Consistent Scaling Laws for Thrusting Environment: A Case Study for Himalayan Region

Consistent Scaling Laws for Thrusting Environment: A Case Study for Himalayan Region

Sunil Kumar (Indian Institute of Technology Roorkee, Roorkee, India), M.L. Sharma (Indian Institute of Technology Roorkee, Roorkee, India) and Josodhir Das (Indian Institute of Technology Roorkee, Roorkee, India)
Copyright: © 2018 |Pages: 17
DOI: 10.4018/IJGEE.2018070104

Abstract

The main objective of the present article is to develop self-consistent empirical relationships between rupture parameters and moment magnitude for the Himalayas. The database includes the fault rupture parameters of significant earthquakes in the Himalayan region and thrusting earthquakes from NGA West-2 database. The existing empirical relationships between magnitude and rupture parameters are reviewed in view of their consistency. The consistent relationships between moment magnitude and rupture parameters are derived and compared with the existing such relationships. The comparison of the developed consistent relationships reveal that the rupture length was being underestimated in the range of magnitude from 7 to 8, whereas it was overestimated in the lower range of magnitudes using inconsistent empirical relationships. While rupture width was overestimated for the entire range of magnitudes using inconsistent relationships, the rupture area was underestimated for magnitude greater than 7.
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1. Introduction

The fault parameters (rupture length, rupture width, rupture area etc.) are important input to seismic hazard analyses using both approaches namely, probabilistic and deterministic. These parameters play an essential part in assessment of the potential of a future earthquake in a seismogenic fault in a region. The future earthquake potential of a fault is generally estimated from assessments of fault rupture parameters which are related to earthquake magnitude (Wells and Coppersmith, 1994). Statistical analyses have been used by many researchers to develop empirical relationships between earthquake magnitude and fault parameters (Tocher, 1958; Iida, 1959; Albee and Smith, 1966; Chinnery, 1969; Bonilla and Buchanon, 1970; Ohnaka, 1978; Slemmons, 1977,1982; Acharya, 1979; Bonilla et al., 1984; Slemmons et al.,1989; Wells and Coppersmith, 1994; Mai and Beroza, 2000; Stirling et al., 2002). Until now, among many the relationship proposed by Wells and Coppersmith (1994) have been recognised as being more reliable.

The theoretical and empirical versions relating fault rupture area to seismic moment give very similar results but not in case of rupture length to seismic moment. Most of the published empirical relations are having the problem of self-inconsistency. The relations that enable seismic moment, fault length, width, area to be estimated from each other, with all these relations being consistent with the seismic moment, are termed as self-consistent relations (Leonard, 2010).

The main objective of the present study is to develop self-consistent empirical relationships between moment magnitude and rupture parameters, which are region-based. The region of study is selected as the Himalayas which is one of the seismically very active regions of the world. Many of the seismic hazard assessment exercises have used the relations developed by Wells and Coppersmith (1994) which are purely empirical and not self-consistent. We are mainly interested in relationships for the Himalayas which prominently a thrust environment. The empirical relationships between magnitude and rupture parameters as developed by Wells and Coppersmith (1994), specifically for reverse (thrust) fault, are found to be statistically insignificant (Leonard 2010).

Therefore, the objective of this paper is to quantify the inconsistency in empirical relations and to develop self-consistent relationship between moment magnitude and fault parameters for the Himalayas. To show the self-inconsistency, an example from Wells and Coppersmith has been considered for demonstration. The methodology followed to develop self-consistent relations is given by Leonard (2010). For the purpose, a total 23 earthquakes (15 from PEER NGA WEST2 data base and 8 historical earthquakes occurred in Himalaya) are selected as the basic data for this study. To make the data more homogenised only thrust environment earthquakes have been selected for the analyses.

In this study, the relationship between fault width and fault length was described by a power law for which the coefficients were worked out based on the regression analyses using the Himalayan data. The predicted values were again regressed with various displacement models. A suitable displacement model was then selected and new empirical relations were developed for seismic moment vs area/width/length. A comparison between the scaling relationship developed in this paper and corresponding relationship suggested by other researchers is made.

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