Papers by Serge A. Shapiro
In recent geothermal projects that were associated with induced seismicity it has been observed t... more In recent geothermal projects that were associated with induced seismicity it has been observed that the largest earthquake or earthquakes occurred after shut-in, the moment when the pressurised fluid injection in the borehole is stopped. We use a probabilistic approach based on Omori's law and a Gutenberg-Richter magnitude distribution to demonstrate that the probability of exceeding a certain maximum magnitude after shut-in is as high or higher than before stopping the fluid injection. The amount of this increase is dependent on the exponent of Omori's law q. For the reference case of q=2 and a 10% probability at shut-in time we obtain an increase to 14.6% for. If we consider a constant probability level of occurrence for an event larger than a given magnitude at shut-in time, this maximum magnitude increases by 0.12 units for. For the Fenton Hill experiment recent studies reveal q=7.5 that corresponds to only a small amount of probability increase for the post-injection phase.
Fluid-Induced Seismicity
By “seismic events” we understand earthquakes of any size. There exists a broad scientific litera... more By “seismic events” we understand earthquakes of any size. There exists a broad scientific literature on earthquakes and on the processing of seismologic data. We refer readers interested in a detailed description of these subjects to corresponding books (see, for example, Lay and Wallace, 1995, and Shearer, 2009). We start this book with an introductory review of the theory of linear elasticity and of the mechanics of seismic events. The aim of this chapter is to describe classical fundamentals of the working frame necessary for our consideration of induced seismicity. We conclude this chapter with a short introduction to methodical aspects of the microseismic monitoring. Linear elasticity and seismic waves Deformations of a solid body are motions under which its shape and (or) its size change. Formally, deformations can be described by a field of a displacement vector u(r) . This vector is a function of a location r of any point of the body in an initial reference state (e.g., the so-called unstrained configuration; see, for example, Segall, 2010). Initially we accept here the so-called Lagrangian formulation, i.e. we observe motions of a given particle of the body. However, the field of displacements describes not only deformations of the body but also its possible rigid motions without changes of its shape and its size, such as translations and/or rotations. In contrast to rigid motions, under deformations, distances (some or any) between particles of the body change. Therefore, to describe deformations, a mathematical function of the displacement field is used that excludes rigid motions of a solid and describes changes of distances between its particles only. This function is the strain tensor ∈ , which is a second-rank tensor with nine components ∈ ij . Here the indices i and j can accept any of values 1, 2 and 3 denoting the coordinate directions of a Cartesian coordinate system in which the vectors u and r have been defined.
We propose an approach for estimating the permeability tensor using seismic emission induced by b... more We propose an approach for estimating the permeability tensor using seismic emission induced by borehole hydraulic tests or by a fluid injection of an arbitrary nature. This approach provides a single estimation of the permeability tensor for the complete heterogeneous rock volume, where the seismic emission was recorded. The approach is an extension of the method proposed by Shapiro et al, (1997) for isotropic case. It is based on the hypothesis, that the triggering front of the hydraulic-induced microseismicity propagates like the low-frequency second-type compressional Biot wave (corresponding to the process of the pore-pressure relaxation) in an effective homogeneous anisotropic poroelastic fluid-saturated medium. The permeability tensor of this effective medium is the permeability tensor of the heterogeneous rock volume upscaled to the characteristic size of the seismic-active region. We demonstrate the method using the microseismic data collected during the Hot-Dry-Rock Soultz...
Recent research has estimated that the tax-exempt status of all charities, including foundations,... more Recent research has estimated that the tax-exempt status of all charities, including foundations, costs local governments between $8 billion and $13 billion in revenues per-year. 5 Based on our analysis of the jobs and incomes generated directly and indirectly by the The Social and Economic Value of Private and Community Foundations
In this work we present the extension of the piezosensitivit y approach to anisotropic media. The... more In this work we present the extension of the piezosensitivit y approach to anisotropic media. The theoretical considerations show that the stress dependenc e of the seismic velocities and of all elastic parameters depends mainly on one parameter. This parameter is qual for all velocities and elastic parameters of a rock in all directions and independent from t he differential stress. We present first results from the application of the piezosen sitivity approach for anisotropic media to a set of ten metamorphic rock samples from the pilot hole of th e German Continental Deep Drilling Project. The laboratory data, three Pand six correspondin g S-wave velocity measurements per sample, cover a differential pressure range up to 600 MPa. All ve locities can be fitted well with our model. As derived from our theoretical considerations the paramet er D is constant for all observed velocities of a sample in any direction. Its magnitude ranges from appro x. 0.01 to 0.05 per MPa. A comparison...
We propose an approach for 3-D mapping the large-scale permeability tensor of heterogeneous reser... more We propose an approach for 3-D mapping the large-scale permeability tensor of heterogeneous reservoirs and aquifers. This approach uses the seismic emission (microseismicity) induced in rocks by fluid injections (e.g., borehole hydraulic tests). The approach is based on the hypothesis that the triggering front of the hydraulic-induced microseismicity propagates like the low-frequency (in respect to the global-flow critical frequency) second-type compressional Biot wave (corresponding to the process of the pore-pressure relaxation) in a heterogeneous anisotropic poroelastic fluid-saturated medium. Assuming that the wavelength of the second-type wave corresponding to the triggering front is shorter than the typical permeability heterogeneity we derive its differential equation. This equation describes kinematical aspects of the propagation of the triggering front in a way similar to the eikonal equation for seismic wavefronts. In the case of isotropic heterogeneous media the inversion...
Nature Communications, 2021
A damaging Mw5.5 earthquake occurred at Pohang, South Korea, in 2017, after stimulating an enhanc... more A damaging Mw5.5 earthquake occurred at Pohang, South Korea, in 2017, after stimulating an enhanced geothermal system by borehole fluid injections. The earthquake was likely triggered by these operations. Current approaches for predicting maximum induced earthquake magnitude ($${M}_{\max }$$ M max ) consider the volume of the injected fluid as the main controlling factor. However, these approaches are unsuccessful in predicting earthquakes, such as the Pohang one. Here we analyse the case histories of induced earthquakes, and find that $${M}_{\max }$$ M max scales with the logarithm of the elapsed time from the beginning of the fluid injection to the earthquake occurrence. This is also the case for the Pohang Earthquake. Its significant probability was predictable. These results validate an alternative to predicting $${M}_{\max }$$ M max . It is to monitor the exceedance probability of an assumed $${M}_{\max }$$ M max in real time by monitoring the seismogenic index, a quantity that...
Stress drop relates the rupture dimension to the seismic moment of earthquakes which makes it a c... more Stress drop relates the rupture dimension to the seismic moment of earthquakes which makes it a central parameter of earthquake source analysis, having both practical implications, for example, on high frequency-ground motion, and theoretical ones on the rupture processes of earthquakes in general. The complex nature of earthquake rupture and with it the behavior of stress drop still raise important questions which have not yet been answered conclusively. Stress drop has been observed to depend on different factors such as depth, stress conditions and tectonic setting (e.g.
64th EAGE Conference & Exhibition, 2002
Using quite general results of the theory of poroelasticity we attempt to analyze the influence o... more Using quite general results of the theory of poroelasticity we attempt to analyze the influence of the confining pressure and of the pore pressure on seismic velocities in rocks. In the first approximation the seismic velocities as well as the porosity depend on the differential stress, i.e., the difference between the confining pressure and the pore pressure only. The stress dependence of the porosity controls the elastic moduli and velocity changes with stress. Here, the most important role plays the compliant porosity which can be just a very small part of the total porosity. The stress dependence of the compliant porosity can be derived from the theory of poroelasticity under several, quite natural assumptions. This result provides the seismic velocities as functions of the differential stress. Corresponding equations coincide with experimentally observed exponentially saturating seismic velocities for increasing differential stresses.
63rd EAGE Conference & Exhibition, 2001
This paper is concerned with a numerical study of effective velocities in two types of fractured ... more This paper is concerned with a numerical study of effective velocities in two types of fractured media. We apply the so-called rotated staggered finite difference grid technique. Using this modified grid it is possible to simulate the propagation of elastic waves in a 2D or 3D medium containing cracks, pores or free surfaces without hardcoded boundary conditions. Therefore it allows an efficient and precise numerical study of effective velocities in fractured structures. We model the propagation of plane waves through a set of different randomly cracked media. In these numerical experiments we vary the crack density. The synthetic results are compared with several theories that predict the effective P-and S-wave velocities in fractured materials. For randomly distributed and randomly oriented rectilinear intersecting thin dry cracks the numerical simulations of velocities of P-, SV-and SH-waves are in excellent agreement with the results of a new critical crack density (CCD) formulation. On the other hand for randomly distributed rectilinear parallel thin dry cracks three different classical theories are compared with our numerical results.
• We derive a relation between the stress drop and the seismogenic index of induced seismicity • ... more • We derive a relation between the stress drop and the seismogenic index of induced seismicity • We derive a simple and rather general phenomenological model of stress drop in various faulting regimes • Rupture-related drop of fault cohesion may control high stress drop of some events induced by long-term reservoir developments
GEOPHYSICS, 2015
We have developed a new approach for reflection seismic imaging using microseismic waveform data.... more We have developed a new approach for reflection seismic imaging using microseismic waveform data. We took the specific character of microseismic downhole data into account and were able to image regions in the direct vicinity or inside of a seismically active zone. We used a directional migration method that reduced imaging artifacts caused by the low aperture of the data, but required estimation of the wavefield polarization. We also used hodogram analysis to identify parts of data that provided reliable polarization estimates. Only these parts were then used for imaging, whereas the rest of the data are excluded. The approach was successfully applied to microseismic waveforms recorded during and after the stimulation of the enhanced geothermal system in Basel, Switzerland. This data set included more than 2000 events recorded at five sparsely distributed borehole sensors. The reflection images revealed a distinct network of reflectors in the vicinity of the open hole section withi...
SEG Technical Program Expanded Abstracts 2006, 2006
ABSTRACT Fluid induced seismicity is often governed by linear pore pressure diffusion. Relating t... more ABSTRACT Fluid induced seismicity is often governed by linear pore pressure diffusion. Relating the perturbed pore pressure to induced seismicity, reservoir properties can be characterized. Analytical solutions of the diffusion equation are well known for the condition of constant injection source strength. But in some injection experiments, such as in Basel, Switzerland, the source strength is not constant over time. Here we present a solution of the diffusion equation which considers the special problem of linearly rising source strength. Using the solution, we accordingly modify already established methods for a seismicity based reservoir characterization (SBRC). These methods are based on a statistical approach and consider features of induced seismicity such as the spatial event density and the seismicity rate. We apply those methods to the Basel microseismic data which result in consistent estimates of hydraulic properties of the stimulated reservoir. We obtain a scalar permeability of 75 microDarcy by as
SEG Technical Program Expanded Abstracts 2001, 2001
ABSTRACT
70th EAGE Conference and Exhibition incorporating SPE EUROPEC 2008, 2008
An analysis of two rock samples, hyaloclastites and basalts, at in-situ reservoir conditions has ... more An analysis of two rock samples, hyaloclastites and basalts, at in-situ reservoir conditions has been done to identify the role of temperature on the seismic velocity and attenuation. The goal is to present the result of using Gassmann equation within the framework of Biot’s poroelasticity for a fluid substitution analysis of geothermal rocks. The analysis of temperature-dependent wave attenuation is shown for hyaloclastites. The results show that P wave velocities decrease with the temperature rise in a systematic way. The general decreasing trend of seismic velocity towards temperature may be related to the fluid characteristics with the temperature. Using Gassmann equation it has been shown that the presence of steam bubbles can reduce the effective elastic property of rocks. The Q factor behaves surprisingly almost in the same way as the seismic velocity with temperature, except in the lower temperature range. The Q factor increase with the temperature is supposed to be a quick viscosity decrease. The later decrease of Q factor may indicate the presence of steam bubbles due to the further temperature increase. This finding demonstrates that the application of Gassmann fluid substitution modelling may be used for the characterization of geothermal reservoir systems.
70th EAGE Conference and Exhibition incorporating SPE EUROPEC 2008, 2008
Due to decline in conventional oil and gas reservoirs, heavy oil has recently become an important... more Due to decline in conventional oil and gas reservoirs, heavy oil has recently become an important resource. In consequence of this demand, it is necessary to have a rock physical model considering the viscoelastic behavior of heavy oils. Such effective properties are modeled on microscale using numerical simulations. Heavy oil rock sample is represented by the realistic digital 3D model. To obtain the effective velocities of such a digital sample, we use the viscoelastic rotated staggered grid FD algorithm. Numerical experiments are performed for transmission and reflection. Synthetic data obtained from numerical simulations are compared with recently developed model of generalized Gassmann equations for porous media with a viscoleastic solid material filling the pore space. The results show a very good agreement and confirm the applicability of the new rock physics model proposed for the modeling of heavy oil rocks.
SEG Technical Program Expanded Abstracts 2012, 2012
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Papers by Serge A. Shapiro