There are no problems provided in this chapter, but the instructor can assign case study essay

Instructor’s Solutions Manual for Introduction to Earthquake Engineering

1 st Edition

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Chapter 1 Introduction:

There are no problems provided in this chapter, but the instructor can assign case study essay style questions regarding past earthquakes, or performance of specific buildings during one of the earthquakes discussed. Students could then write short essays and make brief presentations of their findings. 2 / 4

Introduction to Earthquake Engineering 2

Chapter 2 Engineering Seismology Overview:

2.1 A Richter magnitude earthquake of 6.8 would radiate how much more energy than an ML 5.8 earthquake?

Answer:

Equation 2-2 results in a 32 fold increase in energy radiated for each unit increase in ML.Therefore, in this case we have one unit increase in ML, resulting in an increase of 32 times more energy.

2.2 A Richter magnitude earthquake of 5.0 is how much stronger than an ML3.0 earthquake?

Answer:

The base ten logarithmic scales in Equation 2-1 indicate that each unit increase in ML corresponds to a tenfold increase of the earthquake wave amplitude. Therefore, in this case we have a two unit increase in ML resulting in the 5.0 ML earthquake being 100 (10x10 = 100) times stronger than the 3.0 ML event.

2.3 Estimate the local magnitude of a southern California earthquake recorded using a standard Wood-Anderson seismograph that shows trace amplitude of 23mm, and the P- and S-wave arrival times at the recoding station of 07:19:45 and 07:20:09, respectively.

Answer:

i) The amplitude in millimeters, A is given as 23mm.

ii) Determine the time between the arrival of P- and S-waves in seconds, tp-s.tp-s = 07:20:09 – 07:19:45 = 69sec – 45sec = 24sec iii) Determine the Richter magnitude, ML using Equation 2-1. 92.2)8(log3log 1010

−+=

−spL tAM

= log10 (23mm) +3 log10 (24sec) – 2.92

= 2.58

2.4 An earthquake at a transformed fault caused an average strike-slip displacement of 2.5m over an area equal to 80km long by 23km deep. Assuming the rock along the fault has average shear stiffness of 175kPa; estimate the seismic moment and moment magnitude of the earthquake.

Answer:

i) Determine the fault’s rupture area, Af and fault slip, D in centimeters.

Af = (80km)(23km) = (80x10 5 cm) (23x10 5 cm) = 18.4x10 12 cm 2 Ds = 2.5m = 250cm ii) Determine the seismic moment, M0 using Equation 2-5.M0 = GAfDs = (3.2x10 11 dyne/cm 2 )(18.4x10 12 cm 2 )( 250cm) = 14.72x10 26 dyne-cm iii) Determine the moment magnitude, Mw using Equation 2-7.Mw = 2/3 log10 M0 – 10.7 3 / 4

Introduction to Earthquake Engineering 3 = 2/3 log10 (14.72x10 26 dyne-cm) – 10.7

= 7.41

2.5 Estimate the seismic moment and moment magnitude of the February 27, 2010 Chile earthquake.It is estimated that the thrust fault (the slip plane ends before reaching the Earth's surface) caused an average strike-slip displacement of 5m over an area equal to 600km long by 150km deep.Assume the rock along the fault has average shear rigidity of 3x10 11 dyne/cm 2 .

Answer:

i) Determine the fault’s rupture area, Af and fault slip, D in centimeters.

Af = (600km)(150km) = (600x10 5 cm) (150x10 5 cm) = 9x10 14 cm 2 Ds = 5m = 500cm ii) Determine the seismic moment, M0 using Equation 2-5.M0 = GAfDs = (3x10 11 dyne/cm 2 )(9x10 14 cm 2 )( 500cm) = 1.35 x10 29 dyne-cm iii) Determine the moment magnitude, Mw using Equation 2-7.Mw = 2/3 log10 M0 – 10.7 = 2/3 log10 (1.35x10 29 dyne-cm) – 10.7

= 8.72

It is worth noting that a magnitude 8.8 Mw was widely reported in the media.

2.6 What is the energy difference between the Haiti and Chile earthquakes from Example 2 and Problem 2.5, respectively?

Answer:

Since Equation 2-2 was calibrated using various types of seismic waves, it is also applicable to magnitude scales other than Richter’s. Therefore, Equation 2-2 results in a 32 fold increase in energy radiated for each unit increase in Mw. In this case then we have 8.72 – 6.94 = 1.78 units increase in Mw, resulting in an increase of 32 1.78 = 478 times more energy.

Also, using Equation 2-1we can estimate the relative strength of the two events. The base ten logarithmic scales in Equation 2-1 indicate that each unit increase in Mw corresponds to a tenfold increase of the earthquake wave amplitude. Therefore, in this case we have 8.72 – 6.94 = 1.78 units increase in Mw, resulting in the Chilean earthquake being 10 1.78 = 60 times stronger than the Haiti event.

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