Self-similar circular shear cracks lacking cohesion

1974 ◽  
Vol 64 (6) ◽  
pp. 1789-1808 ◽  
Author(s):  
Robert Burridge ◽  
Cesar Levy

abstract It has recently been shown (Burridge, 1973) that in two dimensions plane-strain shear cracks lacking cohesion may run at speeds ranging from the Rayleigh-wave to the S-wave speed or possibly at the P-wave speed. On the other hand, it has long been known that in antiplane strain, cracks lacking cohesion must run at least at the S-wave speed. Since locally at the edge of a three-dimensional crack there is a combination of plane and antiplane strain, we have sought and found solutions for circular shear cracks expanding at the S-wave speed and at the P-wave speed. These have finite shear tractions ahead of the crack and so may correspond to frictional sliding in the absence of cohesion. The analysis combines the method of Kostrov (1964b) with the results of Burridge (1973). We carry out a complete evaluation for the displacements and tractions on the fault plane, and far-field radiation for the S-wave-speed crack. The corresponding evaluations for the P-wave speed are not elementary and are not attempted here. As far as the authors are aware, these are the first analytic solutions of three-dimensional crack problems which satisfy a physically plausible fracture criterion for failure under shear.

1974 ◽  
Vol 64 (4) ◽  
pp. 1159-1180 ◽  
Author(s):  
F. A. Dahlen

abstract We construct a theoretical three-dimensional kinematical model of shallow-focus earthquake faulting in order to investigate the ratio of the P- and S-wave corner frequencies of the far-field elastic radiation. We attempt to incorporate in this model all of the important gross kinematical features which would arise if ordinary mechanical friction should be the dominant traction resisting fault motion. These features include a self-similar nucleation at a single point, a subsonic spreading of rupture away from that point, and a termination of faulting by smooth deceleration. We show that the ratio of the P-wave corner frequency to the S-wave corner frequency for any model which has these features will be less than unity at all points on the focal sphere.


2019 ◽  
Vol 23 (3) ◽  
pp. 209-223 ◽  
Author(s):  
Caglar Ozer ◽  
Mehmet Ozyazicioglu

Erzurum and its surroundings are one of the seismically active and hydrothermal areas in the Eastern part of Turkey. This study is the first approach to characterize the crust by seismic features by using the local earthquake tomography method. The earthquake source location and the three dimensional seismic velocity structures are solved simultaneously by an iterative tomographic algorithm, LOTOS-12. Data from a combined permanent network comprising comprises of 59 seismometers which was installed by Ataturk University-Earthquake Research Center and Earthquake Department of the Disaster and Emergency Management Authority  to monitor the seismic activity in the Eastern Anatolia, In this paper, three-dimensional Vp and Vp/Vs characteristics of Erzurum geothermal area were investigated down to 30 km by using 1685 well-located earthquakes with 29.894 arrival times, consisting of 17.298 P- wave and 12.596 S- wave arrivals. We develop new high-resolution depth-cross sections through Erzurum and its surroundings to provide the subsurface geological structure of seismogenic layers and geothermal areas. We applied various size horizontal and vertical checkerboard resolution tests to determine the quality of our inversion process. The basin models are traceable down to 3 km depth, in terms of P-wave velocity models. The higher P-wave velocity areas in surface layers are related to the metamorphic and magmatic compact materials. We report that the low Vp and high Vp/Vs values are observed in Yedisu, Kaynarpinar, Askale, Cimenozu, Kaplica, Ovacik, Yigitler, E part of Icmeler, Koprukoy, Uzunahmet, Budakli, Soylemez, Koprukoy, Gunduzu, Karayazi, Icmesu, E part of Horasan and Kaynak regions indicated geothermal reservoir.


2000 ◽  
Vol 31 ◽  
pp. 85-90 ◽  
Author(s):  
N. Deichmann ◽  
J. Ansorge ◽  
F. Scherbaum ◽  
A. Aschwanden ◽  
F. Bernard ◽  
...  

AbstractTo obtain more reliable information about the focal-depth distribution of icequakes, in April 1997 we operated an array of seven portable digital seismographs on Unteraargletscher, central Swiss Alps. Over 5000 events were detected by at least two instruments during the 9 day recording period. P-wave velocities (3770 m f) were determined from several calibration shots detonated at the glacier surface as well as in a 49 m deep borehole, whereas S-wave velocities (1860 ms–1) were derived from a simultaneous inversion for Vp/Vs6 applied to 169 icequakes. So far, hypocentral locations have been calculated for over 300 icequakes. Besides confirming the occurrence of shallow events associated with the opening of crevasses, our results show that a small but significant fraction of the hypocenters are located at or near the glacier bed. One event was found at an intermediate depth of about 120 m. Three-dimensional particle-motion diagrams of both explosions and icequakes clearly demonstrate that all vertical component seismograms from shallow sources are dominated by the Rayleigh wave. On the other hand, for events occurring at depths greater than about 40 m, the Rayleigh wave disappears almost entirely. Therefore, a qualitative analysis of the signal character provides direct information on the focal depth of an event and was used as an independent check of the locations obtained from traditional arrival-time inversions. Thus, our results demonstrate that deep icequakes do occur and that simple rheological models, according to which brittle deformation is restricted to the uppermost part of a glacier, may need revision.


2021 ◽  
Author(s):  
Huihui Weng

Abstract Slow slip events usually occur downdip of seismogenic zones in subduction megathrusts and crustal faults, with rupture speeds much slower than earthquakes. The empirical moment-duration scaling relation can help constrain the physical mechanism of slow slip events, yet it is still debated whether this scaling is linear or cubic and a fundamental model unifying slow slip events and earthquakes is still lacking. Here I present numerical simulations that show that slow slip events are regular earthquakes with negligible dynamic-wave effects. A continuum of rupture speeds, from arbitrarily-slow speeds up to the S-wave speed, is primarily controlled by the stress drop and a transition slip rate above which the fault friction transitions from rate-weakening behaviour to rate-strengthening behaviour. This continuum includes tsunami earthquakes, whose rupture speeds are about one-third of the S-wave speed. These numerical simulation results are predicted by the three-dimensional theory of dynamic fracture mechanics of elongated ruptures. This fundamental model unifies slow slip events and earthquakes, reconciles the observed moment-duration scaling relations, and opens new avenues for understanding earthquakes through investigations of the kinematics and dynamics of frequently occurring slow slip events.


2021 ◽  
Author(s):  
Y.J. Zhou ◽  
Hongtao Wang

Abstract This study solidifies the aeolian sand by microbial induced carbonate precipitation (MICP) technique. The effects of cementation solution with different concentrations, particle size, and grouting batches are examined via the bender element, unconfined compressive test and scanning electron microscope (SEM). The bender element results show that the wave speed of loose aeolian sand is 200m/s; however, after solidify the aeolian sand, the speed of P-wave is about 450-600m/s and S-wave is about 350-500m/s. Additionally, the unconfined compressive strength (UCS) results indicate that when the concentration of cementation solution is 0.75mol/L, the UCS of bio-solidified sand sample is the highest. Then, compared with the aeolian sand with original grade, the particles ranging from 0.1-0.4mm have a better cementation effect. Moreover, the UCS of bio-solidified sand samples increases along with the grouting batch. From the SEM images, it can be seen that when the grouting batch reaches to five times, the particles are almost completely covered by CaCO 3 crystals compared with the three batches and four batches.


1979 ◽  
Vol 69 (4) ◽  
pp. 947-956
Author(s):  
Paul G. Richards

abstract Certain exact solutions to Lamb's problem (the transient response of an elastic half-space to a force applied at a point) involve the computation merely of three square roots, and about ten arithmetic operations (+, −, ×, /). They arise when both source and receiver lie on the free surface. It is just these solutions which are needed in a method due to Hamano for obtaining the slip function (displacement discontinuity), as a function of space and time, for planar tension cracks and shear cracks which grow spontaneously with arbitrary shape. The solutions are described here in detail, for an elastic medium with general Poisson's ratio. They include perhaps the simplest-possible example of the P-wave.


Author(s):  
Mitsutoshi Fujita

Abstract We analyze the holographic subregion complexity in a three-dimensional black hole with vector hair. This three-dimensional black hole is dual to a (1+1)-dimensional $p$-wave superconductor. We probe the black hole by changing the size of the interval and by fixing $q$ or $T$. We show that the universal part is finite across the superconductor phase transition and has competitive behaviors different from the finite part of the entanglement entropy. The behavior of the subregion complexity depends on the gravitational coupling constant divided by the gauge coupling constant. When this ratio is less than the critical value, the subregion complexity increases as temperature becomes low. This behavior is similar to that of the holographic (1+1)-dimensional $s$-wave superconductor [M. K. Zangeneh, Y. C. Ong, and B. Wang, Phys. Lett. B 771, 130 (2014)]. When the ratio is larger than the critical value, the subregion complexity has a non-monotonic behavior as a function of $q$ or $T$. We also find a discontinuous jump of the subregion complexity as a function of the size of the interval. The subregion complexity has a maximum when it wraps almost the entire spatial circle. Due to competitive behaviors between the normal and condensed phases, the universal term in the condensed phase becomes even smaller than that of the normal phase by probing the black hole horizon at a large interval. This implies that the condensate formed decreases the subregion complexity as in the case of the entanglement entropy.


2000 ◽  
Vol 3 (01) ◽  
pp. 88-97 ◽  
Author(s):  
R.D. Benson ◽  
T.L. Davis

Summary This article presents the results of a multidisciplinary, four-dimensional (4D) (time-lapse), three-component (3C) (multicomponent) seismic study of a CO2 injection project in vacuum field, New Mexico. The ability to sense bulk rock/fluid properties with 4D, 3C seismology enables characterization of the most important transport property of a reservoir, namely, permeability. Because of the high volume resolution of the 4D, 3C seismology, we can monitor the sweep efficiency of a production process to see if reserves are bypassed by channeling around lower permeability parts of the reservoir and the rate at which the channeling occurs. In doing so, we can change production processes to sweep the reservoir more efficiently. Introduction Improving reservoir performance and enhancing hydrocarbon recovery while reducing environmental impact are critical to the future of the petroleum industry. To do this, it must be possible to characterize reservoir parameters including fluid properties and their changes with time, i.e., dynamic reservoir characterization. The objectives of our research arerepeated acquisition of a three-dimensional (3D), three-component (3C) seismic survey;demonstrate the ability of 3D, 3C, and four-dimensional (4D), 3C seismology to detect and monitor rock/fluid property change associated with a production process;incorporate geological, petrophysical, petroleum engineering, and other geophysical studies;refine the reservoir model and recommend procedures for scaling up from a pilot injection program to partial field flood to achieve maximum sweep efficiency and minimize bypassed reservoir zones;link bulk rock/fluid property variation monitored by time-lapse multicomponent (4D, 3C) seismic surveying to dynamic attributes of the reservoir including permeability, fluids, and flow characterization. Three-dimensional, 3C seismology involves seismic data acquisition in three orientations at each receiver location—two orthogonal horizontal and one vertical. When three source components are used, nine times the amount of data of a conventional P-wave 3D survey can be recorded. Horizontal components of source and receiver displacements enable shear- (S-) wave recording; this is a powerful complement to vertical P-wave recording. Three-dimensional, 3C seismic surveys provide significantly more information about the rock/fluid properties of a reservoir than can be achieved from conventional P-wave seismic surveys alone. By combining P- and S-wave recording, the seismic ability to determine rock/fluid property changes in the subsurface is increased. Seismic wave propagation includes travel time, reflectivity, and the effects of anisotropy and attenuation. In-situ stress orientation and relative magnitudes can be derived from seismic anisotropy. Rock/fluid properties, including lithology and porosity, may be obtained from comparative travel times or velocities of P and S waves. Other rock/fluid properties, including permeability, may be determined from comparative P and S anisotropy, travel time, reflectivity, and attenuation measurements. By combining P- and S-wave recording, seismic wave propagation characteristics can be transformed into reservoir parameters. Introducing time as the "fourth dimension," new time-lapse (4D), 3C seismology is a tool to monitor production processes and to determine reservoir property variations under changing conditions. Using 4D, 3C seismic monitoring as an integral part of dynamic reservoir characterization, refinements can be made to production processes to improve reservoir hydrocarbon recovery. VP/VS ratios for both the fast S1 shear component and slow S2 shear component may provide a tool for separating bulk rock changes due to fluid property variations from bulk rock changes due to effective stress variations. Changes in shear wave anisotropy may reflect varying concentrations of open fractures and low aspect ratio pore structure in both a spatial and temporal sense across the reservoir. The permeability of a formation, or the connectivity of the pore space, will be the target in 4D, 3C seismology. Refinements made to reservoir characterization techniques and their applications, now extending into the fourth dimension, are an important new area of research. Benefits of this research will include improved reservoir characterization and correlative increased hydrocarbon recovery and reduction in operating costs through improved reservoir management. Geologic Setting Since early Permian time, the general evolution of the portion of the Permian Basin which includes vacuum field is that of a progressively shallowing-upward carbonate platform. Aggrading and prograding cycles represent, respectively, the results of high stand and still stand sea levels. At the shelf edge these platform carbonates typically grade into reef-type deposits such as the Abo, Goat Seep, and Capitan formations. The San Andres is an exception; no reef-like rocks have been detected. Beyond the shelf edge, in the Delaware basin, clastic rocks, especially siliciclastics, were deposited during a lowstand sea level. Vacuum field is located on a large anticlinal structure that plunges slightly to the east-northeast. The San Andres and Grayburg formations correspond to the rim of a broad carbonate shelf province to the north and northwest, northwest shelf, and of a deeper intracratonic basin, Delaware basin, on the southeast and east.1 The overall area including the Midland basin, northern and eastern shelves, and central basin platform are part of a major restricted intracratonic basin which existed during Permian time. West Texas and southeast New Mexico were in the low latitudes throughout the late Paleozoic period, making them an ideal location for carbonate sedimentation. As a consequence of this tropical environment, broad carbonate shelves were established on the margins of the Delaware and Midland basins.2


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