Waterfall SRS, 1940 El Centro Quake




The top figure is the time history from the El Centro earthquake, North-South horizontal component.  The middle is the corresponding Waterfall SRS with 4 second segments and with 50% overlap.  The bottom is the spectrogram.

The Waterfall SRS is calculated by first taking the complete response time history for each natural frequency of interest.  Then the time history for each is divided into segments.  Finally, the shock response spectrum (SRS) is taken for each natural frequency and for each segment, by taking the peak positive and peak negative responses.

The Waterfall SRS function is given in:

Matlab script: Vibrationdata Signal Analysis Package

>> vibrationdata > Time History > Shock Response Spectrum, Various > Waterfall SRS

See also:  El Centro Earthquake

– Tom Irvine

Tom’s Conference Papers & Slide Index

I am trying to collect all my presentations. This is a work-in-progress…

Thank you,
Tom Irvine

* * * * * *

NAFEMS World Congress 2017

Introduction to Vibration

Spectral Functions

Random Vibration

Vibration Fatigue

Shock 1 & 2


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Aerospace Spacecraft & Launch Vehicle (SCLV) Dynamic Environments Conference

2018, Avionics Component FEA Shock Analysis

2017, Statistical Energy Analysis Software & Training Materials, Part 2

2016, Statistical Energy Analysis Software & Training Materials

2015, Seismic Analysis and Testing of Launch Vehicles and Equipment using Historical Strong Motion Data Scaled to Satisfy Shock Response Spectra Specifications

2014, Optimized PSD Envelope for Nonstationary Vibration  &  Alternate link

2013, Extending Steinberg’s Fatigue Analysis of Electronics Equipment to a Full Relative Displacement vs. Cycles Curve

2012,  Keynote, Dynamics Engineering: A Call to Serve  

2012, An Alternate Damage Potential Method for Enveloping Nonstationary Random Vibration

2011, The NASA Engineering & Safety Center (NESC) Shock & Vibration Training Program

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European Space Agency


ESA Pyrotechnic Shock Distance & Joint Attenuation via Wave Propagation Analysis

ESA Shock Analysis of Launch Vehicle Equipment using Historical Accelerometer Records to Satisfy Shock Response Spectra Specifications 

2016, European Conference on Spacecraft Structures Materials and Environmental Testing

Modifying Spectral Fatigue Methods for S-N Curves with MIL-HDBK-5J Coefficients

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Various Vibration & Fatigue Conferences

VAL2015, A review of spectral methods for variable amplitude fatigue prediction and new results

VAL 2015, Using a Random Vibration Test Specification to Cover a Shock Requirement via a Pseudo Velocity Fatigue Damage Spectrum

ICoEV 2015, International Conference on Engineering Vibration, Derivation of Equivalent Power Spectral Density Specifications for Swept Sine-on-Random Environments via Fatigue Damage Spectra

ICoEV 2015, Comparison of Fatigue Cycle Identification Methods

MOVIC & RASD 2016, Multiaxis Fatigue Method for Nonstationary Vibration

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Shock and Vibration Exchange (formerly SAVIAC)

2015, Shock Response Spectra & Time History Synthesis

2014, Rainflow Cycle Counting for Random Vibration Fatigue Analysis  

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Institute of Environmental Sciences and Technology (IEST)

ESTECH 2016, Nonstationary Vibration Enveloping Method Comparison

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Earthquake Engineering Conferences

16th WCEE, Seismic Analysis and Testing of Equipment using Historical Strong Motion Data Scaled to Satisfy Shock Response Spectra Specifications

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2003, A Time Domain, Curve-Fitting Method for Accelerometer Data Analysis

2003, Practical Application of the Rayleigh-Ritz Method to Verify Launch Vehicle Bending Modes

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Multi-axis Shock & Vibration Testing

Equipment must be designed and tested to withstand shock and vibration.  Ideally, all equipment would be tested on a shaker table with six-degree-of-freedom control (three translations and three rotations).  Such tables and control systems exist but are very expensive.  Furthermore, any multi-axis testing requires careful consideration of phase angles between the six degrees.

Another option is to test equipment on a triaxial table where the three translations are controlled, and the three rotational degrees are constrained to zero motion.  Testing on a biaxial table is yet another choice.

The most common test method, however, remains testing in each of three orthogonal axes, one axis at a time, on a single-axis shaker.  This is simplest and least expensive method.

The question arises “Should the acceleration level be increased for the case of single-axis testing?”

There is a tacit understanding that aerospace and military equipment test levels already have a sufficient uncertainty margin or safety factor so that the levels can be used without further increase.  In other words, the specifications are already intended for single-axis testing.  In many cases, a uniform level is used in each axis which is the maximum envelope of the maximum expected levels in the three axes plus some margin.

* * *

The standards which address testing equipment for earthquakes take a different approach. The following descriptions are taken from five common standards.

Only KTA 2201.4 gives a scaling formula.  This is also the only standard from the five samples which may be freely downloaded.

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IEEE 344-2013  Standard for Seismic Qualification of Equipment for Nuclear Power Generating Stations

8.6.6 Multiaxis tests

Seismic ground motion occurs simultaneously in all directions in a random fashion. However, for test purposes, single-axis, biaxial, and triaxial tests are allowed. If single-axis or biaxial tests are used to simulate the 3D environment, they should be applied in a conservative manner to account for the absence of input motion in the other orthogonal direction(s). One factor to be considered is the 3D characteristics of the input motion. Other factors are the dynamic characteristics of the equipment, flexible or rigid, and the
degree of spatial cross-coupling response. Single and biaxial tests should be applied to produce adequate levels of excitation to equipment where cross coupling is significant and yet minimize the level of overtesting where the cross coupling is not significant.

* * *

KTA 2201.4   Design of Nuclear Power Plants against Seismic Events, Part 4: Components

This document may be freely downloaded: link

See paragraphs

5.3.3 Excitation Axes Simultaneity of excitation directions

Simultaneous three-axis testing is preferred. But single-axis testing can be substituted by testing in each of three axes sequentially.

The standard shows, for example, that the uniform single-axis level should be the “square root of the sum of the squares” of the three orthogonal installation site levels.

* * *

IEC 980 Recommended practices for seismic qualification of electrical equipment of the safety system for nuclear generating stations

6.2.9 Qualification test method General

As is well known, seismic excitation occurs simultaneously in all directions in a random way. According to this point of view, the test input motion should consist of three mutually independent waveforms applied simultaneously along the three orthogonal axes of the equipment.

However, taking into account that three axial testing installations are rare and that triaxial testing is desirable when significant coupling exists simultaneously between the two preferred horizontal axis of the specimens, biaxial testing with multifrequency independent input motion in the horizontal and vertical direction is an acceptable test.

Tests shall be performed according to 6.3.2 and, in terms of total duration and fatigue induced, are intended to become conservative.

In some cases, single axis tests with multiple, or single frequency excitation are also acceptable methods of test if properly justified considering the effect of coupling between axes.

* * *

Telcordia GR-63-CORE

Assumes single-axis testing.  The base input time history is specified in the standard.

* * *

IEEE 693-2005 – IEEE Recommended Practice for Seismic Design of Substations

paragraph 4.9

The shaker table shall be biaxial with triaxial preferred.

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See also:

Seismic Test & Analysis Webinars

Hypersphere SRS


– Tom Irvine

Seismic Test & Analysis Webinars

This is a work-in-progress…

I am creating a series of webinars with Matlab exercises for seismic testing.

Here are the slides.

Telcordia Technologies Generic Requirements GR-63-CORE:  Bellcore_GR_63_Core.ppt
This unit contains an alternative waveform for VERTEQII.

CEI.IEC 980, Recommended practices for seismic qualification of electrical equipment of the safety system for nuclear generating stations:  CEI/IEC 980: 1989

IEEE Std 693-2005, Recommended Practice for Seismic Design of Substations: IEEE_693_sine_beat.pptx

IEEE Standard for Seismic Qualification of Equipment for Nuclear Power Generating
Stations: IEEE_std_344.ppt

Matlab script: Vibrationdata Signal Analysis Package

* * *

See also:

Cummins Generator Seismic Shaker Test

Earthquake Conference

Seismic Shock

Webinar 47 – Shock Response Spectrum Synthesis, Special Topics

Seismic Peak Ground Acceleration

Some Earthquake Engineering Terminology

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– Tom Irvine

Hypersphere SRS


Figure 1. El Centro Earthquake 1940, Peak Pseudo Velocity, 36.4 in/sec
Launch vehicle and spacecraft equipment must withstand pyrotechnic shock from stage separation and other flight events. Civil engineering structures and equipment must survive seismic events. There are many other examples where military, automotive, telecommunication and other equipment must be designed and tested to meet shock requirements derived from field or flight data. The specification is commonly given as a shock response spectrum (SRS). An SRS may be calculated for each orthogonal input axis, assuming the availability of triaxial accelerometer data. Each axis may thus have a separate specification. Alternatively, a maximum envelope can be drawn over the three SRS curves and then applied as a uniform specification to each orthogonal axis.

The uniform enveloping method, however, can underestimate the maximum resultant shock when all possible orthogonal axes sets are considered. The purpose of this paper is to introduce a hypersphere method to achieve a true maximum SRS.

Paper link:  hypersphere_SRS

The Matlab script for this calculation is included in the GUI package at:
Vibrationdata Matlab Signal Analysis Package

– Tom Irvine


Energy Response Spectrum

My colleagues at Sandia National Laboratories have presented some conference papers recently on energy response spectrum.

Here is a paper that I wrote on this topic:  energy_response_spectrum.pdf

Also, I have added the energy response spectrum as an option for acceleration time histories to the Vibrationdata GUI package.

See also:
Shock Response Spectrum
David O. Smallwood Papers
Temporal Moments

More later …

Tom Irvine

IEEE Std 693-2005, Recommended Practice for Seismic Design of Substations

I am currently researching IEEE Std 693…

One of its recommended shaker test methods for power equipment is to use a “sine beat” acceleration time history. The main frequency is selected as the equipment’s natural frequency.

The minimum number of beats is 5 with a minimum of 10 cycles within each beat pulse. There is also a pause between beat pulses.

A problem with this approach is that the corresponding displacement has a stair-step effect for a whole number of cycles. This offset disappears if an extra half-cycle is added. An example would be to use 10.5 cycles.

Here is a slide presentation:  IEEE_693_sine_beat.pptx

* * *

I have added a function for generating IEEE sine beat time histories to the Vibrationdata GUI package.

Matlab script: Vibrationdata Signal Analysis Package

>> vibrationdata > Miscellaneous > Generate Signal > IEEE std 693 Sine Beat

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The package also has a function for generating the Required Shock Spectrum (RSS) levels.

>> vibrationdata > Import Data to Matlab > SRS Library Array > IEEE std 693 RSS, Various

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An Implementation of an Earthquake Test, According to the Sine-Beat Method: Sine_beat.pdf

Seismic Considerations of Circuit Breakers: Seismic_Considerations_of_Circuit_Breakers.pdf

IEEE 693 Seismic Qualificaiton of Composites for Substation High-Voltage Equipment: 13_2306.pdf 

– Tom Irvine

Webinar 47 – Shock Response Spectrum Synthesis, Special Topics

Slides & Video:


A high-range Cummins Generator in a Seismic Shaker Test.mp4


1. Shaker Table Seismic Testing of Equipment using Historical Strong Motion Data Scaled to Satisfy a Shock Response Spectrum

2. Temporal Moments

* * *

Matlab script: Vibrationdata Signal Analysis Package

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Reference Papers:


From SRS to Temporal Moments

* * *

– Tom Irvine

Wisconsin Booms

Clintonville, Wisconsin is an inland community, adjacent to Lake Pigeon.

USA Today reported on March 21, 2012 that a series of mysterious booms have been fraying residents’ nerves.

City administrator Lisa Kuss said the booms have roused people from their beds and into the streets — some in pajamas.

“It startled everyone. They thought something had hit their house or a tree fell on their roof,” Kuss said Wednesday. A police dispatcher took more than 30 calls from concerned residents between 5 a.m. and 7:30 a.m.

Possible explanations for the ruckus have been nearly exhausted, she said.

Residents have said they believe the booms come from underground. City officials have checked and rechecked methane levels at the local landfill, monitored water, sewer and gas lines, contacted the military about any exercises in the area, reviewed mining explosive permits and inspected the Pigeon River dam next to city hall.

* * *

CNN reported on March 23, 2012 that the booms were due to a “swarm” of minor earthquakes amplified by the unique bedrock beneath the state of Wisconsin.

Speaking to Clintonville residents Thursday night, Lisa Kuss said the U.S. Geological Survey has determined that “our community did in fact experience an earthquake that registered 1.5 on the earthquake magnitude scale.” That minor quake was measured on Tuesday night by several mobile earthquake monitoring stations that were dispatched to the region, she said.

USGS geophysicist Paul Caruso said that Tuesday’s 1.5 tremor is only the second recorded earthquake in Wisconsin since 1947.

Caruso explained that the rock underneath Wisconsin and in much of the country east of the Rocky Mountains is “very consolidated” and without fault lines. And that means small quakes are actually felt by residents, unlike in California where the energy is absorbed.

Caruso said all seismic shifts generate noise but these sounds cannot be heard during major quakes.

“When seismic waves travel through the ground, they’re moving … faster than the speed of sound and when they hit the surface,” Caruso explained.

“(It) rattles the ground like a speaker … so it’s common for people to hear what they describe as sonic boom sounds accompanying earthquakes. But usually when there’s a big earthquake, people either don’t hear the sounds because the frequency is lower than the threshold of what humans can hear. Or other sounds going on (like) things falling down.”

* * *

Steve Dutch, a geologist at the University of Wisconsin-Green Bay, said a 1.5 magnitude earthquake produces the energy equivalent of 100 pounds of explosives and could produce loud sounds.

But he was reluctant to describe Tuesday’s event as an earthquake, saying the term is generally used to refer to widespread stress in the earth’s crust. What happened in Wisconsin could be near the surface, perhaps caused by groundwater movement or thermal expansion of underground pipes, he said.

Still, Dutch said it was possible that the event could produce a series of sounds over time.

“If you’ve got something causing a little bit of shifting underground, it may take a while for whatever is causing it to play itself out,” he said.

* * *

Clifford Thurber, a seismologist at the University of Wisconsin-Madison who served as a consultant for the city, is still on the fence.

“I won’t be amazed if it turns out to be earthquakes, but it could also be a near surface event, such as rocks fracturing beneath the surface due to erosion from flowing water.”

So far, the booms have only been heard within in a small, cigar-shaped area that encompasses most of Clintonville, Thurber says, suggesting an origin that is close to the surface, a possibility that falls within the uncertainty of the USGS seismic data.

* * *

David Hill is an emeritus scientist with the U.S. Geological Survey in Menlo Park, California. Hill, who has written about such phenomena, said they have been around for a long time and have been reported all over the world.

“Back before the Industrial Revolution, Indians and early explorers talked about booming sounds in the northeast,” he said.

Powerful booms periodically rattle windows on the North Carolina coast. In upstate New York, residents near Seneca Lake call the phenomena the “Seneca Guns.” In Coastal Belgium, the sounds are called “mistpouffers,” or fog belches, Mr. Hill found. In the Ganges Delta and the Bay of Bengal, they are called “Bansal Guns.” People in the Italian Apennines call them “brontidi” or thunder-like, and residents of Shikoku, Japan, have dubbed them “yan.”

* * *

Update:  March 28, 2012

The booming and shaking continues in Clintonville.

Clintonville police say they received about 65 calls Tuesday night, from people reporting three or four loud booms. Officials say the calls came in from 10:35 until 11:40 p.m.

Authorities say the reports came from the same part of the city that has been experiencing the booms for more than a week. Several callers told police that these booms were stronger than those from last week, but no damage has been reported.

Geophysicist John Bellini says he looked at the nearby seismometers and was unable to detect anything Tuesday night.

Seismic Peak Ground Acceleration

The Iwate-Miyagi Nairiku earthquake struck northeast Honshu, Japan, on 14 June 2008.

This earthquake had a moment magnitude Mw 6.9 according to the USGS.

The peak ground acceleration (PGA) had a maximum vector sum (3 component) value of 4278 cm/sec^2 (4.36 G).

This is the highest ever recorded PGA, although other quakes have had higher moment magnitudes.  The Richter and moment magnitudes are a measure of the total energy released by a quake.

The PGA is measured at a point.  It depends on soil conditions, distance from the hypocenter, and other factors.


Masumi Yamada et al (July/August 2010). “Spatially Dense Velocity Structure Exploration in the Source Region of the Iwate-Miyagi Nairiku Earthquake”. Seismological Research Letters v. 81; no. 4;. Seismological Society of America. pp. 597–604. Retrieved 21 March 2011.

* * *

Tohoku, Japan Earthquake 2011

The 2011 earthquake off the Pacific coast of Tōhoku was a magnitude 9.0 (Mw) undersea megathrust earthquake off the coast of Japan that occurred at 14:46 JST (05:46 UTC) on Friday 11 March 2011.

The largest peak ground acceleration (PGA) of 2.7 G was recorded in the North-South direction at Miyagi prefecture – MYG04 station.

Reference 1

Reference 2

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The highest PGA for earthquakes in the USA was 1.7 G for the 1994 Northridge, California quake, which had a 6.7 moment magnitude.

Reference:  Lin, Rong-Gong; Allen, Sam (26 February 2011). “New Zealand quake raises questions about L.A. buildings.” Los Angeles Times (Tribune). Retrieved 27 February 2011.

* * *

The peak ground velocity (PGV) has a better correlation with structural damage according to some sources.

The largest recorded ground velocity from the 1994 Northridge earthquake, made at the Rinaldi Receiving station, reached 183 cm/sec (72 in/sec).

Reference:  USGS ShakeMap

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Further information is given at:  Vibrationdata Earthquake Engineering Page

– by Tom Irvine