earthquake catalogue, seismic catalogue, PSHA, sesimic hazard

1. CONTENT
 INTRODUCTION
 LITERATURE REVIEW
 WORK DONE TILL SO FAR
 WORK TO BE EXECUTED IN NEXT STAGE

2. Evaluation of Building as per ASCE-41
 Performance level of building
 General information about Building like
 Building Type
 building Configuration,
 Component properties,
 Site and Foundation information
 On site investigation

3. Development of Seismic Hazard
 To perform Tier-1 or Tier-2 analysis, Evaluator has to define seismic Hazard at site based
on code or has to develop site specific ground motion acceleration history or site-specific
response spectra depending upon requirement.
 For Non-linear dynamic analysis, we have to develop ground motion time history, which
suits best to seismic Hazard as per the site and has to analyse the building for that ground
motion acceleration history.
 To obtain the site specific ground motion acceleration history, Conditional Mean
Spectrum shall be developed as Target response spectra compare to Uniform hazard
Spectra.
 With the help of CMS, ground motion are selected and acceleration time history is
developed and modified for which structure is analysed.

4. LITERATURE REVIEW OF STANDARDS AND JOURNAL
 As per ASCE-41, development of ground motion acceleration histories shall be
performed according to Section 16.2 of ASCE 7. 5 % damped, MCER response spectra
shall be developed as target response spectra.
 Two or more periods shall be selected, corresponding to those periods of vibration
that significantly contribute to the inelastic dynamic response of the building in two
orthogonal directions.
 For each selected period, a target spectrum shall be created that either matches or
exceeds the MCER value at that period.
 During development of target spectrum, (1) site specific disaggregation shall be
performed to identify earthquake events that contribute most to the MCER ground
motion at the selected period and (2) the target spectrum shall be developed to
capture one or more spectral shapes for dominant magnitude and distance
combinations revealed by the disaggregation.

5.  For Target response spectra developed by Conditional Mean Spectra, Ground motion
shall be developed, modified and used on structural model based on Condition mean
spectra.
 Acceptance criteria as per section 16.4 of ASCE-7 shall be evaluated for each ground
motion suit.
Selection of Recorded Ground Motion
 Minimum 11 Ground motion shall be selected
 Ground motions similar to tectonic regime (e.g., subduction versus active crustal
regions) shall be selected.
 Ground motion shall be selected based on same site soil conditions.
 Ground motion shall be selected based Period/Frequency Sampling.
 Ground motion shall be selected which has same source to site distance.

6.  Spectral shape and Scale factor shall also be considered during selection of ground
motion.
 For developing the Conditional Mean Spectrum, we have to understand the
disaggregation of seismic Hazard so that we would be aware about which M-r
combination would be significantly contributing to the Seismic hazard.
 To Understand disaggregation, we have to understand that how seismic Hazard is
calculated at a particular site.
 In DSHA, we aims at finding out the worst ground motion at a site but we can not
because neither case is worst and we can exactly predict that it is worst ground
motion.
 While in PSHA, we are no longer searching for worst-case ground motion intensity.
Rather, we will consider all possible earthquake events and resulting ground motions,
along with their associated probabilities of occurrence from all the source and find
the combined probability of exceedance of particular intensity measure. PSHA is
composed of below steps

7.  Identify all earthquake sources nearby the site.
 Prepare the good quality of earthquake catalogue with the help of past
Earthquake data from different sources.
 Characterize the distribution of earthquake magnitudes (the rates at which
earthquakes of various magnitudes are expected to occur).
 Characterize the distribution of source-to-site distances associated with potential
earthquakes.
 Predict the resulting distribution of ground motion intensity at the site as a
function of earthquake magnitude, distance, etc.
 Combine uncertainties in earthquake size, location and ground motion intensity,
using a calculation known as the total probability theorem.

8. Gutenberg & Richter (1944) first studied that number of earthquakes in a
region greater than a given size generally follows a particular distribution.
log10λm = a – bm ; where λm is the rate of earthquakes with magnitudes
greater than m, and a and b are constants. This equation is known as
Gutenberg-Richter recurrence law. Where a is the measure of seismic
activity of the region and b indicates the relative ratio of small and large
magnitudes.
The ground motion is usually estimated by using GMPEs, which is an
empirical equation using earthquake distance & magnitude from the
source to site & local conditions. GMPE generally takes the following
general form;
Probability of exceedance of any ground motion of interest by knowledge
of mean & standard deviation.

9. P(PGA > x|m, r) = 𝑥
∞
fPGA (u) du where fPGA(u) is the probability density function of
PGA.
Above PDF can also be written as P PGA > x m, r = 𝑥
∞ 1
2𝜋∗σlnPGA
∗ 𝑒
−0.5
𝑙𝑛𝑢−𝑙𝑛𝑃𝐺𝐴
σlnPGA
2
du
we will almost always be doing these calculations on a computer, it is reasonable to
discretize our continuous distributions for 𝑀 and 𝑅 and transform the integrals into
discrete summations. The PSHA integral equation is evaluated numerically
λ[IM ≥ x] =
𝑖=1
𝑛𝑠𝑜𝑢𝑟𝑐𝑒𝑠
λi (Mi > Mmin)
𝑗=0
𝑛𝑚
𝑘=0
𝑛𝑅
P(IM > x|mj , rk) P(Mi = mj) P(Ri = rk)
The above PSHA equation gives us the probability of exceedance of particular ground
motion intensity parameter due to all sources nearby the fault and also including all
the possibility of generating all type of magnitude from different source as well as
epicentre located at different distance in a particular fault.

10. The Concept of Deaggregation
 The major benefit of PSHA, i.e., its ability considers to all potential sources of earthquakes in a
region while calculating seismic hazard but which scenario of the earthquake is more prone to
cause 𝐼𝑀 > 𝑥.
 In deaggregation, we are looking for the probability of the magnitude of earthquake being
equal to m, assuming a ground motion of 𝐼𝑀 > 𝑥 has happened already. This is equal to the
rate of earthquakes with intensity measure greater than 𝑥 and magnitude equal to 𝑚, divided
by the total rate of all exceedance with intensity measure greater than 𝑥.
 λ(IM > x, M = m, R = r) = 𝑖=1
𝑛𝑠𝑜𝑢𝑟𝑐𝑒𝑠
λi Mi > Mmin P IM > x m , r P(Mi = m) P(Ri = 𝑟)
 % contribution of any hazard in Total Hazard =
λ(IM > x,R = r,M = m)
λ(IM > x)

11.  The minimum magnitude of complete recording, Mc, is the smallest magnitude
of earthquake that is reliably recorded in earthquake catalogue. Mc is defined as
the magnitude at which 90% of the data can be modelled by a power law fit.
 Step-1 Identify or specify the starting time of high-quality catalogue (High
quality of catalogue is data that is complete and accurate. It means that it has all
the earthquake that has occurred in that region and magnitude of earthquake
has been measured accurately).
 Step-2 Estimate the a and b value of G-R law as a function of Mmin based on
the event with M>Mi.
 Step-3 Then compute a synthetic distribution of magnitudes with the same b-,
a- and Mi values, which represents a perfect fit to power law.
Minimum Level of Completeness of Earthquake Catalogue

12.  Step-4 Estimate the goodness of fit by computing the absolute difference, R,
between the no of event in each magnitude bin in observed and synthetic
distribution data.
 Step-5 Mc, minimum level of completeness, is defined as the point at which
power law can be model 90 % of data of FMD.
 𝑅 𝑎, 𝑏, 𝑀𝑖 = 100 − 𝑀𝑖
𝑀𝑚𝑎𝑥
𝐵𝑖−𝑆𝑖
𝑖=1
𝑛 𝐵𝑖
∗ 100
 Completeness of earthquake data is tested by examining it in reference to G-R
laws. Assessment of magnitude of completeness is one of the specific aspects of
quality control of dataset.
 Mc is developed as the lowest magnitude at which 100 % of events in space time
interval is detected. Completeness of dataset of earthquake is generally
investigated by fitting G-R laws to frequency magnitude distribution.
 log10N(λ) = a – bm

13.  Generic equation for the evaluation of the maximum earthquake magnitude
Mmax for a given seismogenic zone or entire region. The equation is capable of
generating solutions in different forms, depending on the assumptions of the
statistical distribution model and/or the available information regarding past
seismicity.
 It includes the cases (i) when earthquake magnitudes are distributed according to
the doubly-truncated Gutenberg-Richter relation, (ii) when the empirical
magnitude distribution deviates moderately from the Gutenberg-Richter relation,
and (iii) when no specific type of magnitude distribution is assumed.
 Maximum earthquake magnitude, Mmax, is defined as the upper limit of
magnitude for a given seismogenic zone or entire region.
 𝑀𝑚𝑎𝑥 = 𝑀𝑚𝑎𝑥
𝑜𝑏𝑠. + 𝑀𝑚𝑖𝑛
𝑀𝑚𝑎𝑥
FM (m) 𝑛 dm ; FM(m) is CDF for distribution of
magnitude.
Maximum Magnitude of Earthquake in Earthquake Catalogue

14.  Case-I: - when earthquake magnitudes follow the Gutenberg-Richter magnitude
distribution.
 For the frequency-magnitude Gutenberg-Richter relation, the respective CDF of
magnitudes, which are bounded by Mmax, is
 𝐹M m =
0 if m < Mmin
1−exp −β m−Mmin
1−exp −𝛽 𝑀𝑚𝑎𝑥−𝑀𝑚𝑖𝑛
if Mmin ≤ M < Mmax
1 if M ≥ Mmin
β = b*ln(10)
 Then Mmax is estimated as 𝑀𝑚𝑎𝑥 = 𝑀𝑚𝑎𝑥
𝑜𝑏𝑠. +
𝐸1 𝑛2 −𝐸1(𝑛1)
𝛽∗exp(−𝑛2)
+ 𝑀𝑚𝑖𝑛 ∗ exp(−𝑛)
 Where 𝑛1 =
𝑛
1−exp[−𝛽(𝑀𝑚𝑎𝑥−𝑀𝑚𝑖𝑛)]
; 𝑛2 = 𝑛1 ∗ exp[−𝛽 𝑀𝑚𝑎𝑥 − 𝑀𝑚𝑖𝑛 ];
 𝐸1 𝑧 =
𝑧2+𝑎1𝑧+𝑎2
𝑧(𝑧2+𝑏1𝑧+𝑏2)

15.  where a1 = 2.334733, a2 = 0.250621, b1 = 3.330657, and b2 = 1.681534
 For good accuracy of above equation Mmax - Mmin >= 2, and n >= 100
 Case-II: - Application of the Generic Formula to the Gutenberg-Richter Magnitude
Distribution in the case of uncertainty in the b value.
 𝐹M(m) = 𝐶𝛽
0 if m < Mmin
1 −
p
𝑝+𝑚−𝑀𝑚𝑖𝑛)]
𝑞
if Mmin ≤ M < Mmax
1 if M ≥ Mmin
 where 𝑝 =
𝛽
𝜎𝛽
2 and 𝑞 =
𝛽
𝜎𝛽
2
𝜎𝛽 is the known standard deviation of 𝛽, and
 𝐶𝛽 = 1 −
p
𝑝+𝑀𝑚𝑎𝑥−𝑀𝑚𝑖𝑛)]
𝑞 −1

16.  𝑀𝑚𝑎𝑥 = 𝑚𝑚𝑎𝑥
𝑜𝑏𝑠.
+
𝛿
1
𝑞+2
exp(
𝑛.𝑟𝑞
1−𝑟𝑞)
𝛽
𝜏 −
1
q
, δ ∗ r𝑞
− τ(−
1
q
, δ)
 Where τ the complementary Incomplete Gamma Function
 and 𝑟 =
p
𝑝+𝑀𝑚𝑎𝑥−𝑀𝑚𝑖𝑛)]
and δ = n*𝐶𝛽.
 By allowing for such uncertainty in the b value, it is reasonable to drop the
implicit assumptions (i), (ii), and (iii) of Case I
 (i) seismic activity remains constant in time, (ii) the selected functional form of
magnitude distribution properly describes the observations, and (iii) the
parameters of the assumed distribution functions are known without error

17.  Author proposes that Mmin is therefore an engineering parameter that is ultimately
related to seismic risk rather than seismic hazard.
 Rmin can be zero and the maximum value of distance considered depends primarily
on the relative levels of seismic activity in the host source zone (for diffuse seismicity)
or the closer seismogenic faults, and the activity levels of more distant sources.
 In cases where there are no significant sources of seismicity with far greater levels of
activity than those in close proximity to the site, significant hazard contributions will
be limited to at most 200–300 km depending on the attenuation rates.
 It is advisable approach is to initially define sources extending 300 km or more from
the site—and farther if there is a remote but highly active source of seismicity—and
then reducing the upper limit of the integrations if disaggregation indicates null
contributions beyond a certain limit.
Minimum Magnitude in Earthquake Catalogue

18.  b value for G-R Reoccurrence law
 𝑏′
=
1
𝑖=1
𝑛 𝑀𝑖
𝑛
−𝑀𝑜
where Mo is the minimum magnitude of earthquake in earthquake
catalogue.
 What is not Mmin: -
1. Mmin is not chosen to make hazard calculation simpler.
2. Mmin is not the minimum magnitude of completeness nor the smallest magnitude used in
fitting of G-R reoccurrence relationship.
3. Mmin also not the minimum magnitude of earthquake at which chosen GMPE is applicable.
4. Mmin is also not set to ensure that sufficient hazard is estimated specially in low seismic
region where sufficient data are not available to estimate accurate hazard.

19.  What is Mmin: -
 The landmark paper by Cornell (1968, p. 1586) says “….and m0 is some magnitude
small enough, say 4, that events of lesser magnitude may be ignored by engineers.”
 McGuire (2004, p. 39) makes the following assertions regarding Mmin: “The lower
bound, Mmin, is chosen on the basis of the minimum magnitude that will cause
damage or loss and that must be considered for risk mitigation purposes.”
 Kramer (1996, p. 123) makes the following statements: “For engineering purposes,
the effects of very small earthquakes are of little interest and it is common to
disregard those that are not capable of causing significant damage………In most
PSHAs, the lower threshold magnitude is set at values from about 4.0 to 5.0 since
magnitudes smaller than that seldom cause significant damage.”