Seismic Hazard and Ground-Motion Characterization

Introduction and Context

Earthquake engineering begins with a description of the shaking that a site may experience during its design life. Structural analysis is meaningful only when the intensity, frequency content, duration, and variability of expected ground motion are represented appropriately. Seismic hazard analysis provides the framework for estimating this shaking, while ground-motion characterization converts hazard estimates into response spectra, time histories, and other engineering parameters suitable for design.

The central distinction is between seismic hazard and seismic risk. Hazard describes the probability or intensity of earthquake effects at a location. Risk additionally includes exposure, vulnerability, consequences, and losses. This chapter concentrates on hazard and ground motion, while recognizing that these are inputs to risk-informed decision-making.

Two principal approaches are used:

• Deterministic seismic hazard analysis (DSHA): evaluates shaking from specified earthquake scenarios, usually controlling magnitude–distance combinations.
• Probabilistic seismic hazard analysis (PSHA): integrates the effects of all relevant earthquake sources, magnitudes, distances, and uncertainties to estimate the frequency of exceeding a specified ground-motion level.

Neither approach is universally superior. DSHA is transparent and useful for scenario-based design, emergency planning, and critical facilities. PSHA explicitly represents recurrence and uncertainty and is the basis of many modern building codes and seismic maps.

Learning Objectives

After studying this chapter, the learner should be able to:

1. Distinguish seismic source, path, and site effects.

2. Formulate and interpret deterministic and probabilistic seismic hazard analyses.

3. Explain the meaning and limitations of response spectra and spectral ordinates.

4. Use ground-motion models and identify their principal uncertainties.

5. Interpret accelerograms and select, scale, and modify records for analysis.

6. Explain site response, liquefaction-related hazards, microzonation, and spatial variability.

7. Critically evaluate hazard results for professional design and research applications.

1. Earthquake Hazard as a Chain of Physical Processes

Recorded ground motion results from a chain:

earthquake source → wave propagation → local site response → structural demand.

1.1 Earthquake source

Source characteristics include magnitude, fault geometry, rupture dimensions, rupture velocity, stress drop, hypocentral depth, and directivity. Magnitude is a logarithmic measure of earthquake size. Moment magnitude, \(M_w\), is based on seismic moment:

\[

M_0=\mu A D

\]

where \(M_0\) is seismic moment, \(\mu\) is shear modulus, \(A\) is fault rupture area, and \(D\) is average slip. A commonly used magnitude relationship is

\[

M_w=\frac{2}{3}\log_{10}(M_0)-6.07

\]

when \(M_0\) is expressed in N·m. The numerical constant depends on the unit convention; therefore, the units must always be stated.

Magnitude is not the same as intensity. Magnitude characterizes the earthquake source, whereas intensity describes the observed effect at a particular location. A single earthquake has one source magnitude but many spatially varying intensities.

1.2 Wave propagation and attenuation

As waves travel away from the source, amplitudes generally decrease through geometric spreading and anelastic energy loss. The path also modifies frequency content. High-frequency components commonly attenuate more rapidly than low-frequency components, although the exact behavior depends on geological structure and distance.

A simplified conceptual expression is

\[

Y = S(M)P(R)G(f)\,\epsilon

\]

where \(Y\) is a ground-motion measure, \(S(M)\) represents source scaling with magnitude, \(P(R)\) represents path effects with distance \(R\), \(G(f)\) represents frequency dependence, and \(\epsilon\) represents residual variability. This is a conceptual decomposition rather than a universal predictive equation.

1.3 Site effects

Near-surface soils can amplify, de-amplify, lengthen shaking duration, or alter the frequency content. Important mechanisms include impedance contrast, resonance, nonlinear soil behavior, topographic amplification, basin effects, and soil–structure interaction. Site classification based only on one parameter, such as average shear-wave velocity, is useful but incomplete, particularly in deep basins, nonlinear soils, and topographically complex terrain.

2. Measures of Ground Motion

Ground motion may be described in the time domain, frequency domain, or response-spectrum domain.

2.1 Peak values

Peak ground acceleration (PGA), peak ground velocity (PGV), and peak ground displacement (PGD) are the largest absolute acceleration, velocity, and displacement values in a record. They are simple and useful for screening, but each captures only one aspect of a complex signal. PGA is especially sensitive to high-frequency pulses and filtering, whereas PGV often correlates better with damage to some structures and infrastructure systems.

2.2 Response spectra

For a specified damping ratio, a response spectrum gives the maximum response of a family of linear single-degree-of-freedom (SDOF) oscillators subjected to the same acceleration record. For an oscillator with natural circular frequency \(\omega_n\), period \(T=2\pi/\omega_n\), and damping ratio \(\xi\), the relative-displacement equation is

\[

\ddot u+2\xi\omega_n\dot u+\omega_n^2u=-\ddot u_g(t)

\]

where \(u\) is relative displacement and \(\ddot u_g(t)\) is ground acceleration. The pseudo-spectral acceleration is

\[

S_a=\omega_n^2 S_d

\]

where \(S_d\) is the maximum relative displacement. This relation is exact for pseudo-acceleration as defined; it is not necessarily equal to the maximum absolute oscillator acceleration for every record.

Similarly,

\[

S_v=\omega_n S_d

\]

is pseudo-spectral velocity. Response spectra are therefore not records of actual motion; they are summaries of maximum oscillator responses. They do not preserve duration, phase, sequence of cycles, or cumulative damage effects.

A design spectrum is a smoothed or idealized spectrum intended for design. It is not identical to the spectrum of any particular earthquake record. Code spectra generally incorporate hazard level, damping, site class, and regional calibration.

2.3 Fourier and energy measures

The Fourier amplitude spectrum describes the distribution of amplitude with frequency but does not directly show how a structure responds. Arias intensity is an energy-related measure commonly written as

\[

I_A=\frac{\pi}{2g}\int_0^{T_d}a^2(t)\,dt

\]

where \(a(t)\) is ground acceleration, \(g\) is gravitational acceleration, and \(T_d\) is the record duration. Its units are velocity. Because it depends on the squared acceleration, it reflects both amplitude and duration, although it is not a direct measure of structural damage.

Significant duration is often defined as the time interval between specified percentages of cumulative Arias intensity, such as 5% and 95%. Different definitions exist, so the adopted convention must be reported.

3. Deterministic Seismic Hazard Analysis

DSHA estimates ground motion for one or more specified earthquake scenarios. A typical procedure is:

1. Identify active faults, seismic zones, and historical earthquake sources.

2. Define credible magnitudes for each source.

3. Determine source-to-site distances and geometry.

4. Select an appropriate ground-motion model.

5. Evaluate site effects and obtain the scenario spectrum or time history.

6. Compare scenarios and identify the controlling case.

A controlling scenario may be the earthquake producing the largest PGA, the largest long-period spectral acceleration, or the greatest structural demand. These need not be the same earthquake.

Example: scenario comparison

Suppose two sources are considered for a site:

• Source A: \(M_w=6.5\), distance 15 km, predicted \(S_a(1.0\text{ s})=0.22g\).
• Source B: \(M_w=7.2\), distance 45 km, predicted \(S_a(1.0\text{ s})=0.31g\).

Although Source A is closer, Source B controls the one-second-period design demand. If the structure has a fundamental period near 0.2 s, however, Source A may control at that period. DSHA must therefore compare spectra, not only a single peak value.

Strengths and limitations

DSHA is readily communicated and supports questions such as, “What shaking could result from rupture of this fault?” It is valuable for dams, nuclear facilities, hospitals, bridges, and emergency response planning. Its principal limitation is that it does not inherently indicate how frequently the scenario occurs. Results can also be strongly influenced by subjective choices concerning maximum magnitude, fault segmentation, and distance.

4. Probabilistic Seismic Hazard Analysis

PSHA estimates the annual frequency or probability that a ground-motion intensity will exceed a specified level. It integrates over all relevant earthquake scenarios.

For a set of mutually identified source zones, the annual exceedance rate may be expressed conceptually as

\[

\lambda_Y(y)=\sum_i\int\int P(Y>y\mid m,r,i)\,f_{M,R,i}(m,r)\,dm\,dr

\]

where:

• \(\lambda_Y(y)\) is the annual rate of exceeding level \(y\);
• \(i\) identifies a seismic source;
• \(m\) is magnitude;
• \(r\) is source-to-site distance;
• \(P(Y>y\mid m,r,i)\) is the conditional exceedance probability from the ground-motion model;
• \(f_{M,R,i}(m,r)\) describes the occurrence rate distribution of magnitude and distance for source \(i\).

If exceedances are modeled as a Poisson process, the probability of at least one exceedance in time \(t\) is

\[

P(Y>y\text{ in }t)=1-e^{-\lambda_Y(y)t}.

\]

The Poisson assumption concerns the occurrence process used in the model; it does not mean that earthquakes are physically random in every respect. It may be inappropriate where earthquake clustering, aftershock sequences, or time-dependent renewal behavior are important.

4.1 Return period and probability of exceedance

The mean return period associated with annual exceedance rate \(\lambda\) is

\[

T_R=\frac{1}{\lambda}.

\]

It is a statistical average, not a schedule or prediction. A “475-year return-period” level corresponds to \(\lambda=1/475\) per year under the adopted model. Its probability of exceedance in 50 years is

\[

1-e^{-50/475}=0.100\text{ approximately}.

\]

Thus, a 475-year level has approximately a 10% probability of being exceeded in 50 years under a Poisson model. It does not imply that the event will occur once every 475 years.

4.2 Hazard curves and deaggregation

A hazard curve plots ground-motion level against annual exceedance frequency or probability. The curve includes contributions from many magnitudes and distances. Deaggregation separates a selected hazard level into contributions by magnitude, distance, and sometimes epsilon, the number of standard deviations by which a prediction differs from the median ground-motion model. Deaggregation supports record selection and scenario interpretation.

4.3 Epistemic and aleatory uncertainty

Aleatory variability is irreducible randomness or natural variability in the modeled process, such as record-to-record variation for earthquakes with similar magnitude and distance. Epistemic uncertainty results from incomplete knowledge, such as alternative fault geometries or competing ground-motion models. Logic trees are commonly used to represent epistemic alternatives through branches and weights. Care is required: assigning weights is a technical judgment, not a way to eliminate uncertainty.

5. Ground-Motion Models

A ground-motion model (GMM), formerly called a predictive equation, estimates a selected intensity measure from parameters such as magnitude, distance, fault mechanism, site condition, and sometimes depth or basin position. A generic logarithmic form is

\[

\ln Y=\mu(M,R,F,S)+\sigma(M,R,F,S)\,\varepsilon

\]

where \(Y\) is the intensity measure, \(\mu\) is the median logarithmic prediction, \(\sigma\) is logarithmic standard deviation, and \(\varepsilon\) is a standardized residual, usually modeled as having mean zero and unit variance. The model is valid only within its stated magnitude, distance, tectonic, site, and intensity-measure ranges.

Modern models may separate total variability into between-event and within-event components. This is important when analyzing multiple records from one earthquake or multiple stations, because residuals are correlated rather than fully independent.

Selection of a GMM should consider:

• tectonic environment, such as active crust, stable continental region, or subduction zone;
• magnitude and distance ranges;
• faulting mechanism;
• site parameters and nonlinear response;
• intensity measure required by the analysis;
• regional empirical calibration;
• treatment of near-fault directivity and hanging-wall effects.

Blind extrapolation outside a model’s domain can produce apparently precise but unreliable hazard estimates.

6. Site Response and Microzonation

6.1 One-dimensional site response

For horizontally layered soil over rock, one-dimensional wave propagation models are often used. The fundamental site period can be approximated, for a uniform layer, by

\[

T_s\approx\frac{4H}{V_s}

\]

where \(H\) is layer thickness and \(V_s\) is shear-wave velocity. This quarter-wavelength estimate assumes a simple layer, approximately vertical wave propagation, and a strong impedance contrast. Real profiles require transfer-function analysis or numerical simulation.

The average shear-wave velocity over the upper 30 m, commonly denoted \(V_{S30}\), is widely used for site classification. It is defined by

\[

V_{S30}=\frac{30}{\sum_{i=1}^{n}h_i/V_{S,i}}

\]

where \(h_i\) and \(V_{S,i}\) are the thickness and shear-wave velocity of layer \(i\) within the upper 30 m. This is a travel-time-weighted harmonic average, not an arithmetic average.

6.2 Nonlinear response

At low strain, soil response may be approximated as linear or equivalent-linear. At stronger shaking, modulus decreases and damping increases with strain. Nonlinear analysis updates stress–strain behavior during shaking and is often preferable for soft soils, shallow deposits, and high hazard levels. Equivalent-linear methods are efficient but can misrepresent strong, transient, or highly nonlinear response.

6.3 Microzonation

Seismic microzonation divides a region into areas with relatively similar hazard or site response. A professional microzonation study may integrate:

• geological and geomorphological mapping;
• active-fault and source characterization;
• geophysical measurements, including \(V_s\) profiles and ambient vibration;
• geotechnical investigation;
• local seismic response analysis;
• liquefaction and landslide susceptibility;
• basin, topographic, and groundwater effects;
• uncertainty assessment and validation.

Microzonation maps should identify scale, intended use, data quality, and uncertainty. They are not substitutes for project-specific investigation. A map suitable for regional planning may be inadequate for foundation design.

7. Strong-Motion Records and Ground-Motion Selection

7.1 Record characteristics

A useful accelerogram should be compatible, as appropriate, with magnitude, distance, mechanism, site condition, duration, pulse characteristics, and spectral shape. The record-processing workflow includes checking instrument metadata, baseline correction, filtering, orientation, sampling, clipping, and integration stability. Processing choices can materially alter displacement and long-period spectral ordinates.

Three-component records should be treated consistently. Rotational measures, geometric mean horizontal spectra, maximum-direction measures, and vertical components are not interchangeable.

7.2 Scaling records

Record selection and scaling should be linked to the analysis objective. For linear response-spectrum analysis, matching the target spectrum over the structural period range may be adequate. For nonlinear time-history analysis, excessive scaling of records can distort duration, energy, and physical realism.

Common approaches include:

• amplitude scaling by a constant factor;
• spectrum-compatible selection or modification;
• conditional-spectrum selection, which accounts for spectral correlation;
• simulated or hybrid records where observations are insufficient.

For a suite of records, the median or mean response is often compared with the target spectrum according to the governing code or standard. The acceptance criterion must be stated explicitly. Matching a spectrum does not ensure matching of duration, cyclic content, pulse behavior, or cumulative damage potential.

7.3 Near-fault motions

Near-fault records may contain velocity pulses caused by rupture directivity or permanent displacement associated with fling. A pulse can produce severe demand in structures whose periods align with the pulse period. Ordinary record selection based only on average spectral matching may fail to represent this hazard. Near-fault classification and pulse-sensitive selection are therefore important for structures close to capable faults.

8. Applied Case: Illustrative Hazard Study for a Hospital

Background

Consider an illustrative 12-storey hospital planned on 20 m of medium-dense alluvial soil over weathered rock. The building has a fundamental period near 1.0 s, contains emergency services, and must remain functional after a major earthquake.

Problem

A regional code map provides a 475-year spectral acceleration at 1.0 s, but the site lies near a mapped strike-slip fault and within a deep sedimentary basin. The design team must determine whether the regional value adequately represents local hazard and select records for nonlinear analysis.

Analysis

The team first performs a source review, identifying the nearby fault, distributed seismicity, and regional background sources. A DSHA considers a maximum credible rupture on the nearby fault and a larger but more distant event on a regional source. PSHA is then performed using alternative source models and several regionally appropriate GMMs. A logic tree represents uncertainty in fault recurrence, maximum magnitude, and model choice.

The hazard deaggregation for the 1.0 s target shows that the dominant contribution comes from earthquakes around \(M_w=6.8\)–7.1 at distances of approximately 15–25 km. This differs from the controlling scenario at short periods, which is a smaller, closer event.

Site investigation obtains layered shear-wave velocity profiles and groundwater data. One-dimensional nonlinear site-response analyses indicate amplification near the soil-column period and reduced amplification at very large strains. Liquefaction screening is conducted using corrected in-situ penetration resistance, groundwater level, and earthquake loading; zones of potential triggering are identified outside the primary foundation footprint but near critical utility corridors.

For nonlinear analysis, seven three-component records are selected from earthquakes with compatible magnitude, distance, mechanism, and soil conditions. Selection is guided by the deaggregated hazard and a conditional target spectrum near 1.0 s. Records are scaled within a justified period range, and duration and pulse characteristics are checked separately. The engineering team also analyzes an unscaled near-fault pulse record as a sensitivity case.

Approach and outcome

The final design uses the code-prescribed probabilistic spectrum, adjusted through a documented site-response study. Nonlinear analyses show that the median drift demand is governed by the pulse-sensitive record, while the largest foundation demand occurs in a different record with stronger long-period content. Emergency utilities are relocated away from the liquefaction-susceptible corridor, and seismic joints and nonstructural restraints are redesigned.

Learning points

1. A single hazard value cannot represent all structural periods.

2. DSHA and PSHA answer different questions and are complementary.

3. Deaggregation provides a rational basis for record selection.

4. Site response can alter both amplitude and spectral shape.

5. Nonstructural and lifeline consequences may govern hospital performance.

6. A spectrum-matched record suite still requires checks on duration, pulses, and cumulative effects.

9. Professional Practice, Governance, and Emerging Methods

Hazard analysis influences public safety, land-use planning, insurance, infrastructure investment, and emergency preparedness. Analysts should document source models, assumptions, data quality, model domains, logic-tree weights, site parameters, processing decisions, and sensitivity results. Reproducibility is essential, particularly where results affect critical facilities.

Ethically, uncertainty must not be hidden behind excessive numerical precision. A hazard curve should be communicated with its epistemic alternatives and limitations. Maps must not be presented as guaranteeing safety or predicting the date of an earthquake.

Digital databases, automated waveform processing, cloud computation, and machine-learning methods are increasingly used. AI can assist with phase picking, event association, waveform classification, clustering, and surrogate site-response modeling. However, training-data bias, domain shift, explainability, and error propagation remain important. AI outputs require physical validation and expert review; they should not replace source characterization or engineering judgment.

Contemporary developments include physics-informed simulations, regional 3D wave-propagation models, nonergodic ground-motion models, time-dependent hazard, cross-correlation of spatially distributed motions, and performance-based seismic design. Nonergodic models seek to distinguish repeatable site- and path-specific effects from regional average variability, potentially reducing uncertainty when sufficient local data exist.

Best-Practice Checklist

Before accepting a hazard or record-selection study, verify that:

• source zones and faults are comprehensively identified;
• magnitude recurrence and maximum magnitude assumptions are documented;
• GMMs are appropriate for the tectonic setting and parameter range;
• aleatory and epistemic uncertainties are distinguished;
• site characterization includes relevant stratigraphy and groundwater;
• hazard levels and exposure durations are clearly stated;
• deaggregation is used where scenario selection is required;
• records are checked for metadata, processing, scaling, duration, and pulses;
• vertical and spatial components are treated consistently;
• liquefaction, landslide, basin, and topographic effects are considered where relevant;
• results are peer reviewed and reproducible.

Chapter Summary

Seismic hazard analysis describes the likelihood and intensity of earthquake-induced ground motion at a site. Ground motion is controlled by source, path, and site effects. PGA, PGV, PGD, Fourier measures, energy measures, and response spectra describe different aspects of shaking; a response spectrum is a maximum oscillator-response summary rather than a complete record.

DSHA evaluates specified earthquake scenarios and is transparent but does not inherently describe frequency. PSHA integrates source recurrence, magnitude, distance, conditional ground-motion variability, and uncertainty to produce hazard curves and probabilities of exceedance. Return periods are statistical measures, not predictions. Deaggregation helps identify the magnitude–distance combinations controlling a hazard level.

Ground-motion models require appropriate tectonic, magnitude, distance, and site domains. Site response, nonlinear soil behavior, basin effects, liquefaction, and microzonation can substantially modify regional hazard. Record selection must consider spectrum, duration, mechanism, distance, site, pulses, and the intended structural analysis. Modern practice increasingly combines probabilistic hazard, site-specific analysis, conditional spectra, nonergodic models, numerical simulation, and carefully governed computational tools.

Key Terms

Seismic hazard: Probability or intensity of earthquake effects at a location.

Seismic risk: Expected consequences considering hazard, exposure, vulnerability, and losses.

Deterministic seismic hazard analysis: Scenario-based evaluation of specified earthquake events.

Probabilistic seismic hazard analysis: Integration of all relevant earthquake scenarios and uncertainties.

Moment magnitude: Magnitude scale based on seismic moment.

Seismic moment: Product of shear modulus, rupture area, and average slip.

PGA: Maximum absolute ground acceleration in a record.

Response spectrum: Maximum response of SDOF oscillators versus period for specified damping.

Pseudo-spectral acceleration: Quantity equal to \(\omega_n^2S_d\).

Ground-motion model: Statistical model predicting an intensity measure from earthquake and site parameters.

Aleatory variability: Natural randomness represented within a model.

Epistemic uncertainty: Uncertainty caused by incomplete knowledge.

Deaggregation: Separation of hazard contributions by magnitude, distance, or other parameters.

Site response: Modification of incoming waves by local geological materials.

\(V_{S30}\): Harmonic-average shear-wave velocity in the upper 30 m.

Microzonation: Division of an area according to local seismic hazard or site-response characteristics.

Arias intensity: Energy-related integral of squared acceleration.

Significant duration: Time interval containing a specified fraction of cumulative energy measure.

Near-fault pulse: Long-period velocity or displacement pulse related to rupture directivity or fling.

Conditional spectrum: Target spectrum conditioned on a specified spectral value at a reference period.

Review Questions

Short Answer Questions

1. Distinguish seismic hazard from seismic risk.

2. What information does a response spectrum provide, and what information does it omit?

3. Define aleatory variability and epistemic uncertainty.

4. Why is \(V_{S30}\) calculated as a harmonic average?

5. What is the purpose of hazard deaggregation?

Long Answer Questions

1. Explain the complete source–path–site chain of ground-motion generation.

2. Compare DSHA and PSHA, including their assumptions, strengths, and limitations.

3. Derive and interpret the Poisson probability of exceedance relationship.

4. Discuss the role of ground-motion models in PSHA and explain why model-domain validity matters.

5. Explain the principal requirements for selecting records for nonlinear response-history analysis.

Analytical / Application Questions

1. A site has a 475-year hazard level. Calculate its approximate probability of exceedance in 50 years under a Poisson model and explain the meaning of the result.

2. A close moderate earthquake controls short-period PGA while a larger distant earthquake controls 1.0-second spectral acceleration. Explain why both scenarios should be considered for a multi-storey building.

3. Develop a concise investigation and analysis plan for microzonation of a basin containing soft soils, liquefaction-susceptible deposits, and several critical hospitals.

Multiple Choice Questions with Answers

Question 1

Which statement best distinguishes seismic hazard from seismic risk?

A. Hazard includes losses, whereas risk includes only shaking

B. Hazard describes earthquake effects or likelihood; risk additionally includes exposure and vulnerability

C. Hazard applies only to faults, whereas risk applies only to buildings

D. Hazard and risk are interchangeable terms

Correct Answer: B. Hazard describes earthquake effects or likelihood; risk additionally includes exposure and vulnerability

Question 2

For a linear SDOF oscillator, pseudo-spectral acceleration is defined as:

A. \(S_d/\omega_n^2\)

B. \(\omega_n S_d\)

C. \(\omega_n^2 S_d\)

D. \(S_d+\omega_n\)

Correct Answer: C. \(\omega_n^2 S_d\)

Question 3

Under a Poisson model, the probability of at least one exceedance in time \(t\) is:

A. \(e^{-\lambda t}\)

B. \(1-e^{-\lambda t}\)

C. \(\lambda/t\)

D. \(1-\lambda t\) for all values of \(t\)

Correct Answer: B. \(1-e^{-\lambda t}\)

Question 4

A 475-year mean return period corresponds to an annual exceedance rate of approximately:

A. 0.475 per year

B. 475 per year

C. 0.0211 per year

D. 0.00211 per year

Correct Answer: D. 0.00211 per year

Question 5

Which quantity is a travel-time-weighted harmonic average over the upper 30 m?

A. PGA

B. Arias intensity

C. \(V_{S30}\)

D. PGD

Correct Answer: C. \(V_{S30}\)

Question 6

The main purpose of PSHA deaggregation is to:

A. Remove all epistemic uncertainty

B. Identify magnitude–distance contributions controlling a selected hazard level

C. Convert acceleration into displacement exactly

D. Determine the earthquake occurrence date

Correct Answer: B. Identify magnitude–distance contributions controlling a selected hazard level

Question 7

Which feature is particularly associated with near-fault directivity effects?

A. A long-period velocity pulse

B. Zero duration of shaking

C. Elimination of site amplification

D. Constant acceleration at every period

Correct Answer: A. A long-period velocity pulse

Question 8

For a uniform soil layer over stiff material, the approximate quarter-wavelength site period is:

A. \(H/(4V_s)\)

B. \(4H/V_s\)

C. \(V_s/(4H)\)

D. \(4V_sH\)

Correct Answer: B. \(4H/V_s\)

Question 9

Which statement about a design response spectrum is correct?

A. It is necessarily the spectrum of one recorded earthquake

B. It preserves the phase and duration of a time history

C. It is an idealized representation of oscillator demand for design

D. It gives the exact displacement of every building

Correct Answer: C. It is an idealized representation of oscillator demand for design

Question 10

Why can a spectrum-matched record suite still be inadequate for nonlinear analysis?

A. Response spectra contain no information about amplitude

B. Spectrum matching does not necessarily reproduce duration, pulses, phase sequence, or cumulative damage effects

C. Matched records cannot be used with damping

D. A response spectrum applies only to stationary signals

Correct Answer: B. Spectrum matching does not necessarily reproduce duration, pulses, phase sequence, or cumulative damage effects