path, site and engineered system each contribute to observed impact. A magnitude is not a direct measure of local shaking or expected losses. Teaching oscillators are valuable for reasoning about resonance but cannot certify real structures or replace seismic design standards.

Observational method. Compare hypothetical intensity descriptions with measured motion and a mixed building inventory; keep reports and measurements separate. Specify the coordinate frame, observation period, relevant units, acquisition and calibration limitations before interpreting the resulting figure.

Common interpretive trap. Equal ground-motion amplitudes do not imply equal damage in engineered and unreinforced construction. 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. Create a non-operational table explaining what monitoring data can and cannot say about losses. Provide a labeled sketch, a short reproducible table and a paragraph separating observed evidence from inferred process.

Interpretation and quantitative example

Worked case 5.5: Quarter-wavelength fundamental site frequency. Synthetic input: 149.65 m. Apply the explicitly declared relationship 350/(4*x) to obtain 0.584698 Hz. Restrictions: One-dimensional uniform low-velocity layer Vs=350 m/s above rigid base. 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. The shaking at a point contains contributions from rupture direction, travel distance, attenuation and local stratigraphy. Compare frequency content and duration as well as one peak amplitude. Explain why a field observation of damage needs construction and vulnerability information before the physical motion can be converted into a loss statement.

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: Equal ground-motion amplitudes do not imply equal damage in engineered and unreinforced construction. 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 (Create a non-operational table explaining what monitoring data can and cannot say about losses.) 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 synthetic urban transect crosses bedrock, alluvium and a sedimentary basin. Stations recorded the same distant event but display different frequency content, durations and amplitudes. 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. The shaking at a point contains contributions from rupture direction, travel distance, attenuation and local stratigraphy. Compare frequency content and duration as well as one peak amplitude. Explain why a field observation of damage needs construction and vulnerability information before the physical motion can be converted into a loss statement.

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. Source, path, site and engineered system each contribute to observed impact. A magnitude is not a direct measure of local shaking or expected losses. Teaching oscillators are valuable for reasoning about resonance but cannot certify real structures or replace seismic design standards. 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.