### hypoDD-A Program to Compute Double-Difference Hypocenter Locations

#### Open-File Report 2001-113

- By:
- Felix Waldhauser

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#### Abstract

HypoDD is a Fortran computer program package for relocating earthquakes with the double-difference algorithm of Waldhauser and Ellsworth (2000). This document provides a brief introduction into how to run and use the programs ph2dt and hypoDD to compute double-difference (DD) hypocenter locations. It gives a short overview of the DD technique, discusses the data preprocessing using ph2dt, and leads through the earthquake relocation process using hypoDD. The appendices include the reference manuals for the two programs and a short description of auxiliary programs and example data. Some minor subroutines are presently in the c language, and future releases will be in c.

Earthquake location algorithms are usually based on some form of Geiger’s method, the linearization of the travel time equation in a first order Taylor series that relates the difference between the observed and predicted travel time to unknown adjustments in the hypocentral coordinates through the partial derivatives of travel time with respect to the unknowns. Earthquakes can be located individually with this algorithm, or jointly when other unknowns link together the solutions to indivdual earthquakes, such as station corrections in the joint hypocenter determination (JHD) method, or the earth model in seismic tomography.

The DD technique (described in detail in Waldhauser and Ellsworth, 2000) takes advantage of the fact that if the hypocentral separation between two earthquakes is small compared to the event-station distance and the scale length of velocity heterogeneity, then the ray paths between the source region and a common station are similar along almost the entire ray path (Fréchet, 1985; Got et al., 1994). In this case, the difference in travel times for two events observed at one station can be attributed to the spatial offset between the events with high accuracy.

DD equations are built by differencing Geiger’s equation for earthquake location. In this way, the residual between observed and calculated travel-time difference (or double-difference) between two events at a common station are a related to adjustments in the relative position of the hypocenters and origin times through the partial derivatives of the travel times for each event with respect to the unknown. HypoDD calculates travel times in a layered velocity model (where velocity depends only on depth) for the current hypocenters at the station where the phase was recorded. The double-difference residuals for pairs of earthquakes at each station are minimized by weighted least squares using the method of singular value decomposition (SVD) or the conjugate gradients method (LSQR, Paige and Saunders, 1982). Solutions are found by iteratively adjusting the vector difference between nearby hypocentral pairs, with the locations and partial derivatives being updated after each iteration. Details about the algorithm can be found in Waldhauser and Ellsworth (2000).

When the earthquake location problem is linearized using the double-difference equations, the common mode errors cancel, principally those related to the receiver-side structure. Thus we avoid the need for station corrections or high-accuracy of predicted travel times for the portion of the raypath that lies outside the focal volume. This approach is especially useful in regions with a dense distribution of seismicity, i.e. where distances between neighboring events are only a few hundred meters. The improvement of double-difference locations over ordinary JHD locations is shown in Figure 1 for about 10,000 earthquakes that occurred during the 1997 seismic crisis in the Long Valley caldera, California. While the JHD locations (left panel) show a diffuse picture of the seismicity, double-difference locations (right panel) bring structural details such as the location of active fault planes into sharp focus.

#### Additional publication details

- Publication type:
- Report
- Publication Subtype:
- USGS Numbered Series
- Title:
- hypoDD-A Program to Compute Double-Difference Hypocenter Locations
- Series title:
- Open-File Report
- Series number:
- 2001-113
- Edition:
- Version 1.0
- Year Published:
- 2001
- Language:
- English
- Contributing office(s):
- Earthquake Science Center
- Description:
- 25 p.
- Online Only (Y/N):
- Y