A new analytical method for finding the upper mantle velocity structure from P and S wave travel times of deep earthquakes

1969 ◽  
Vol 59 (2) ◽  
pp. 755-769
Author(s):  
K. L. Kaila
Keyword(s):  
Velocity Structure ◽  
Focal Depth ◽  
Least Square ◽  
Travel Times ◽  
S Wave ◽  
The Earth ◽  
Straight Line ◽  
Wave Travel ◽  
Deep Focus ◽  
Mantle Velocity

abstract A new analytical method for the determination of velocity at the hypocenter of a deep earthquake has been developed making use of P- and S-wave travel times. Unlike Gutenberg's method which is graphical in nature, the present method makes use of the least square technique and as such it yields more quantitative estimates of the velocities at depth. The essential features of this method are the determination from the travel times of a deep-focus earthquake the lower and upper limits Δ1 and Δ2 respectively of the epicentral distance between which p = (dT/dΔ) in the neighborhood of inflection point can be considered stationary so that the travel-time curve there can be approximated to a straight line T = pΔ + a. From p = (1/v*) determined from the straight line least-square fit made on the travel-time observation points between Δ1 and Δ2 for various focal depths, upper-mantle velocity structure can be obtained by making use of the well known relation v = v*(r0 − h)/r0, h being the focal depth of the earthquake, r0 the radius of the Earth, v* the apparent velocity at the point of inflection and v the true velocity at that depth. This method not only gives an accurate estimate of p, at the same time it also yields quite accurate value of a which is a function of focal depth. Calibration curves can be drawn between a and the focal depth h for various regions of the Earth where deep focus earthquakes occur, and these calibration curves can then be used with advantage to determine the focal depths of deep earthquakes in those areas.

Upper Mantle velocity structure in the Hindukush region from travel time studies of deep earthquakes using a new analytical method

1969 ◽  
Vol 59 (5) ◽  
pp. 1949-1967
Author(s):  
K. L. Kaila ◽  
V. G. Krishna ◽  
Hari Narain
Keyword(s):  
Analytical Method ◽  
Upper Mantle ◽  
Velocity Structure ◽  
Focal Depth ◽  
P Wave ◽  
S Wave ◽  
Deep Earthquakes ◽  
Calibration Curves ◽  
Depth Determination ◽  
Mantle Velocity

abstract Upper Mantle velocity structure in the Hindukush region has been determined from the P- and S-wave travel times of 28 deep earthquakes making use of a new analytical method given by Kaila (1969). From a depth of 45 to 230 kms, the present analysis reveals a continuous linear increase of P-wave velocity from 8.21 to 8.52 km/sec. For S waves, however, the velocity increases linearly from 4.58 km/sec at a depth of 85 kms to 4.77 km/sec at 230 kms depth. Upper mantle velocities in the Hindukush region are found to be considerably higher in comparison to those for other regions of the Earth. Within the accuracy of the velocity determination from the present method, no inferences can be drawn regarding the existence or otherwise of the low-velocity channel in this region. Calibration curves for focal depth determination in the Hindukush region are also drawn. The accuracy of focal depth determination from these calibration curves is of the same order as that obtained in the focal depths determined by making use of pP, sS and other reflected phases.

On locating local earthquakes using small networks

1969 ◽  
Vol 59 (3) ◽  
pp. 1201-1212
Author(s):  
David E. James ◽  
I. Selwyn Sacks ◽  
Eduardo Lazo L. ◽  
Pablo Aparicio G.
Keyword(s):  
Least Squares ◽  
Focal Depth ◽  
P Wave ◽  
Time Interval ◽  
Travel Times ◽  
Origin Time ◽  
Average Value ◽  
Fundamental Properties ◽  
P Wave Velocity ◽  
Wave Travel

abstract Mathematical instability in four-parameter least squares hypocenter solutions arises primarily from the fact that the four computed variables—origin time (T0), focal depth (h), latitude (θ), and longitude (λ)—are not strictly independent. Specifically, T0 exhibits a non-independent relationship with the geometric parameters. For small networks (< 10–15 stations), the lack of independence between T0 and the other variables results in unstable least-squares solutions. This instability is manifest most clearly by the fact that different station subsets of the observational network produce significantly different solutions for the same earthquake. The instability can be eliminated by computing T0 independently for each station using the formula ( T 0 ) i = ( T p ) i − V k ( T s − p ) i V p , where Tp = P-wave arrival time, Vk = S-P velocity, Vp = P-wave velocity, and Ts-p = time interval between P and S arrivals. An average value of T0 can be obtained from the individually calculated origin times and the P-wave travel times calculated. The variables ϕ, λ and z are then computed by the usual least-squares procedure using P-wave travel times only. The method is iterative and an average T0 is recalculated in the course of each iteration. Fundamental properties of travel times within the Earth impose definite limitations upon the accuracy of the locations. Low values of the derivative dTp/dh at epicentral distances of a few degrees introduce a large uncertainty in focal depth, particularly for shallow (0–60 km) earthquakes. There is normally little error in epicenter, however, even for solutions in which depth is poorly determined. The dimensions and geometric configuration of the network in relation to the epicenter and the proximity of the epicenter to any one station are controlling factors in predicting the minimum uncertainty for any given hypocenter solution.

Crust-Mantle Velocity Structure of S Wave and Dynamic Process Beneath Burma Arc and Its Adjacent Regions

2008 ◽  
Vol 51 (1) ◽  
pp. 105-114 ◽  
Author(s):  
Jia-Fu HU ◽  
Yi-Li HU ◽  
Jin-Yu XIA ◽  
Yun CHEN ◽  
Hong ZHAO ◽  
...  
Keyword(s):  
Dynamic Process ◽  
Velocity Structure ◽  
S Wave ◽  
Mantle Velocity

Travel-time errors in the laterally inhomogeneous earth

1971 ◽  
Vol 61 (6) ◽  
pp. 1639-1654 ◽  
Author(s):  
Cinna Lomnitz
Keyword(s):  
Travel Time ◽  
Root Mean Square ◽  
Time Estimation ◽  
Systematic Errors ◽  
Least Square ◽  
Travel Time Estimation ◽  
Mean Square ◽  
Travel Times ◽  
The Earth ◽  
Lateral Inhomogeneity

abstract Travel times from earthquakes or explosions contain both positive and negative systematic errors. Positive skews in travel-time residuals due to epicenter mislocation, and negative skews due to lateral inhomogeneity in the Earth, are analyzed. Methods for travel-time estimation are critically reviewed. Recent travel-time tables, including the J-B tables, are within the range of root-mean-square travel-time fluctuations; the J-B tables are systematically late but cannot be reliably improved by least-square methods. Effects of lateral inhomogeneity at teleseismic distances can be estimated by chronoidal methods independently of standard tables, but the available explosion data are insufficiently well-distributed in azimuth and distance for this purpose.

Time-lapse changes within the Groningen gas field caused reservoir by compaction and distant borehole drilling

2020 ◽  
Author(s):  
Hanneke Paulssen ◽  
Wen Zhou
Keyword(s):  
Travel Time ◽  
Pore Pressure ◽  
Velocity Structure ◽  
Time Lapse ◽  
P Wave ◽  
S Wave ◽  
Gas Field ◽  
Water Contact ◽  
Wave Travel ◽  
Groningen Gas Field

<p>Between 2013 and 2017, the Groningen gas field was monitored by several deployments of an array of geophones in a deep borehole at reservoir level (3 km). Zhou & Paulssen (2017) showed that the P- and S-velocity structure of the reservoir could be retrieved from noise interferometry by cross-correlation. Here we show that deconvolution interferometry of high-frequency train signals from a nearby railroad not only allows determination of the velocity structure with higher accuracy, but also enables time-lapse measurements. We found that the travel times within the reservoir decrease by a few tens of microseconds for two 5-month periods. The observed travel time decreases are associated to velocity increases caused by compaction of the reservoir. However, the uncertainties are relatively large. <br>Striking is the large P-wave travel time anomaly (-0.8 ms) during a distinct period of time (17 Jul - 2 Sep 2015). It is only observed for inter-geophone paths that cross the gas-water contact (GWC) of the reservoir. The anomaly started 4 days after drilling into the reservoir of a new well at 4.5 km distance and ended 4 days after the drilling operations stopped. We did not find an associated S-wave travel time anomaly. This suggests that the anomaly is caused by a temporary elevation of the GWC (water replacing gas) of approximately 20 m. We suggest that the GWC is elevated due to pore-pressure variations during drilling. The 4-day delay corresponds to a pore-pressure diffusivity of ~5m<sup>2</sup>/s, which is in good agreement with the value found from material parameters and the diffusivity of (induced) seismicity for various regions in the world. </p>

scholarly journals Joint inversion of P-, and S-wave travel times for characterisation of anisotropic materials using laser Doppler interferometry measurements

2015 ◽  
Vol 2015 (1) ◽  
pp. 1-4
Author(s):  
Andrej Bóna ◽  
Boris Gurevich ◽  
Roman Pevzner ◽  
Maxim Lebedev ◽  
Mahyar Madadi
Keyword(s):  
Joint Inversion ◽  
Anisotropic Materials ◽  
Laser Doppler ◽  
Travel Times ◽  
S Wave ◽  
Wave Travel

Amplitude spectra of PcP and P phases

1968 ◽  
Vol 58 (6) ◽  
pp. 1797-1819 ◽  
Author(s):  
Goetz G.R. Buchbinder
Keyword(s):  
Amplitude Spectrum ◽  
Focal Depth ◽  
General Shape ◽  
Core Mantle Boundary ◽  
Straight Line ◽  
Short Period ◽  
Amplitude Spectra ◽  
Systematic Effects ◽  
Deep Focus

ABSTRACT Amplitude spectra were obtained from short-period PcP and P phases from seven explosions and six earthquakes. Long-period PcP and P amplitude spectra were obtained from two earthquakes. PcP and P amplitude spectra for both explosions and earthquakes are similar for any one event; therefore, station and core-mantle boundary effects are small and the general shape of the spectra is related to the source. All of the explosions studied have characteristic spectra with a pronounced minimum in the spectrum near one second. The period of this minimum increases with magnitude of the event. Short-period amplitude spectra from some intermediate- and deep-focus earthquakes resemble those from explosions. Spectra from the other earthquakes studied differ markedly from those of explosion; they have either no minimum in the spectrum near one second or very little energy for periods less than one second. The characteristics of the spectra may be of help in the classification of sources. On a plot of magnitude mb versus period of the minimum Td in the spectrum of explosions, the data form a straight line. Earthquakes with an amplitude spectrum similar to that of an explosion are randomly distributed on the plot of mb versus Td. Systematic effects of focal depth were not observed. Layering at the coremantle boundary was not detected.

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