Hypocentral Coordinates Research Articles

Simulated annealing for earthquake location

SUMMARY The Metropolis algorithm for simulated annealing has been applied to earthquake location. The method combines linear and non-linear search techniques, and is able to locate events reliably and efficiently. A separation of the spatial and temporal components of the search improves performance. This arises from decoupling the strong correlation between depth and origin time and by taking advantage of the low computational cost of re-computing the misfit for multiple origin times. In addition, a method of generating new models is applied which progressively concentrates attention on more favourable regions while still allowing the algorithm to avoid local minima in the misfit function. In contrast to other non-linear algorithms there is no requirement to explicitly delineate bounds on the hypocentral coordinates. The simulated-annealing technique is an example of a global optimization routine. Consequently, it does not require the computation of derivatives and so can be used with arrival times of multiple phases, azimuth and slowness information and any type of velocity model, including laterally heterogeneous 3-D models, without modification to the basic algorithm. In addition, robust statistical functions describing the data misfit can be easily incorporated. The performance of the algorithm is illustrated on three events with different types of data, including one event with array information. Travel times are calculated relative to the 1-D iasp91 velocity model. In each case, starting from widely separated initial locations the algorithm converges to a region of a few cubic kilometres. This region represents the neighbourhood of the global minimum of the misfit function. By including the maximum amount of available information and using robust statistical functions, the final locations are more accurate than those obtained using linear methods. In addition, the algorithm is able to locate the immediate region of the global minimum with much less computational effort than standard non-linear algorithms.

Earthquake location in strongly heterogeneous media

Traveltime computation methods for strongly heterogeneous 3-D media developed during recent years are well suited for earthquake location. We present here a new method based on the traveltime algorithm of Podvin-Lecomte, related to the inverse problem formulation of Tarantola & Valette. The Podvin-Lecomte method, based on the Huygens principle, is very robust and allows arbitrary surface topography and station placement even for borehole instruments. First arrival traveltimes are computed for each of the recording stations using a fine 3-D velocity mesh (up to 106 cells on a workstation). The traveltime grid allows the use of the Tarantola & Valette formulation, which enables a full non-linear approach. The solution is given as a 3-D probability density function of hypocentre coordinates, which accounts for the arrival time measurements as well as a priori information for the location, the accuracy of both the arrival time readings and the computation of the theoretical traveltimes. This powerful method called 3dgridloc gives the location of the induced seismicity of the gas field of Lacq (France) using 443 520 cells of a 3-D velocity mesh and the observations from nine recording stations, one of which is located at the bottom of a 3880 m deep borehole. Location of synthetic foci as well as more than 500 actual earthquakes shows the real advantages of this new method versus the classical hypo71. A new insight into the induced seismicity is now possible: induced seismicity may occur as far away as 10 km from the gas reservoir and involve a much greater volume of rock than expected using earlier locations.

震源座標の関数としての観測点補正値を用いた震源決定方法

震源座標の関数としての観測点補正値を用いた震源決定方法

Initial rupture and the main fault of earthquakes: a comparison of the body wave first arrivals and CMT data for the Kamchatka-Commander region

Centroid-moment tensor (CMT) data by Dziewonski and coworkers, and body wave first-arrival earthquake parameters obtained from local networks were simultaneously investigated for 55 earthquakes in the Kamchatka-Commander region. which occurred from 1977 to 1986. The magnitude range considered was 4.5–7.5; the focal depths were 0–190 km. The following parameters were studied: origin time, hypocenter coordinates, focal mechanism and seismic moment. The first-arrival data were referred to the initial rupture in the earthquake focus and CMT estimates to the main earthquake fault. The principal results obtained are as follows: shifts of the centroid location with respect to initial hypocenters and the change or stability of the type of faulting from the initial rupture to the main fault depend on the tectonic position of the hypocentral area; the character of the source-time function depends on the sign of the main fault propagation (i.e. downwards, upwards, horizontally).

A preliminary earthquake location method based on a hyperbolic approximation to travel times

We present a fast, two-step method for preliminary earthquake location using the direct arrivals recorded by a local network by assuming that travel times follow a hyperbolic relationship. For a layered medium, hypocentral coordinates ( xe , ye , h ), arrival times ( ), origin time ( To ), travel times of either P or S waves (τ), and station coordinates ( x, y ) are approximately related by an equation describing a hyperbolic surface: τ = t − T o = ( x − x e ) 2 + ( y − y e ) 2 + h 2 / v ( 1 ) , where v is the rms velocity between the surface and depth h . This equation is a good approximation when the angle between the vertical and the ray path is small. In the first step To and the coefficients of the hyperboloid that best fit the observed arrival times are determined by nonlinear inversion. The coordinates of the minimum of the hyperboloid give the event epicenter. In the second step all the unknown parameters are computed simultaneously by nonlinear inversion of equation (1). Testing with synthetic data shows that the method performs better than might have been expected given the approximations involved. The determination of epicentral locations is very robust even in the presence of noise. When the events are under or near the network and only P arrivals are used, the epicenters are mislocated by a few kilometers at most. When S arrivals are included, depths and origin times are also reliably estimated. This method can be applied when approximate, but expeditious, earthquake locations are required. It can be used, for example, as part of an automatic event location program, first to produce a set of P and S arrival times uncontaminated by gross errors, and then to generate initial estimates of hypocentral location and origin time to be used by standard, and more time-consuming, locating programs. Furthermore, in optimal cases, it is possible to obtain reliable and independent estimates of rms velocities.

国立大学観測網地震カタログの震源決定処理

The Earthquake Prediction Data Center (EPDC) of the Earthquake Research Institute, University of Tokyo, has been receiving the hypocentral parameters and arrival time data acquired through the University Information System for Earthquake Prediction Research, which is operated by Japanese national universities under the national program for earthquake prediction. Through the cooperation of these universities, the data and hypocenters were compiled and stored in the database system of the EPDC. There are two types of database; one is the real-time database and the other is the revised database which is sent by magnetic tapes from each regional center. EPDC has prepared to open these database for every seismologists to use and now the real-time database can be used by the real-time monitoring system and the revised database is open to be public as the Japan University Network Earthquake Catalog. The hypocentral coordinates and orgin times listed in the catalog are redetermined by EPDC using the arrival time data of the revised database. Although, the minimun magnitude of the earthquakes listed in the catalog is 2.0, the earthquakes listed in the catalog covers the microearthquake activities in Japan. In the present paper, we discuss the hypocenter determination procedure of the catalog and also the characteristics of the hypocenters listed in the catalog.

Estimation of hypocentral parameters of local earthquakes when crustal layers have constantP-velocities and dipping interfaces

The paper describes an algorithm for estimating the hypocentral coordinates and origin time of local earthquakes when the wave speed model to be employed is a layered one with dipping interfaces. A constrained least-squared error problem has been solved using the penalty function approach, in conjunction with the sequential unconstrained optimization technique of Fiacco and McCormick. Joint confidence intervals for the computed parameters are estimated using the approach of Bard for nonlinear problems. These results show that when a hypocentre lies outside the array of recording stations and head waves from a dipping interface are involved, then its inclination must be taken into account for dip angles exceeding 5°.

HYPOCENTER: An earthquake location method using centered, scaled, and adaptively damped least squares

AbstractWe present an earthquake location method, HYPOCENTER, which combines features of the two well-known algorithms HYPO71 and HYPOINVERSE, with a new technique which we term adaptive damping. Each column of the linearized condition matrix T, which relates changes in arrival time to changes in hypocentral position, is centered and scaled to have zero mean and a norm of one. Origin time is defined as the mean arrival time minus the mean travel time. The three least-squares normal equations for hypocentral coordinates, with diagonal terms equal to one, are then solved iteratively by adding a variable damping factor, θ2, to their diagonal terms before inversion. If the residual sum of squares increases, we return to the previous iteration, increase θ2, then try again. This procedure, which we term adaptive damping, always results in residuals which are less than or equal to the HYPO71 or HYPOINVERSE residuals. We demonstrate HYPOCENTER by comparing it to HYPO71 and HYPOINVERSE using synthetic and real arrival time data for four- and eight-station seismic arrays.

The refinement of hypocenter parameters on the basis of three-dimensional velocity models of focal zones

A complex approach to the processing of seismological data to determine hypocenter coordinates and to construct three-dimensional velocity fields of focal zones is considered. The iterative process includes the determination of focal coordinates under the assumption of a laterally homogeneous medium, the construction of a three-dimensional velocity model, and subsequent redefinition of the focal coordinates taking into account the inhomogeneous structure of the medium. The principal results of calculations of three-dimensional velocity fields and refined earthquake hypocenters are presented for focal zones in Vrancea (Carpathians), the Caucasus, and Kamchatka.

Coseismic and other short-term strain changes recorded with Sacks-Evertson strainmeters in a deep mine, South Africa

Summary. During 1977 March and April, three Sacks-Evertson borehole dilatometers were installed at the ends of boreholes drilled into the sidewall of an experimental tunnel at a depth of 3.1 km in the ERPM gold mine near Johannesburg. In the following year coseismic strain changes ranging from 5 ± 10−10 to values exceeding 5 ± 10−6 were recorded for hundreds of mine tremors in the magnitude range -1 to 3.7 and at hypocentral distances of 50 m to about 2 km. Hypocentral coordinates and magnitudes were determined from seismograms recorded from an underground array of geophones. Amplitudes and polarities of the coseismic strain steps are generally in excellent agreement with theoretical expectations based on point-source dislocation theory; specifically, the strain steps are proportional to the seismic moment divided by the cube of hypocentral distance. At a strain level of 5 ± 10−9 or greater the tremors do not appear to be preceded by any short-term indications of instability even for tremors producing coseismic steps greater than 5 ± 10−6 and for which the strainmeters were within a source radius of the hypocentre. Continuous strain changes observed at the times when the mine excavation, at a distance of about 100 m, is extended are in good agreement with calculated changes based on the theory of elasticity. A similar calculation is consistent with post-seismic strain changes observed to follow some of the closer tremors. These post-seismic strains show a logarithmic dependence on time following the tremor and appear to be due to the interaction of a tremor with the adjacent mine excavation rather than to deformation within the actual seismic source region.

Study of the Montenegro earthquake sequence (March-July 1979)

abstract Data from more than 80 European seismic stations, concerning foreshocks, the main shock, and aftershocks of the earthquake which occurred near the coast of Montenegro on 15 April 1979, have been collected and analyzed. The data have allowed the focal mechanism of the two strongest shocks to be estimated. The hypocentral coordinates of more than 180 aftershocks and some foreshocks have been also computed, giving the time-space distribution of the sequence. The shocks are mostly contained in an area about 100 km long and 30 km wide, almost corresponding to the Adriatic coast line of the Yugoslavia-Albania border region. The hypocentral depths, although determined approximately, appear to be in the order of 15 to 20 km. The results have been compared with previous knowledge of the tectonics of the zone.

Determination of earthquake source parameters from waveform data for studies of global and regional seismicity

It is possible to use the waveform data not only to derive the source mechanism of an earthquake but also to establish the hypocentral coordinates of the ‘best point source’ (the centroid of the stress glut density) at a given frequency. Thus two classical problems of seismology are combined into a single procedure. Given an estimate of the origin time, epicentral coordinates and depth, an initial moment tensor is derived using one of the variations of the method described in detail by Gilbert and Dziewonski (1975). This set of parameters represents the starting values for an iterative procedure in which perturbations to the elements of the moment tensor are found simultaneously with changes in the hypocentral parameters. In general, the method is stable, and convergence rapid. Although the approach is a general one, we present it here in the context of the analysis of long‐period body wave data recorded by the instruments of the SRO and ASRO digital network. It appears that the upper magnitude limit of earthquakes that can be processed using this particular approach is between 7.5 and 8.0; the lower limit is, at this time, approximately 5.5, but it could be extended by broadening the passband of the analysis to include energy with periods shorter that 45 s. As there are hundreds of earthquakes each year with magnitudes exceeding 5.5, the seismic source mechanism can now be studied in detail not only for major events but also, for example, for aftershock series. We have investigated the foreshock and several aftershocks of the Sumba earthquake of August 19, 1977; the results show temporal variation of the stress regime in the fault area of the main shock. An area some 150 km to the northwest of the epicenter of the main event became seismically active 49 days later. The sense of the strike‐slip mechanism of these events is consistent with the relaxation of the compressive stress in the plate north of the Java trench. Another geophysically interesting result of our analysis is that for 5 out of 11 earthquakes of intermediate and great depth the intermediate principal value of the moment tensor is significant, while for the remaining 6 it is essentially zero, which means that their mechanisms are consistent with a simple double‐couple representation. There is clear distinction between these two groups of earthquakes.

Travel-time inversion for simultaneous earthquake location and velocity structure determination in laterally varying media

Travel times are observed at a network of seismometers from a number of earthquakes. The seismic velocity of the medium through which the waves pass is allowed to vary in all three dimensions and is represented in terms of a finite number (P) of parameters. The travel-time data is inverted for the velocity parameters and the hypocentre coordinates of the earthquakes. A linearized least squares inversion technique is used and both the stochastic and generalized inverses are considered. The method is computationally efficient and requires inversion (or decomposition) of only P × P and 4 × 4 matrices. The method is applied to a dataset of travel times reported to the I. S. C. from 56 earthquakes recorded at stations on the North Island of New Zealand. The velocity structure is characterized by only five parameters, so that only 5 × 5 matrices need be inverted. The inversion gives a 30 per cent reduction in residuals. The resulting velocity model is substantially different from that obtained when the hypocentres are kept fixed and only the velocity parameters are inverted for. A parallel study of synthetic data gives insight into the interpretation of results. In particular, the depth and origin time of some of the earthquakes, together with two of the five velocity parameters, are very poorly determined.

Interpreting the seismic glut moments of total degree two or less

The stress glut Γ(x, t) (Backus & Mulcahy 1976a) is a symmetric second-order tensor field which completely describes the mechanical properties of an indigenous seismic source. The equivalent force γ(x,t)=-ΔΓ(x,t) is all that can be determined by observing the motion. The glut moment tensor Λ(m,n)(ζ, r) is the polynomial moment of Λ=ΔtΓ relative to position ζ and time r with spatial degree m and temporal degree n. It affects the seismic motion only through the force moment tensor γ(m+1,n)(ζ,τ), which is obtained by symmetrizing Λ(m,n)f(ζ,τ) on its last m+1 indices. Here we show how to obtain the force moment tensors of low total degree m+ n+ 1 from the long-period motion produced by the source. We show that in faulting with rupture propagation, all the Λ(m,n)(ζ, τ) with m + n = p will usually produce motion of comparable intensity, and that they are all parts of a single tensor Λ(ρ, r) of order p+ 2 over R4, four-dimensional space time. We extend the definitions of centroid and variance tensor to tensor fields and show that the centroid of Λ in R4 gives the position and time of the source centroid. The variance tensor estimates the time duration of anelastic behaviour at the source, the rupture velocity, and the size, shape and orientation of the source region. The hypocentral coordinates, the time duration, and the rupture velocity are always calculable from the glut moments with m+n < 2, m < 1, and these can be measured from the long-period motion. The geometry of the source region requires knowledge of Γ(2,0), only part of which can be calculated from γ(3,0) for a general indigenous seismic source. We illustrate the general theory with four different types of seismic sources, and we find that when all six tensors γ(m+1,n)(ζ, τ) with m + n<2 have been measured, there are three ways to resolve the fault-plane ambiguity, one using long-period information, and the other two using measurements of the final static deformation produced by the source.

Application of prediction analysis to hypocenter determination using a local array

Abstract Prediction analysis provides an efficient means of estimating errors in local earthquake hypocenter determinations using a dense array of seismometers. The standard errors of the hypocentral coordinates and the origin time due to random errors in the data and model parameters may be calculated rigorously for a least-squares hypocenter inversion procedure using arbitrary earth models. Contour maps of the estimated standard errors in the hypocenter parameters are plotted for two array configurations and for several earth models and event depths. These maps are useful in predicting the relative accuracy and difficulty of hypocenter location as a function of position in the array, and in selecting events with small relative error to be used in velocity-structure refinement in the vicinity of the array. In particular, the method may be used to provide a means of optimizing array geometry to provide maximum hypocenter control in specific target regions. Tests were made using hypothetical data with prescribed error distributions showing good agreement with the error analysis.