We have developed an efficient method to determine high-resolution hypocenter locations over large distances. The location method incorporates ordinary absolute travel-time measurements and/or cross-correlation P-and S-wave differential travel-time measurements. Residuals between observed and theoretical travel-time differences (or double-differences) are minimized for pairs of earthquakes at each station while linking together all observed event-station pairs. A least-squares solu- tion is found by iteratively adjusting the vector difference between hypocentral pairs. The double-difference algorithm minimizes errors due to unmodeled velocity struc- ture without the use of station corrections. Because catalog and cross-correlation data are combined into one system of equations, interevent distances within multiplets are determined to the accuracy of the cross-correlation data, while the relative lo- cations between multiplets and uncorrelated events are simultaneously determined to the accuracy of the absolute travel-time data. Statistical resampling methods are used to estimate data accuracy and location errors. Uncertainties in double-difference locations are improved by more than an order of magnitude compared to catalog locations. The algorithm is tested, and its performance is demonstrated on two clus- ters of earthquakes located on the northern Hayward fault, California. There it col- lapses the diffuse catalog locations into sharp images of seismicity and reveals hor- izontal lineations of hypocenters that define the narrow regions on the fault where stress is released by brittle failure.

/pdf/a-double-difference-earthquake-location-algorithm-method-and-13ttz2fahg.pdf

A Double-Difference Earthquake Location Algorithm: Method and Application to the Northern Hayward Fault, California

The inverse problem of three-dimensional (3-D) local earthquake tomography is formulated as a linear approximation to a nonlinear function. Thus the solutions obtained and the reliability estimates depend on the initial reference model. Inappropriate models may result in artifacts of significant amplitude. Here, we advocate the application of the same inversion formalism to determine hypocenters and one-dimensional (1-D) velocity model parameters, including station corrections, as the first step in the 3-D modeling process. We call the resulting velocity model the minimum 1-D model. For test purposes, a synthetic data set based on the velocity structure of the San Andreas fault zone in central California was constructed. Two sets of 3-D tomographic P velocity results were calculated with identical travel time data and identical inversion parameters. One used an initial 1-D model selected from a priori knowledge of average crustal velocities, and the other used the minimum 1-D model. Where the data well resolve the structure, the 3-D image obtained with the minimum 1-D model is much closer to the true model than the one obtained with the a priori reference model. In zones of poor resolution, there are fewer artifacts in the 3-D image based on the minimum 1-D model. Although major characteristics of the 3-D velocity structure are present in both images, proper interpretation of the results obtained with the a priori 1-D model is seriously compromised by artifacts that distort the image and that go undetected by either resolution or covariance diagnostics.

/pdf/initial-reference-models-in-local-earthquake-tomography-1uwqgwr2xs.pdf

Initial reference models in local earthquake tomography

[1] Since their development in the 1960s, seismic arrays have given a new impulse to seismology. Recordings from many uniform seismometers in a well-defined, closely spaced configuration produce high-quality and homogeneous data sets, which can be used to study the Earth's structure in great detail. Apart from an improvement of the signal-to-noise ratio due to the simple summation of the individual array recordings, seismological arrays can be used in many different ways to study the fine-scale structure of the Earth's interior. They have helped to study such different structures as the interior of volcanos, continental crust and lithosphere, global variations of seismic velocities in the mantle, the core-mantle boundary and the structure of the inner core. For this purpose many different, specialized array techniques have been developed and applied to an increasing number of high-quality array data sets. Most array methods use the ability of seismic arrays to measure the vector velocity of an incident wave front, i.e., slowness and back azimuth. This information can be used to distinguish between different seismic phases, separate waves from different seismic events and improve the signal-to-noise ratio by stacking with respect to the varying slowness of different phases. The vector velocity information of scattered or reflected phases can be used to determine the region of the Earth from whence the seismic energy comes and with what structures it interacted. Therefore seismic arrays are perfectly suited to study the small-scale structure and variations of the material properties of the Earth. In this review we will give an introduction to various array techniques which have been developed since the 1960s. For each of these array techniques we give the basic mathematical equations and show examples of applications. The advantages and disadvantages and the appropriate applications and restrictions of the techniques will also be discussed. The main methods discussed are the beam-forming method, which forms the basis for several other methods, different slant stacking techniques, and frequency–wave number analysis. Finally, some methods used in exploration geophysics that have been adopted for global seismology are introduced. This is followed by a description of temporary and permanent arrays installed in the past, as well as existing arrays and seismic networks. We highlight their purposes and discuss briefly the advantages and disadvantages of different array configurations.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2000RG000100

Array seismology: Methods and applications

We have developed a double-difference (DD) seismic tomography method that makes use of both absolute and relative arrival times. By reducing systematic errors using the more accurate relative arrival times, the method produces an improved velocity model. Simultaneously, it yields event locations of a quality equivalent to those of the DD location method, while avoiding simplifying assumptions of that method. We test this method on a synthetic dataset and find that it produces a more accurate velocity model and event locations than standard tomography. We also test this method on a Hayward fault, California, earthquake dataset spanning 1984–1998. The earthquakes relocated by this method collapse to a thin line along the fault trace, consistent with previous results. The DD velocity model has sharper velocity contrasts near the source region than the standard tomography model.

Double-Difference Tomography: The Method and Its Application to the Hayward Fault, California

Unconventional oil and gas production provides a rapidly growing energy source; however, high-production states in the United States, such as Oklahoma, face sharply rising numbers of earthquakes. Subsurface pressure data required to unequivocally link earthquakes to wastewater injection are rarely accessible. Here we use seismicity and hydrogeological models to show that fluid migration from high-rate disposal wells in Oklahoma is potentially responsible for the largest swarm. Earthquake hypocenters occur within disposal formations and upper basement, between 2- and 5-kilometer depth. The modeled fluid pressure perturbation propagates throughout the same depth range and tracks earthquakes to distances of 35 kilometers, with a triggering threshold of ~0.07 megapascals. Although thousands of disposal wells operate aseismically, four of the highest-rate wells are capable of inducing 20% of 2008 to 2013 central U.S. seismicity.

https://science.sciencemag.org/content/sci/345/6195/448.full.pdf

Sharp increase in central Oklahoma seismicity since 2008 induced by massive wastewater injection

The GSETT-3 experiment was conducted for more than two years and the International Data Center (IDC) reported more than 20,000 events for 1995 in the Reviewed Event Bulletins (REB). We have used this data base to investigate the location bias of arrays and selected three-component stations in the Alpha network, for which the recorded data is automatically processed to determine earthquake locations in near-real time. The Alpha network, which consists of 14 arrays, provides estimates of event azimuths determined by f-k processing. We selected 19 three-component stations that were operated all or most of 1995 and for which event azimuth was estimated by polarization analysis. Only events with epicentral distances of less than 100° were considered in order to exclude phases with steep incidence angles, associated with unreliable azimuth estimates. Teleseismic P phases and the major regional and local phases were examined. Only data for which a signal-to-noise ratio was given were included in this analysis. The signal-to-noise ratios were used as a weighting factor for the statistical parameters and the graphical representation of the azimuth residuals. The preliminary analysis of azimuth residuals identified some arrays that give significantly erroneous azimuths; in some cases, the error is systematic, in other cases, it is random. One array with systematic azimuthal bias is CMAR. This array shows positive residuals for event paths from the south, while phases for events with paths from the north show negative residuals. Similar patterns, which strongly suggest azimuthal bias, are observed for PDAR, TXAR, and SPITS. In the case of MJAR, the large azimuthal errors observed particularly for regional and local distances are not a function of direction. The scatter in the azimuth residuals is much larger for 3-C stations than for the arrays. Clear systematic errors were identified for SCHQ and CPUP, which show constant offsets, and at VNDA, which has negative residuals for events to the north and positive residuals for events from the south. The most significant azimuth bias was observed for PDY, where the azimuth residuals change from about −90° to more than +90° at backazimuths near 120°, meaning that all rays appear from the northwest.

Urs Kradolfer

Papers

Investigation of azimuth residuals observed at stations of the GSETT-3 alpha network