Quantifying capability of a local seismic network in terms of locations and focal mechanism solutions of weak earthquakes

Abstract

Extension of permanent seismic networks is usually governed by a number of technical, economic, logistic, and other factors. Planned upgrade of the network can be justified by theoretical assessment of the network capability in terms of reliable estimation of the key earthquake parameters (e.g., location and focal mechanisms). It could be useful not only for scientific purposes but also as a concrete proof during the process of acquisition of the funding needed for upgrade and operation of the network. Moreover, the theoretical assessment can also identify the configuration where no improvement can be achieved with additional stations, establishing a tradeoff between the improvement and additional expenses. This paper presents suggestion of a combination of suitable methods and their application to the Little Carpathians local seismic network (Slovakia, Central Europe) monitoring epicentral zone important from the point of seismic hazard. Three configurations of the network are considered: 13 stations existing before 2011, 3 stations already added in 2011, and 7 new planned stations. Theoretical errors of the relative location are estimated by a new method, specifically developed in this paper. The resolvability of focal mechanisms determined by waveform inversion is analyzed by a recent approach based on 6D moment-tensor error ellipsoids. We consider potential seismic events situated anywhere in the studied region, thus enabling “mapping” of the expected errors. Results clearly demonstrate that the network extension remarkably decreases the errors, mainly in the planned 23-station configuration. The already made three-station extension of the network in 2011 allowed for a few real data examples. Free software made available by the authors enables similar application in any other existing or planned networks.

Appendix—LocErr method/program

A hypocenter location error is the sum of errors caused by inaccurate onset picking and simplified velocity model. In the case of relative master event location (which is implemented in LocErr), the errors caused by simplified velocity model are much smaller than in case of the absolute location. The errors are sensitive mainly to the geometrical configuration of the network under study.

The LocErr method (and also available computer program) is based on an original algorithm described below and in Fig. 8. Error bodies of a general shape (not ellipsoids) are used to characterize the so called relative double differences. They are defined as travel time differences between two stations of differences between two close hypocenters. They are normalized with expected theoretical errors.

Fig. 8

The flowchart of the LocErr algorithm. Rectangles represent the inputs and output; ovals represent the procedures

During the location process, the origin time of earthquake is unknown (as it is the result of the location procedure). Therefore, one can measure only differences of the travel times between stations not the travel times itself. Two close hypocenters can be distinguished by a relative location procedure only in case that the double difference for a couple of stations is larger than the error of onset determination at the most sensitive pair of stations. This means that the pair of stations with minimum errors is considered here (not the average value). The computation is performed in a cubic grid of assumed master event hypocenters. For every node of the grid, the error body is computed in the following steps:

• 1. Travel times t ^j₀ are computed between the assumed master-event hypocenter and jth station of the network. Various types of velocity models can be used (homogeneous, layered, gradient, etc.), but the velocity model is the same for all stations and all hypocenters.

• 2. A sphere of a small radius around the hypocenter of master event in a grid node is defined. The choice of r ₀ affects the results only slightly. The radius r ₀ should be of the same order as the expected error of the location. It is important to use the same r ₀ for all grid nodes, as we want to compare location errors in the whole area of seismic network.

• 3. A set of regularly distributed vectors and corresponding points on the sphere is defined. These points represent hypocenters of virtual slave events. The travel times t ^j _i for ith slave event and jth station are computed.

• 4. Travel time differences dt ^j _i  = t ^j _i  − t ^j₀ between the master and slave events on the sphere are computed for all stations.

• 5. Relative double differences are computed for all combinations of stations (j ≠ k).

  $$ D{t}_i^{jk}=\frac{d{t}_i^j-d{t}_i^k}{\sigma^j+{\sigma}^k}, $$

  (1)

  where σ ^j is the time picking error at jth station.

  The picking errors σ are in general different for the P and S waves and can depend also on other factors such as epicentral distance, magnitude, or noise.

• 6. Estimate of the location error ε ^jk _i in the direction of ith slave event corresponding to the double differences from jth and kth stations is

  $$ {\varepsilon}_i^{jk}={r}_0\kern0.5em /D{t}_i^{jk},\;j\ne k $$

  (2)

• 7. For every slave event, the combination of stations that gives the minimum location error E, is found

  $$ {E}_i={ \min}^{jk}\left({\varepsilon}_i^{jk}\right),\;j\ne k $$

  (3)

  This expression defines an error body around the grid node. The shape of the error body is a general polyhedron.

• 8. The maximum error on the error body is “total error,” E _T .

• 9. Projection of the error body to the horizontal plane is computed, and the maximum error in this projection corresponds to an “epicentral error,” E _E .

• 10. Similarly, projection of the error body to the vertical axis is computed and the maximum error in this projection corresponds to “depth error,” E _D .