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We investigated the method of estimating seismic moment and moment magnitude for microseismic events. We determined that the [Formula: see text] defined by Bowers and Hudson is the proper scalar moment to be used in microseismic studies for characterizing the size of an event and calculating its moment magnitude. For non-double-couple sources, the proportional relationship between body-wave amplitude and seismic moment in the Brune model breaks down. So under such situations, the Brune model is not an appropriate way to estimate the seismic moment and magnitude. Moreover, the S-wave alone is not sufficient for determining the total seismic moment. Instead, the P-wave must be analyzed. An example Barnett Shale data set was studied, and the results concluded that the magnitudes estimated with the Brune model could be off by as much as 1.92, with an absolute average of 0.35. The moment magnitudes based on the scalar moment [Formula: see text] also gave a significantly different event size distribution and b-value estimation. Finally, attenuation also played a role in estimating the moment magnitude. With a typical average attenuation factor of [Formula: see text], the average magnitude correction for our field data set was on the order of 0.15. However, it could reach 0.3 for events far away from the monitoring well.

We evaluated a method of deriving seismic fracture parameters from vertical-well-log data with the assumption that the fractured medium is transversely isotropic with a horizontal axis of symmetry (HTI). One approximation we used is that the observed vertical P-wave velocity is the same as the background isotropic P-wave velocity of the HTI medium. Another assumption was that the fractures and cracks are noninteractive and penny shaped. Using these approximations, we generated the fracture compliance matrix for each layer. Fracture parameters were then derived by constructing the HTI stiffness matrix for those layers. We tested our method using vertical-well-log data from a tight sand reservoir in Colorado, USA. “Thomsen-style” parameters were derived, and gas-filled fractures were identified on this log. The identified gas-filled fractures were compared to the production log data. The fracture density was also obtained at the well location within the depth of interest. We also found some problems and limitations caused by approximating vertical P-wave velocity the same as the background isotropic P-wave velocity.

Many regions of subsurface interest are, or will be, fractured. Seismically characterizing these zones is a complicated but essential task for resource development. Physical modeling, using ultrasonic sources and receivers over scaled exploration targets, can play a useful role as an analog for reservoir imaging and assessment. We explored the anisotropic response of glass blocks containing internal fractures created by a novel laser-etching technique. We compared transmitted and reflected signals for P- and S-waves from fractured and unfractured zones in a suite of ultrasonic (1–5 MHz) experiments. The unaltered glass velocities have averages of [Formula: see text] and [Formula: see text] for P- and S-waves, respectively (giving [Formula: see text]). The unfractured glass has a very high quality (Q) factor of over 500 for P-waves and S-waves. The fractured zones have a small (up to 1.5%) velocity decrease. Signals propagating through the fractured zone have diminished amplitudes and increased coda signatures. Reflection surveys (zero-offset and with variable polarizations) record significant scatter from the fractured zones. The fracture-scattered energy can be migrated to provide a sharper image. The glass specimens with laser-etched fractures display a rich anisotropic response, which can help inform field-scale imaging.

Based on a large quantity of laboratory ultrasonic measurement data of sedimentary rocks and using Monte Carlo simulation and Backus averaging, we have analyzed the layering effects on seismic anisotropy more realistically than in previous studies. The layering effects are studied for different types of rocks under different saturation conditions. If the sedimentary strata consist of only isotropic sedimentary layers and are brine-saturated, the [Formula: see text] value for the effective transversely isotropic (TI) medium is usually negative. The [Formula: see text] value will increase noticeably and can be mostly positive if the sedimentary strata are gas bearing. Based on simulation results, [Formula: see text] can be determined by other TI elastic constants for a layered medium consisting of isotropic layers. Therefore, [Formula: see text] can be predicted from the other Thomsen parameters with confidence. The theoretical expression of [Formula: see text] for an effective TI medium consisting of isotropic sedimentary rocks can be simplified with excellent accuracy into a neat form. The anisotropic properties of the interbedding system of shales and isotropic sedimentary rocks are primarily influenced by the intrinsic anisotropy of shales. There are moderate to strong correlations among the Thomson anisotropy parameters.

To improve quantitative interpretation of seismic data, we analyze the effect of fluid substitution in a porous and fractured medium on elastic properties and reflection coefficients. This analysis uses closed-form expressions suitable for fluid substitution in transversely isotropic media with a horizontal symmetry axis (HTI). For the HTI medium, the effect of changing porosity and water saturation on (1) P-wave moduli, (2) horizontal and vertical velocities, (3) anisotropic parameters, and (4) reflection coefficients are examined. The effects of fracture density on these four parameters are also studied. For the model used in this study, a 35% increase in porosity lowers the value of P-wave moduli by maximum of 45%. Consistent with the reduction in P-wave moduli, P-wave velocities also decrease by maximum of 17% with a similar increment in porosity. The reduction is always larger for the horizontal P-wave modulus than for the vertical one and is nearly independent of fracture density. The magnitude of the anisotropic parameters of the fractured medium also changes with increased porosity depending on the changes in the value of P-wave moduli. The reflection coefficients at an interface of the fractured medium with an isotropic medium change in accordance with the above observations and lead to an increase in anisotropic amplitude variation with offset (AVO) gradient with porosity. Additionally, we observe a maximum increase in P-wave modulus and velocity by 30% and 8%, respectively, with a 100% increase in water saturation. Water saturation also changes the anisotropic parameters and reflection coefficients. Increase in water saturation considerably increases the magnitude of the anisotropic AVO gradient irrespective of fracture density. From this study, we conclude that porosity and water saturation have a significant impact on the four studied parameters and the impacts are seismically detectable.

Availability of a fracture map of a producing reservoir aids in increasing productivity. Generally, accurate information related to fracture orientation is only available at a few sparse well log locations. However, fractures introduce velocityanomaliesinseismicdatabymakingthemediumazimuthallyanisotropic.Whenmulti-azimuthdataisavailablethen itispossibletomapthefractureattributesintheentirereservoirzonebyanalysingtheanisotropyinducedvelocityanomalies in the seismic data. In the absence of 3D data, seismic anisotropy induced velocity anomaly from 2D data (as fracture strikes are not constant and data contains multi-azimuthal effect even when it is 2D) can still be used as a secondary source of information for the purpose of fracture strike simulation. To validate the above hypothesis, fracture strike information in a reservoir from the Mexican part of the Gulf of Mexico is derived using Markov-Bayes stochastic simulation. In this simulation process, accurate well log derived fracture information is used as hard or primary data and seismic velocity anomaly/uncertainty based fracture information is used as soft or secondary data. The Markov-Bayes Stochastic simulation provides multiple realisations of the fracture patterns and thus helps to estimate the uncertainty associated with the fracture strikes of the reservoir. Accuracy of the simulation process is also estimated and the simulation result is compared with simple and ordinary kriging methods of fracture strike simulation.

Seismic critical-angle reflectometry is a relatively new field for estimating seismic anisotropy parameters. The theory relates changes in the critical angle with azimuth of the seismic line to the principal axis and anisotropy parameters. Current implementation of the critical-angle reflectometry process has certain shortcomings in that the critical angle is determined from critical offset and the process is vulnerable to different approximation errors. Seismic critical-angle analysis in the plane-wave [Formula: see text] domain can handle these issues and has the potential to become an independent tool for estimating anisotropy parameters. The theory of seismic critical-angle reflectometry is modified to make it suitable for [Formula: see text] domain analysis. Then using full-wave synthetic seismograms at three different azimuths for a transversely isotropic medium with a horizontal axis of symmetry (HTI), the effectiveness of anisotropy parameter estimation is demonstrated.

SUMMARY For the purpose of transversely isotropic (TI) normal moveout (NMO) correction, we propose analysis of plane wave transformed azimuthal gathers, interactively using a single azimuth data at a time and a new delay time equation (developed in this paper), which is a function of two parameters at each azimuth. Results from independently estimated multi-azimuth gathers, then, can be combined to estimate stiffness or Thomsen coefficients. Azimuthal τ–p analysis also avoids numerical ray tracing, resulting in a rapid algorithm. We demonstrate the applicability of our method using a set of P-wave synthetic seismograms from a multilayered medium, consisting of isotropic and HTI layers. Azimuth-dependent anisotropy parameters are derived by delay time fitting and NMO correction. The reflections from the bottom interface of an isotropic layer with an anisotropic overburden show apparent anisotropic traveltime behaviour, which is easily accounted for by our layer-stripping based azimuthal NMO analysis. Unlike the previous approximate HTI NMO correction equation, this equation performs better NMO correction for the HTI medium and is also applicable to the VTI medium. Presence of only two reduced parameters in the equation helps the anisotropic parameter estimation become less ambiguous.

The Mw 9.3 great Sumatra-Andaman earthquake of December 26, 2004 induced water level changes in Fairbanks, Alaska, at an epicentral distance of 10,800 km. Spike like water level changes followed by a step of water level rise were observed in at least four wells. We modeled the timing and magnitude of the water level rise using a combination of a linear trend and a step function. We calculated the misfit between the observed water level rises and our model by systematically shifting the timing of occurrence of step in water level. The minimum value of cumulative misfit suggested the timing of occurrence of steps. A previous study showed persistent water level rises in all these wells from the 2002 Denali fault earthquake and it’s major aftershocks. From those observations, we developed an empirical relationship between water level changes, epicentral distances and earthquake magnitude. This relationship attributed water level changes in the wells to ground shaking by seismic waves. The estimated average water level changes due to the Sumatra earthquake using that relationship was in agreement with the observed water level changes. Thus we concluded that ground shaking in Fairbanks, induced by surface waves from the Sumatra earthquake was sufficient to change water levels.

We derive equations for HTI and orthorhombic symmetries to analyze fluid substitution effects in porous fractured media. The derivations are based on the anisotropic Gassmann equation and linear slip theory. We assess the influence of fluid substitution (gas, brine, and oil) on elastic moduli, velocities, anisotropy, and azimuthal amplitude variations. We find that in the direction normal to fractures, P-wave moduli increase as much as 56% and P-wave velocity increases up to 19% for gas-to-brine substitution. For the direction parallel to fractures, P-wave velocity remains almost constant when porosity is low (5%) but can increase up to 4% if porosity is high (25%). Since P-waves in two different directions have different sensitivities to fluids and fractures, the Thomsen's parameters (defined for HTI and orthorhombic symmetries), ϵ and δ, are sensitive to fluid types and fractures. We also found that δ is sensitive to porosity for liquid saturation but insensitive to porosity for the case of gas saturation. Gassmann assumes (and as has been observed) that shear modulus does not depend on fluids. And we observe no changes in shear-wave splitting (γ) for different fluids. The azimuthal amplitude variation is dependent on fluid types, fractures, and porosity. We observe up to 12% increase in azimuthal amplitude variation for low porosity gas sands after brine saturation and 6% decrease for high porosity gas sands. We find that the percentage changes in gas-to-oil substitution are about half that of the gas-to-brine case. The equations we have derived provide a useful tool to quantitatively evaluate the effects of fluid substitution on seismic anisotropy.

We describe a method of determining enhanced permeability from hydraulic fracturing. This method depends on the analysis of the transient pressure after shutin and integrating it with microseismic derived fracture geometry. We present an example of permeability prediction using a laboratory data set from the University of Oklahoma. In this laboratory experiment, a tight sandstone sample is hydraulically fractured. Acoustic emission data during hydraulic fracturing is recorded and sources relocated. Permeability of the sample is measured before and after the fracturing. Predicted permeability using the described method matches reasonably well with the laboratory measured permeability of the post fractured sample.

The general equations for fluid dependency of the elastic moduli of anisotropic media were first given by Gassmann (1951). For the case of an HTI medium, Gurevich (2003) derived the explicit equations based on a linear-slip model. Gurevich’s complex equations are recast here in a more accessible format. Those equations depend on four parameters: λ , μ , δN and δT . They are quite similar to the well-known isotropic Gassmann’s equations. We also propose a valid method for the application of these equations.

Summary Velocity variation with azimuth (VVAZ) has become a standard technique to extract fracture signatures from wide azimuth seismic data (WAZ). Zheng (2006) proposed a target-oriented VVAZ approach to directly invert Thomsen’s HTI delta and fracture strike of an HTI medium, but it requires traveltimes between the top and base of a target horizon. If the target layer becomes thin, the top reflected event interferes with the base event. Little research has been done to fully address the thickness limit. Evaluations of this technique on a number of synthetic HTI models with various scenarios of HTI-layer thickness conclude that this inversion is robust in estimating HTIanisotropic attributes, even for a relatively thin fracture layer. This paper focuses on its application on a highdensity WAZ data set. The HTI anisotropic-magnitude map from the target-oriented VVAZ is more comparable with the map derived from the analysis of amplitude variation with azimuth (AVAZ) than conventional VVAZ. In addition, the HTI anisotropic-orientation map from the target-oriented VVAZ correlates remarkably well with fracture orientations measured from formation microimaging (FMI) logs in areas with high anisotropy, and generally follows the regional-fracture trend.

In 2010, ConocoPhillips acquired microseismic data targeting the Barnett shale from Stocker field in Texas, USA. Two horizontal wells were fractured in eighteen stages. More than 7,000 microseismic events were located using two down-hole receiver arrays. The b values were calculated using the magnitude distribution of the events in each stage by maximum likelihood methods. This work analyzed the temporal and spatial variations of b values in every simulation stage. We showed (1) that the spatial variation of the b value may help to delineate reservoir heterogeneity and (2) that the temporal variation of the b value in each stage may be related to the mechanism of fracture growth.

Summary Near-surface anisotropy can distort P-wave traveltime and amplitude analysis from deep target layers. When the target layer is azimuthally anisotropic, the traveltime/velocity variation with azimuth (VVAZ) or amplitude variation with azimuth (AVAZ) from the target layer may show anomalous behavior due to the influence of the near-surface anisotropy. This study uses two synthetic cases to analyze the effect of near-surface anisotropy on a deep anisotropic target. Our results suggest that the traveltime data (or VVAZ signals) from the target layers can be distorted significantly due to the presence of near-surface anisotropy; but the near-surface anisotropy influence may be negligible on the AVAZ signals from the deep target layer.

Summary The prestack analysis of amplitude variation with offset/angle (AVO/AVA) has been a useful hydrocarbon exploration tool for a number of years. As this technology matured, forward modeling became an important tool to understand the seismic response, to ensure acquisition parameters were adequate for its detection, and to calibrate and validate the data processing sequence and analysis tools. There has been significant recent interest in using azimuthal variations in seismic amplitudes to detect high productivity sweet spots related to in situ natural fractures. The role of forward modeling has not been as significant in azimuthal AVO as in conventional AVO. We describe a robust azimuthal processing analysis workflow based on a series of 1D and 3D elastic modeling exercises designed to validate the azimuthal processing flow and extracted azimuthal attributes. Our results indicate that forward modeling is necessary to understand the offset range that might exhibit an azimuthal amplitude variation and the magnitude of the variation, and its detectability in the presence of noise.

Many regions of subsurface interest are, or will be, fractured. Seismically characterizing these zones is a complicated but essential task for resource development. Physical modeling, using ultrasonic sources and receivers over scaled exploration targets, can play a useful role as an analog for reservoir imaging and assessment. We explored the anisotropic response of glass blocks containing internal fractures created by a novel laser-etching technique. We compared transmitted and reflected signals for P- and S-waves from fractured and unfractured zones in a suite of ultrasonic (1–5 MHz) experiments. The unaltered glass velocities have averages of 5804 and 3447 m/s for P- and S-waves, respectively (giving VP/VS=1.68). The unfractured glass has a very high quality (Q) factor of over 500 for P-waves and S-waves. The fractured zones have a small (up to 1.5%) velocity decrease. Signals propagating through the fractured zone have diminished amplitudes and increased coda signatures. Reflection surveys (...

In 2005, a multicomponent ocean bottom node data set was collected by BP and BHP Billiton in the Atlantis field in the Gulf ofMexico. Our results are based on data from a few sparse nodes with millions of shots that were analysed as common receiver azimuthal gathers. A first-order look at P-wave arrivals on a common receiver gather at a constant offset reveals variation of P-wave arrival time as a function of azimuth indicating the presence of azimuthal anisotropy at the top few layers. This prompted us to investigate shear arrivals on the horizontal component data. After preliminary processing, including a static correction, the data were optimally rotated to radial (R) and transverse (T) components. The R component shows azimuthal variation of traveltime indicating variation of velocity with azimuth; the corresponding T component shows azimuthal variation of amplitude and phase (polarity reversal). The observed shear-wave (S-wave) splitting, previously observed azimuthal P-wave velocity variation and azimuthal P-wave amplitude variation, all indicate the occurrence of anisotropy in the shallow (just below the seafloor) subsea sediment in the area. From the radial component azimuthal gather, we analysed the PP- and PS-wave amplitude variation for the first few layers and determined corresponding anisotropy parameter and VP/VS values. Since fracture at this depth is not likely to occur, we attribute the observed azimuthal anisotropy to the presence of microcracks and grain boundary orientation due to stress. The evidence of anisotropy is ubiquitous in this data set and thus it argues strongly in favour of considering anisotropy in depth imaging for obtaining realistic subsurface images, at the least.

We study the effect of fluid substitution in a porous fractured medium using explicit expressions developed for aligned fractured medium. We investigate the effect of porosity and water saturation on (1) P-wave moduli, (2) horizontal and vertical velocities, (3) anisotropic parameters, and (4) reflection coefficients. Effects of fracture density on these four parameters are also analyzed. The systematic variations of the moduli and reflection coefficients reported in this paper can thus be used in developing AVO with azimuth in a porous fractured reservoir.

Reservoir models are built using disparate datasets each of which may be prone to experimental and interpretational errors and therefore a resulting reservoir model is generally associated with uncertainties. One of the primary sources of uncertainties lies in the structure (or reservoir architecture) estimation from seismic data. Geostatistics can be used to integrate seismic data with well data for the purpose of structural uncertainty estimation. In this paper we present a case study from the Gulf of Mexico, where structural uncertainty associated with a seismic horizon is modeled using Markov-Bayes stochastic simulation. For this simulation, seismic data is used as “soft” or secondary data while well log derived marker depths are used as hard data. Simulation results show uncertainty distributions with smaller variance in the vicinity of the wells. However, in regions away from the wells, the interpreter-picked horizon appears to fall outside the error bounds predicted by our stochastic algorithm. Lack of well control, existence of faults, improper choice of seismic processing parameters (error in time migrated images) and interpreters’ bias are some of the plausible causes of this disparity.

Incorporating the effect of anisotropy during seismic processing and estimating anisotropic parameters is an active area of research. In general five elastic coefficients are needed to describe a traveltime curve in a HTI medium. The problem of estimating five elastic parameters by iterative fitting of travel time data from a single azimuth recording is highly non-unique. This can possibly be achieved by simultaneous fitting of multiple azimuth travel time data. However that would require picking travel time and accurate estimation will require numerical ray tracing for multi-layered media. To circumvent these difficulties we propose analysis of plane wave transformed azimuthal gathers interactively using a single azimuth data at a time and a new delay time equation which is a function of two parameters at each azimuth. Results from independently estimated multi-azimuth gathers can be combined to estimate stiffness or Thomsen coefficients. Azimuthal τ-p analysis also avoids numerical ray tracing resulting in a rapid algorithm. We demonstrate the applicability of our method using a set of P wave synthetic seismograms from a multi-layered medium consisting of isotropic and HTI layers. Azimuth dependent anisotropy parameters are derived by delay time fitting and NMO correction. The reflections from the bottom interface of an isotropic layer with an anisotropic overburden show apparent anisotropic travel time behavior which is easily accounted for by our layer-stripping based azimuthal NMO analysis.

Two-way traveltime (TWT) is one of the most important seismic attributes for reservoir characterization. Erroneous analysis of TWT can lead to incorrect estimates of velocity models resulting in improper structural interpretation of the subsurface. TWT analysis starts with the most fundamental step of seismic data processing, namely, normal moveout (NMO) correction. NMO correction is generally performed in the offset-time (X-t) domain, by fitting a hyperbolic curve to the observed traveltimes corresponding to each reflection event. The commonly used NMO equation is valid for small offsets and does not consider anisotropy — an effect commonly observed in fractured media. The performance of NMO correction depends on the quality of data in the prestack domain and the underlying geology. In the plane wave (τ-p) domain, the estimation of layer parameters can be done using an exact equation for delay-time free from the approximation errors present in the X-t domain. In this domain, a layer stripping approach can also be used to account for the presence of multiple anisotropic and isotropic layers.