- Ground-motion model is:
where Y is in cm∕s2, c0 = 0.86, c1 = 0.45, c2 = -1.27, c3 = 0.10, c5 = 0.06 and σ = 0.286.
- Use three site classes (from NEHRP):
S = 0
- B: 19 stations plus 6 stations between A and B
S = 1
- C: 68 stations
S = 2
- D: 25 stations
No stations in NEHRP class A or E. Use geotechnical information where available and geological maps for
the other stations.
- Focal depths, h, between 0.0 and 30.1km.
- Classify earthquakes into three faulting mechanism classes:
F = 0
- Normal, 101 earthquakes
F = 1
- Strike-slip, 89 earthquakes
F = 1
- Thrust, 35 earthquakes
but only retain two categories: normal and strike-slip/thrust. Classify using plunges of P and T axes and
also knowledge of the geotectonic environment. Have fault-plane solutions for 67 earthquakes.
- Choose data that satisfies at least one of these criteria:
- from earthquake with Mw ≥ 4.5;
- record has PGA ≥ 0.05g, independent of magnitude;
- record has PGA < 0.05g but at least one record from earthquake has PGA ≥ 0.05g.
- Relocate all earthquakes.
- Redigitise all records using a standard procedure and bandpass filter using cut-offs chosen by a comparison
of the Fourier amplitude spectrum (FAS) of the record to the FAS of the digitised fixed trace. Find that
PGAs from uncorrected and filtered accelerograms are almost identical.
- Convert ML to Mw, for earthquakes with no Mw, using a locally derived linear equation
- Most data from earthquakes with Mw < 6 and rhypo < 60km.
- Note correlation in data between Mw and rhypo.
- Note lack of near-field data (R < 20km) for Mw > 6.0.
- Plot estimated distance at which instruments would not be expected to trigger and find that all data lie
within the acceptable distance range for mean trigger level and only 14 records fall outside the distance
range for trigger level plus one σ. Try excluding these records and find no effect. Hence conclude that
record truncation would not affect results.
- Use an optimization procedure based on the least-squares technique using singular value decomposition
because two-step methods always give less precise results than one-step techniques. Adopted method allows
the controlling of stability of optimization and accurate determination and analysis of errors in solution.
Also method expected to overcome and quantify problems arising from correlation between magnitude and
- Test assumption that site coefficient for site class D is twice that for C by deriving equations with two site
terms: one for C and one for D. Find that the site coefficient for D is roughly twice that of site coefficient
- Test effect of focal mechanism by including two coefficients to model difference between normal, strike-slip
and thrust motions. Find that the coefficients for difference between strike-slip and normal and between
thrust and normal are almost equal. Hence combine strike-slip and thrust categories.
- Try including quadratic M term but find inadmissible (positive) value due to lack of data from large
- Also derive equations using this functional form: log Y = c0 + c1M + c2 log(R + c4) + c3F + c5S where
c4 was constrained to 6km from an earlier study due to problems in deriving reliable values of c2 and c4
directly by regression.
- Plot observed data scaled to Mw6.5 against predictions and find good fit.
- Find no systematic variations in residuals w.r.t. remaining variables.
- Find reduction in σ w.r.t. earlier studies. Relate this to better locations and site classifications.