HYPO3D is a software tool designed to determine the hypocenter and magnitude of local earthquakes. The program aims to solve earthquake location within a 3-dimensional velocity model. Authored by Milan Werl under the guidance of Petr Firbas between 1986 and 1988, this software has been utilized at the Institute of Physics of the Earth, Masaryk University in Brno.

HYPO3D implements the classical Geiger’s method for earthquake location, with inspiration drawn from HYPO71 [Lee and Lahr 1975]. Ray tracing is based on a modified TRVDRV subroutine developed by [Eaton 1969].

The 3-dimensional velocity model consists of rectangular homogeneous blocks of rectilinear structure with irregular spacing in three perpendicular directions. The model is limited to 100x100x100 blocks, with seismic wave velocities assigned in units of [km/s].

Rectilinear structure of the 3-d velocity model

The upper boundary of the model is defined by a surface, interpolated using splines.

HYPO3D reflects the 3-dimensional model by solving ray tracing in a 1-dimensional layered model for each section between the earthquake source and receiver point. The travel-time computation involves several steps:

1. Creating a vertical plane cross-section of the 3-dimensional velocity model between the source and receiver.
2. Converting the 3-dimensional model into a 1-dimensional model, preserving horizontal layers.
3. Computing the ray trajectory in the 1-dimensional velocity model, utilizing a two-point fast ray-tracing scheme similar to HYPO71.
4. Calculating the travel-time by integrating along the ray path in the 3-dimensional velocity model.

The authors of the computer program justify this approach by reference to [Romanov 1972, Firbas 1984] and consider this solution to be a linearization approach.

The method assumes regularity, making it suitable for some seismic phases but not for all. It is known that this approach may not provide sufficient accuracy for refracted or head waves passing along curved or sloping interfaces, as discussed by [Ryaboy 2001].

Hypo3d approximate ray tracing along the dipping planar interface.

Originally designed for short-distance direct phases, HYPO3D may have limitations in locating regional-distance earthquakes within complex 3-dimensional velocity models.

The map coordinate system S-JTSK Křovák EPSG:5513 is utilized for program input and output (with units in [km]). The velocity model, however, is defined in local coordinates, which may impose limitations, particularly in fixing hypocenters.

The weighted least squares algorithm considers weight codes for phase arrivals measurements. These weight codes range from full weight (0) to no weight (4), following the conventions of HYPO71 and HYPOINVERSE.

The program includes parts of the library FITPACK (coded by Alan Kaylor Cline) and subroutines of IBM SSP (Scientific Subroutine Package).

The project aims to maintain code and documentation, and to identify program limitations. No further development is intended.

Minor changes compared to the original version were primarily focused on code clarity and bug fixes. Further upgrades enhanced functionality, addressing issues such as coordinate consistency and model limitations.

1. To streamline the code, approximately 9,000 lines of program code were removed. Removing unreachable or redundant code had no impact on functionality.
2. Originally, the parameter reading_error was hardcoded. Now, its default value can be overridden as a second optional argument in the velocity model file (line number 5). (v10.50)
3. The coordinates (x, y) of the epicenter and their estimated errors (dxer, dyer) were previously presented in different coordinate systems (Epicenter in map coordinates Křovák EPSG:5513 but errors in model local coordinates). Now, they are consistently presented in map coordinates. (v10.62)
4. In cases of coordinate fixation, the calculation of the error covariance matrix is not reduced in dimensions unless the hypocenter is on or near the surface. (v10.73)
5. The azimuth of rays emerging from the focus and the angle of rotation of the error ellipse are now calculated with respect to the meridian convergence of Křovák coordinates at the focal point. (v10.64)
6. The limitation on the number of blocks in the velocity model has been extended from the original 15x15x40 to 100x100x100. (v10.73)
7. Previously, the a posteriori estimate of the arrival variance was not unbiased because the individual residuals were first adjusted based on the a priori determined reading error. Now, the arrival variance estimate is calculated first and then adjusted according to the value of the reading error. (v10.70)
8. If a small number of measurements does not provide any degree of freedom, only the 'a priori' part of the standard deviation (parameter reading error) is used to calculate the error ellipse. If the error interval cannot be estimated, NaN is printed. (v10.73)
9. Previously, the seismic location program assumed a constant ratio between P-wave and S-wave velocities. With the update to version 10.79, the program now allows the input of two velocity models, enabling seismic location based on a more accurate relationship between P-wave and S-wave velocities. (v10.79)
10. Station corrections can be entered separately for both P-wave and S-wave seismic phases. (v10.80)

HYPO3D is adapted for the Linux environment and the gfortran compiler. Compilation is facilitated through the supplied Makefile, resulting in the binary hypo3d, which can be manually copied to the binary path.

The original documentation of the program is available in the report by Firbas P. and Werl M. (PDF). Additional information, including running the program and formats, is provided in the wiki.

HYPO3D is freely available, primarily for users at the Institute of Physics of the Earth, Masaryk University in Brno. However, it's a working repository, not intended for end-user release.

Eaton, J. P. (1969). HYPOLAYR, a computer program for determining hypocenters of local earthquakes in an earth consisting of uniform flat layers over a half space, Open File Report, U.S. Geological Survey, 155 pp.

Firbas, P. & Vaněk, J. (1984). Travel time curves for complex inhomogeneous slightly anisotropic media. Stud Geophys Geod (1984) 28: 393-406. DOI https://doi.org/10.1007/BF01642992

Lee, W. H. K. and J. C. Lahr (1975). HYP071 (Revised): A computer program for determining hypocenter, magnitude, and first motion pattern of local earthquakes, U. S. Geological Survey Open File Report 75-311, 113 pp.

Романов В. Г. (1972). Некоторые обратные задачи для уравнений гиперболического типа. Издательство "Наукa", Новосибирск, 1972

Ryaboy V., Baumgardt D.R., Firbas P., Dainty A.M. (2001). Application of 3-D crustal and upper mantle velocity model of North America for Location of Regional Seismic Events. Pure appl. geophys. 158 (2001) 79-103. Birkhäuser Verlag, Basel, 2001. DOI https://doi.org/10.1007/PL00001169