# Low-angle Normal Fault Likelihood IPython Notebook

#### Richard Styron

This is an IPython Notebook version of a paper I have just submitted to Geophysical Research Letters. This is the complete paper, but with all the code embedded, and is executable. However, it does need a Python module called eq_stats.py as well as some of the typical Python scientific stack. The notebook can be downloaded from github here. I will also probably post the updated version once it's through review.

# Estimated likelihood of observing a large earthquake on a continental low-angle normal fault, and implications for low-angle normal fault activity¶

## Abstract¶

The lack of observed continental earthquakes that clearly occurred on low-angle normal faults (LANFs) may indicate that these structures are not seismically active, or that these earthquakes are simply rare events. To address this, we compile all potentially active continental LANFs (twenty in total) and calculate the likelihood of observing a significant earthquake on them over periods of 1-100 years. This probability depends on several factors including the frequency-magnitude distribution. For either a characteristic or Gutenberg-Richter distribution, we calculate a probability of about 0.5 that an earthquake greater than $M6.5$ (large enough to avoid ambiguity in dip angle) will be observed on any LANF in a period of 35 years, which is the current length of the Global CMT catalog. We then use Bayes' Theorem to illustrate how the absence of observed significant LANF seismicity over the catalog period moderately decreases the likelihood that the structures generate large earthquakes.

## 1 Introduction¶

Low-angle normal faults (LANFs), with dips less than 30$^\circ$, are well described in the geologic record. They are thought to play an important role in accommodating large-magnitude continental extension [Howard and John, 1987] and crustal thinning [Lister et al., 1986], and their recognition has been a major development in continental tectonics [Wernicke, 2009]. However, despite widespread field observations of inactive LANFs and their central role in extensional tectonic theory, they remain enigmatic and contentious structures, and it is not clear if they are seismically active at low dip angles in the upper crust. This is for two reasons: because brittle faulting on LANFs is in apparent conflict with standard Andersonian rock mechanical theory as typically applied to the upper crust [Axen, 2004], and because observations of active faulting on LANFs are sparse and at times ambiguous [Wernicke, 1995]. A considerable amount of research has been performed to address the former concern, reconciling LANF slip with rock mechanics [e.g., Axen and Bartley, 1997; Collettini, 2011]. The latter issue is highlighted by studies that have searched the focal mechanism catalogs and found no normal faulting earthquakes with focal mechanisms and surface ruptures clearly indicating slip on planes $\le30^\circ$ [Jackson, 1987; Collettini and Sibson, 2001], which is taken as conclusive evidence that LANFs are inactive or aseismic. However, the lack of observed seismic slip on continental LANFs may be simply because they are rare structures with long recurrence intervals, so earthquakes on them are very infrequent. Without knowing the likelihood of observing an LANF rupture in a time window of a few decades, it is not clear if an empty search result is strong evidence against LANF seismicity. If this likelihood is known, though, Bayesian probability theory provides a framework for quantifying how the negative search results impact the probability that LANFs are seismogenic.

In this work, we estimate the maximum likelihood of a significant LANF event occurring in time windows from 1 to 100 years, and then we interpret the lack of observed LANF seismicity in a quantified, probabilistic context using Bayes' Theorem. We estimate the maximum observation likelihood by treating all potentially active LANFs described in the literature as seismically active at their surface dip angles throughout the upper crust. Under these assumptions, we create synthetic earthquake catalogs with both Gutenberg-Richter and characteristic' frequency--magnitude distributions, using each fault's geometry and slip rate. We then calculate the probability of observing earthquakes on at least one LANF over different observation periods. Finally, we use Bayes' Theorem to incorporate the negative catalog search results and the observance likelihood to show how the negative results reduce the probability that LANFs are seismically active, but do not bring the final probability to zero.

### 1.1 LANF Slip, Mohr-Coulomb Failure Theory, and Earthquakes¶

Areas of the crust undergoing active extension are generally assumed to have a subvertical maximum compressive stress. Mohr-Coulomb theory, as applied to the crust, predicts that a fault with a typical coefficient of friction for rocks (0.6-0.8) should lock up if it is oriented at an angle greater than 60$^\circ$ to the maximum compressive stress (i.e., fault dips less than 30$^\circ$), and new, optimally oriented faults should form [Sibson, 1985]. Therefore, for normal faults with dips less than 30$^\circ$, either much lower fault friction or elevated pore fluid pressure is required for fault slip.

Evidence for seismic slip on LANFs is sparse. This is partly due to the ambiguity of the rupture plane in earthquake focal mechanisms, as a focal mechanism with a low angle nodal plane will also by definition have a high angle nodal plane. Without ancillary information indicating which nodal plane corresponds to the slip surface, searches of earthquake catalogs cannot yield unique results as to whether they contain LANF events. Several collections of normal fault earthquakes with known surface breaks Jackson, 1987; Collettini and Sibson, 2001], thereby resolving dip ambiguity, contain no low-angle events, although we note the total number of events in these collections are small ($\le$ 25 events). Some candidate LANF events exist, but they are undersea [e.g., Abers, 2001] or difficult to verify [e.g., Doser, 1987].

## 2. Potentially Active LANFs¶

Over the past decade or so, many field studies have found evidence for LANF activity in orogens throughout the world. These studies typically find arrays of Quaternary normal fault scarps on the fault traces and/or in the hanging walls of mapped or inferred low-angle detachment faults [e.g., Axen et al., 1999] . Some studies also have bedrock thermochronology data from the exhumed detachment footwalls that are suggestive of ongoing rapid exhumation [e.g., Sundell et al. 2013], although this data does not preclude a recent cessation of faulting. In some cases, additional evidence for LANF activity comes from geophysical data such as GPS geodesy [e.g., HreinsdÃ³ttir and Bennett, 2009] and seismic waves [e.g., Doser, 1987].

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from IPython.core.display import Image
Image(filename='active_lanfs_map_insets.png')
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