Michael Fehler

Source mechanism of volcanic tremor: fluid-driven crack models and their application to the 1963 kilauea eruption

Abstract We propose a model for the mechanism of magma transport based on a fluid-filled tensile crack driven by the excess pressure of fluid. Such a transport mechanism can generate seismic waves by a succession of jerky crack extensions, if the fracture strength of rock varies in space, or if there is a difference between the dynamic and static values of the critical stress intensity factor. We also find that the opening and closing of a narrow channel connecting two fluid-filled cracks may be a source of seismic waves. Using the finite-difference method, we calculated the vibration of dry and fluid-filled cracks generated by: (1) a jerky extension at one end or at both ends and (2) a jerky opening of a narrow channel connecting two cracks. We then calculated the far-field and near-field radiation from these vibrating cracks. The spectra show peaked structures, but interestingly, most high-frequency peaks are only present in the near-field and cannot be transmitted to the far-field. The spectral features described above are often observed for volcanic tremors and in some cases for seismic signals associated with hydraulic fracturing experiments. We first consider as a model of volcanic tremor randomly occurring jerky crack extensions, and derive a formula relating the tremor amplitude to the excess pressure in the magma, the incremental area in each extension, and the frequency of extensions. These parameters are also constrained by other observations, such as the rate of magma flow. Our model was tested quantitatively against observations made in one of the best-described case histories of volcanic tremor: the October 5–6, 1963 Kilauea flank eruption. We found that a single, long crack extending from the summit to the eruptive site cannot explain the observations. The model of a steadily expanding crack ran into difficulties when quantitative comparisons were made with observations. The extension of crack area needed to explain the amplitude of volcanic tremor should accompany a large increase in tremor period which was not observed. Our second model is a chain of cracks connected by narrow channels which open and close. The length of each crack is around 1 km, the channel area connecting neighboring cracks is about 103m2, and the channel opens jerkily with the magmatic excess pressure of about 20 bars. The frequency of jerky opening of each channel is about once in 15 seconds. The channel is closed after each jerky opening, as soon as magma is moved through the channel.

Petroleum reservoir characterization using downhole microseismic monitoring

Imaging of microseismic data is the process by which we use information about the source locations, timing, and mechanisms of the induced seismic events to make inferences about the structure of a petroleum reservoir or the changes that accompany injections into or production from the reservoir. A few key projects were instrumental in the development of downhole microseismic imaging. Most recent microseismic projects involve imaging hydraulic-fracture stimulations, which has grown into a widespread fracture diagnostic technology. This growth in the application of the technology is attributed to the success of imaging the fracture complexity of the Barnett Shale in the Fort Worth basin, Texas, and the commercial value of the information obtained to improvecompletions and ultimately production in the field. The use of commercial imaging in the Barnett is traced back to earlier investigations to prove the technology with the Cotton Valley imaging project and earlier experiments at the M-Site in the Piceance ...

Seismic Wave Propagation and Scattering in the Heterogeneous Earth : Second Edition

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Envelope Broadening of Outgoing Waves in 2D Random Media: A Comparison between the Markov Approximation and Numerical Simulations

Observations of seismic waves from earthquakes at depths between 100 and 200 km beneath Japan show that the initial portion of the S-wave arrival has greater duration than can be accounted for by earthquake source-time duration. The observed long duration of S waves has been explained as being caused by multiple forward scattering around the ray path between source and receiver. Array obser- vations of Lg waveforms have also shown that multiple forward scattering along the path between the source and receiver are important influences on the character of Lg waveforms and that the scattering cannot be explained only by vertical variations in velocity. Multiple forward scattering in 3D has been modeled using the Markov approximation for the parabolic-wave equation, which allows the calculation of seis- mogram envelopes in statistically characterized random media. To test the range of validity of the Markov approximation-derived solutions, we made 2D numerical calculations of wavefields in random media using approximations to the parabolic wave equation, which only models forward scattering, and by finite-difference so- lution of the scalar-wave equation, which gives complete wavefields. Media of back- ground velocity 4 km/sec are characterized using a Gaussian autocorrelation function with a5k mcorrelation distance and 5% rms fractional fluctuation. To compare with envelopes obtained from the Markov approximation, we calculated wavefields for source-receiver distances ranging from 50 to 200 km for several statistically identical realizations of random media. We obtain ensemble average envelopes by averaging envelopes from the realizations. We find a good agreement between ensemble- average envelopes obtained from the numerical solution of the parabolic-wave equa- tion and envelopes obtained from the Markov approximation. The later portion of the ensemble-average envelopes calculated using finite difference have larger am- plitudes than those from the Markov approximation, which is probably due to the late-arriving energy that has been scattered at wide angles from the global propa- gation direction between the source and the receiver. We observe that the variations among the numerically calculated envelopes of individual realizations of random media are well fit by a Rayleigh distribution, which describes the distribution of envelope amplitude when signals of one frequency but random phase are summed. Our results show that the Markov approximation provides reliable information about envelope shapes for forward-scattered wavefields but that the influence of wide-angle scattering and backscattering have some influences on envelope shapes and should be considered when analyzing data using random media models.

Development of the active doublet method for measuring small velocity and attenuation changes in solids

The measurement of small changes in elastic wave velocity and attenuation is important to a broad range of problems, such as earthquake prediction and early detection of rock failure in mines. Previous authors proposed a method for estimating small temporal velocity changes in the earth’s crust by analyzing progressive relative phase delays between the scattered waves of two signals generated by nearly identical earthquake sources, called doublets, recorded at different times at the same receivers. Several improvements have been made to the original method and are presented here. The reliability of measured velocity changes has been increased by using active, repeatable sources instead of natural earthquakes. The robustness of the analysis technique has been improved by eliminating unnecessary intermediate phase regression steps and thus reducing the sensitivity to spurious data. Finally, the phase‐delay algorithm has been extended to allow measurement of small attenuation changes from relative amplitude ...

Simulating the Envelope of Scalar Waves in 2D Random Media Having Power-Law Spectra of Velocity Fluctuation

During propagation through random media, impulsive waves radiated from a point source decrease in amplitude and increase in duration with increasing travel distance. The excitation of coda waves is prominent at long lapse time. We use a finite-difference method to numerically simulate scalar waves that propagate through random media characterized by a von Karman autocorrelation function. The power spectral density function of fractional velocity fluctuation for κ -th order von Karman-type random media obeys a power law at large wavenumbers. Such media are considered to be appropriate models for the random component of the structure of the Earths lithosphere. The average of the square of numerically calculated wave traces over an ensemble of random media gives the reference envelope for the evaluation of envelope simulation methods. The Markov approximation method gives reliable quantitative predictions of the entire envelope for random media that are poor in short wavelength components of heterogeneity ( κ = 1.0), while it fails to predict the coda envelope for random media that have rich short-wavelength components ( κ = 0.1). The radiative-transfer theory reliably predicts the coda excitation for κ = 0.1 when the momentum-transfer scattering coefficient is used as the effective isotropic scattering coefficient. Replacing the direct term of the radiative-transfer solution with the envelope of the Markov approximation, we propose a new method for simulating the entire envelope from the direct arrival through the coda. The method quantitatively explains the whole envelope for κ = 0.1. For the case of κ = 0.5, however, our method predicts too much coda excitation. In such a case, the method can explain whole envelopes by using the effective scattering coefficient estimated from coda excitation. Manuscript received 10 April 2002.

Cross-hole seismic surveys; applications for studying subsurface fracture systems at a hot dry rock geothermal site

The use of cross hole seismic surveys for delineating the location and size of subsurface fracture systems is investigated. The radiation pattern for P and S waves emitted by a seismic source in a borehole is derived. Experimental work in relatively homogeneous granite suggests that the derived relationship adequately describes the radiation patten for both explosive sources and acoustic transducers placed in fluid-filled boreholes. Using the above functional expressions for the S- and P-wave amplitudes, we have developed a technique to estimate Q and locate discrete fractures in crystalline rock that compose the Hot Dry Rock Geothermal Reservoir at Fenton Hill, New Mexico. To calculate Q, we measure the P- and S-wave amplitudes as a function of distance and geometrical spreading effects, and match the relative attenuation to a function of the form exp (-1R/QV) using a least-squares regression technique. For undisturbed parts of the reservoir, we obtain values of Q on the order of 160 for P waves and from 170 to 150 for S waves. Using our method we are able to detect a decrease in the average Q due to extensive fracturing following heat extraction from the Fenton Hill reservoir. We have also been able to locate discrete large-scale fractures in the reservoir by noting regions characterized by a sudden change in signal amplitude, waveform or frequency content that cannot be explained by radiation pattern effects or increases in source-receiver separation. These localized attenuating regions in the Fenton Hill Hot Dry Rock reservoir are probably open fractures. (Author)

More Than Cloud: New techniques for characterizing reservoir structure using induced seismicity

Interest in using microearthquakes for characterizing petroleum and geothermal reservoirs and the region surrounding underground mines has grown considerably over the last several years. A comprehensive understanding of the fracture distribution and hydrogeomechanical processes occurring during operation provides valuable information for reservoir development and optimization of production. Some of this information can be obtained from well logs, but they only provide direct information about conditions near the well. Microseismic (MS) monitoring techniques can be primary methods for obtaining detailed information about reservoirs and fracture systems at locations as far as 1 km from boreholes.

SEG Advanced Modeling (SEAM): Phase I first year update

The SEAM Consortium and SEG subsidiary SEAM Corporation exist to provide the geophysical exploration community with geophysical model data for subsurface geological models at a level of complexity and size that cannot be practicably computed by any single company or small number of companies. (A general introduction to the SEAM initiative and Phase I Project can be found in TLEs June and August 2007 issues.) SEAMs Phase I Consortium, which recently commemorated its first full year of activity, now consists of 24 companies from the hydrocarbon and geophysical exploration industries. Quarterly meetings of the SEAM Management Committee, made up of representatives of all the participating companies and led by Chairman Kevin Bishop (of BHP Billiton), provide technical direction for this multifaceted project, while the functional body leading the technical development of the project consists of six committees (listed below). While these technical committees meet as needed, the co-chairs of the six committees ...

13 – Scattering and Attenuation of Seismic Waves in the Lithosphere

The scattering and attenuation of high-frequency seismic waves are considered important characteristics to be quantified to physically characterize the Earth medium. This chapter presents the measurements of attenuation of seismic waves and discusses physical mechanisms of attenuation in the lithosphere, including intrinsic absorption and scattering loss because of distributed heterogeneities. As a model of attenuation, it introduces an approach for calculating the amount of scattering loss in a manner consistent with conventional seismological attenuation measurements. Use of stochastic seismology has led to significant advances in understanding of the character of seismic waveforms and has enabled to model portions of the waveforms that cannot be explained deterministically. The fundamental observations leading to advances in using stochastic seismology to model scattered waves involves existence of coda, envelope shape of local earthquakes, attenuation, and array phase. Some of the methods used to explain these observations include coda normalization method, energy-flux model, and Born approximation.