- Ground-motion model is:
where y is in cm∕s2, θ1 = -3.4712, θ2 = 2.2639, θ3 = -0.1546, θ4 = 0.0021, θ5 = -1.8011, θ6 = 0.0490,
θ7 = 0.2295, σr = 0.2203 (intra-event) and σe = 0.2028 (inter-event).
- All records from rock sites.
- Strong correlation between magnitude and distance in dataset.
- Use a derivative-free approach based on a hybrid genetic algorithm to derive the model. Use a simplex
search algorithm to reduce the search domain to improve convergence speed. Then use a genetic algorithm
to obtain the coefficients and uncertainties using one-stage maximum-likelihood estimation. Believe that
approach is able to overcome shortcomings of previous methods in providing reliable and stable solutions
although it is slower.
- In hybrid genetic algorithm an initial population of possible solutions is constructed in a random way
and represented as vectors called strings or chromosomes of length determined by number of regression
coefficients and variance components. Population size is usually more than twice string length. Each value
of population array is encoded as binary string with known number of bits assigned according to level of
accuracy or range of each variable. Use three operations (reproduction/selection, crossover and mutation)
to conduct directed search. In reproduction phase each string assigned a fitness value derived from its
raw performance measure given by objective function. Probabilities of choosing a string is related to its
fitness value. Crossover or mating combines pairs of strings to create improved strings in next population.
In mutation one or more bits of every string are altered randomly. The process is then repeated until a
termination criterion is met. Demonstrate approach using test function and find small maximum bias in
results. Conclude that method is reliable.
- Use Taiwanese dataset of Chen and Tsai (2002) to demonstrate method.
- Compare results with those obtained using methods of Brillinger and Preisler (1985), Joyner and
Boore (1993) and Chen and Tsai (2002). Find differences in coefficients (although predictions are very
similar except at edges of dataspace) and standard deviations (slightly lower for proposed method).
- Compare predicted motions for ML5.5 with observations for ML5–6. Find good fit.
- Plot total residuals against magnitude and distance and find no trends.
- Note that residuals show that model is satisfactory up to 100km but for larger distances assumption of
geometric spreading of body waves in not appropriate due to presence of waves reflected off Moho.
- Note that near-source saturation should be included. Apply proposed method using a complex functional
form with different equations for three distance ranges and compare results to those using simple functional
form. Find differences at short and large distances.