Geotechnical Hazards L3

Using travel-time curves of P-S waves. We know vs and vp, alongside the time difference between the two, so r can be found using this relation.

0.25

Soil is infinite, homogeneous, and isotropic

The earth is bounded and layered, so in reality waves curve and can reflect

Additionally S waves cannot travel through liquid regions

Uncertainty from conversion equation and uncertainty from original magnitude scale.

This is dealt with using :

Often the moment conversion is easy:

M= a0 + a1Mi

Seismicity analysis = comparing magnitude to number of events

Need to sort the data out

Converting all events to the common moment magnitude scale

depth redistribution is done: fixing depths artificially at reference depths where they can be assumed (ie shallow crustal earthquakes are easy to do this for) - this constrains lateral positions

The measuring capability of the seismograph. Only in recent years can lower magnitudes be measured. Exclude mags where rates don't equate to those assumed

Removal of events which happen right after each other due to aftershocks - we assume Poisson distribution (independent events) so these need removal

Each event is related to responsible source based on proximity

Events which can't be assigned get pushed to area sources

Gutenberg-Richter

Characteristic earthquake model

becomes...

when bounded

Because there's a finite rate of occurrence

mmin historically was used for completeness but it also sets a lower bound of magnitudes which are of engineering interest

mmax is considered as the max plausible magnitude a source is capable of producing

where b usually ~1

Rate of exceedance = (1-CDF)x

CDF found as F(m- dmi/2)

Set dm = 0.2 (very small) and assess:

using the CDFs

In the case where seismic energy release is conserved increasing mmax reduces the occurrence rates of smaller amplitude earthquakes

The regional rate of energy release associated with crustal loading

Using an exponential distribution (GR) for small-to-moderate events and a uniform distribution for high magnitude 'characteristic' events which occur characteristically on given faults - these events tend to rupture the same segments, have similar magnitudes, and constant recurrence intervals

Be careful not to assume uniform behaviour because of the low probability of exceedance due to a limited time of observation

f= dF/dx

1/Length of fault

F(x)= F(re)

as we want f(re), we solve dFre/dre = dFre/dx * dx/dre= dFx/dx * dx/dre= (1/L)* dx/dre if the epicentres are assumed uniform distributed across fault

67% = 1 SD

84-50= 34% corresponds to 1SD up

for RA, if it depends on moment mag too, the SD ->

where oM is derived uncertainty from moment magnitude calcs including conversion uncertainty and final uncertainty

This can then be added to expression for RA

Other measures are observations made at a distance, with inferences made about the source size. There is a limit to what these equipment can record, so at very low frequencies they often saturate as motion is beyond what the equipment can pick up on