Fault Modeling by a Specific Barrier Model Using a New Approach for Circular Cracks’ Arrangement

In order to develop a reliable fault simulation process, there are three crucial parameters which needs to be accurately introduced. The mentioned parameters are seismic source specifications, wave propagation path, and seismic site effects. Relationships of strong ground motion attenuation are important for seismic hazard analysis at a specific site. Attenuation relationships may be obtained using two different approaches depending upon the region under study. In the first approach which is appropriate for regions with abundant records of strong ground motion, the statistical model can be used for developing the attenuation relationships employing regression techniques. The common required data for developing attenuation relationships consist of magnitudes, source-to-site distances, and peak ground characteristics. For regions such as California, Japan, and Taiwan, with sufficient data, these methods are suitable and have been successfully developed. Obviously, the validity and accuracy of these methods strongly depend on data sufficiency, the type of regression technique, and the classification of data. On the other hand, for the regions of limited records of strong ground motion, the first approach may not be appropriate and the application of physical models, as the second approach, will be necessary for successful predicting. In this approach, limited records are basically employed for the physical model calibration. These models usually have been developed in the context of the random vibration theory and the stochastic modeling approach. Among various seismic source specifications, a more physically realistic source model is the specific barrier model (SBM). The SBM is known as one of the most complete, simple, and self-consistent statement of the faulting process which is applicable in both "near-fault" and "far-field" regions. Consequently, the SBM may provide consistent ground motion simulations over the entire necessary frequency range and for all distances of engineering interests. The SBM is specifically more suitable for regions with poor seismological data-base and/or ground motions from large earthquakes with large recurrence intervals. An essential part of the seismological model used in this method is the quantitative description of the far-field spectrum of seismic waves emitted from the seismic source. Since shear (S) wave is primarily the main factor of earthquake damages, the application of stochastic approach of the SBM has almost been focused on the far-field S wave spectrum, in which two corner frequencies of observed earthquake are represented. The ‘two-corner-frequency’ shows two considerable length-scales of an earthquake source: a length-scale that quantifies the overall size of the fault that ruptures (e.g., the length L of a strike-slip fault) and another length-scale that measures the size of the subevents. Associated with these length-scales are two corresponding time scales: (1) the overall duration of rupture, and (2) the rise time. The SBM has a few main source parameters which have been calibrated to earthquakes of different tectonic regions. The SBM may be considered as a general idealization of the faulting process of an earthquake. For example, the SBM originally is an aggregate of some circular cracks which take place on the fault plane. In initial version of the SBM, the size of all cracks was assumed to be equal; however, the random nature of earthquake phenomenon leads to considering some modifications on such an assumption. In the present paper, a new method of so-called geometry packing is introduced to locate circular cracks of different radii in the fault plane. Using different size of circles is expected to result in more realistic model of earthquake source. In this method, the mentioned circles are set next to each other with no intersections between them. In other words, the proposed method guarantees the existence of barriers between of circular cracks of random radii. The aspect ratio of length to width (𝐿𝑊⁄) as an important parameter which effects on the number and arrange of circular cracks, is usually being ignored by recent modifications of the SBM.
In other words, the mentioned methods usually use equivalent circular fault by radius of 𝑅𝐶 and the same area as rectangular fault, instead of the rectangular one. In this study, by using the fault’s geometry as the basis of calculations, the aspect ratio of the fault plane may effect on the number and arrangement of circular cracks in the model. Also, this method has capability to set specific size of circles in specified location of the fault, which may become useful in more complex future models. Afterwards, by using the proposed method, source spectra of different faults are investigated.