Ran Bachrach

High-resolution shallow-seismic experiments in sand, Part I: Water table, fluid flow, and saturation

A high‐resolution, very shallow seismic reflection and refraction experiment was conducted to investigate the seismic response of groundwater level changes in beach sand in situ. A fixed 10-m-long receiver array was used for repeated seismic profiling. Direct measurements of water level in a monitoring well and moisture content in the sand were taken as well. The water table in the well changed by about 1 m in slightly delayed response to the nearby ocean tides. In contrast, inversion of the seismic data yielded a totally different picture. The reflection from the water table at high tide appeared at a later time than the reflection at low tide. This unexpected discrepancy can be reconciled using Gassmann’s equation: a low‐velocity layer must exist between the near‐surface dry sand and the deeper and much faster fully saturated sand. This low‐velocity layer coincides with the newly saturated zone and is caused by a combination of the sand’s high density (close to that of fully saturated sand), and its hig...

Seismic velocities and Poisson's ratio of shallow unconsolidated sands

We determined P- and S-wave velocity depth profiles in shallow, unconsolidated beach sand by analyzing three-component surface seismic data. P- and S-wave velocity profiles were calculated from traveltime measurements of vertical and tangential component seismograms, respectively. The results reveal two discrepancies between theory and data. Whereas both velocities were found to be proportional to the pressure raised to the power of 1/6, as predicted by the Hertz-Mindlin contact theory, the actual values of the velocities are less than half of those calculated from this theory. We attribute this discrepancy to the angularity of the sand grains. Assuming that the average radii of curvature at the grain contacts are smaller than the average radii of the grains, we modify the Hertz-Mindlin theory accordingly. We found that the ratio of the contact radius to the grain radius is about 0.086. The second disparity is between the observed Poisson’s ratio of 0.15 and the theoretical value (0.008 for random pack of quartz spheres). This discrepancy can be reconciled by assuming slip at the grain contacts. Because slip decreases the shearing between grains, Poisson’s ratio increases.

Joint estimation of porosity and saturation using stochastic rock-physics modeling

Sediment porosity and saturation affect bulk modulus, shearmodulus,anddensity.Consequently,estimatinghydrocarbon saturation and reservoir porosity from seismic data is a joint estimation problem: Uncertainty in porosity will lead toerrorsinsaturationprediction,andviceversa.Porosityand saturation can be jointly estimated using stochastic rockphysicsmodelingandformalBayesianestimationmethodology. Knowledge of shear impedance reduces the uncertainty inporosityandthusalsoreducesuncertaintyinsaturationestimation. This study investigates joint estimation of porosity and saturation by using rock-physics, stochastic modeling, and Bayesian estimation theory to derive saturation and porosity maps of expected pay sands. In the field example, the uncertainty in porosity, quantified by the standard deviation STDassociatedwiththeposteriorprobabilitydensityfunctionpdf,derivedfrominversionofseismicdataismuchless than the uncertainty in the derived saturation. For a typical case, the STD associated with saturation is 24% while porositySTDisabout1.34porosityunitsgivenseismic-derived inversionattributeswithreasonableaccuracy.Comparisonof these numbers with prior estimates showed that inversion of seismic data decreased the uncertainty in porosity to 15% of the prior uncertainty while saturation uncertainty was only reduced to 92% of the prior uncertainty. Although these resultsmayvaryfromonelocationtoanother,themethodology isgeneralandcanbeappliedtootherlocations.

High‐resolution shallow‐seismic experiments in sand, Part II: Velocities in shallow unconsolidated sand

We conducted a shallow high‐resolution seismic reflection and refraction experiment on a sandy beach. The depth of investigation was about 2 m. We interpret the data using the Hertz‐Mindlin contact theory combined with Gassmann’s equation. These were used to obtain the vertical velocity profile. Then the profile was computed from seismic data using the turning‐rays approximation. The normal moveout (NMO) velocity at the depth of 2 m matches the velocity profile. As a result, we developed a method to invert measured velocity from first arrivals, i.e., velocity versus distance into velocity versus depth using only one adjustable parameter. This parameter contains all the information about the internal structure and elasticity of the sand. The lowest velocity observed was about 40 m/s. It is noteworthy that the theoretical lower bound for velocity in dry sand with air is as low as 13 m/s. We find that modeling sand as a quartz sphere pack does not quantitatively agree with the measured data. However, the the...

Rock physics modeling of unconsolidated sands: Accounting for nonuniform contacts and heterogeneous stress fields in the effective media approximation with applications to hydrocarbon exploration

By treating contact stiffness as a variable, one can extend the effective medium approximation used to obtain elastic stiffness of a random pack of spherical grains. More specifically, we suggest calibrating effective media approximation based on contact mechanics by incorporating nonuniform contact models. The simple extension of the theory provides a better fit for many laboratory and field experiments and can provide insight into the micromechanical bonds associated with unconsolidated sediments. This approach is motivated by repeated observations of shear-wave measurements in unconsolidated sands where observed shear-wave velocities are lower than predicted by the Hertz-Mindlin contact theory. We present the calibration process for well-log data from a North Sea well penetrating a shallow-gas discovery and a deepwater well in the Gulf of Mexico. Finally, we demonstrate the benefit of using this model for amplitude variation with angle (AVA) analysis of shallow sand targets in exploration and reservoir studies.

Uncertainty in seismic-based pay volume estimation Analysis using rock physics and Bayesian statistics

Pay volume (PV) is a measure of the amount of hydrocarbon volume or pay in the overall reservoir and is used to appraise reservoir quality and the economics associated with reservoir development. As seismic-based reservoir characterization technology is advancing, lithology and porosity information derived from seismic inversion is often used to derive an estimate of PV. In general, PV estimation from seismic data is based on some sort of rock physics transformation and seismic inversion algorithm, and both may be nonunique. As PV estimates are often used for economic decision making, it is important to associate expected risk or confidence associated with the prediction. This article presents a workflow to compute quantitative estimates of PV, along with associated uncertainties, from well-log calibrated prestack seismic inversion attributes. The main tools used in this workflow are seismic (AVO) inversion, rock physics, and Bayesian statistics. The PV is estimated from the seismically derived rock prope...

Combining rock physics analysis, full waveform prestack inversion and high-resolution seismic interpretation to map lithology units in deep water: A Gulf of Mexico case study

A successful seismic-based reservoir properties estimation effort has three steps: accurate seismic inversion in 3D to obtain relevant reservoir parameters, rock physics transformation to relate reservoir parameters to the seismic parameters, and mapping these parameters in 3D. This problem is nonunique and thus any available information—specifically geologic interpretation—should be used to improve our ability to infer the reservoir properties of interest with confidence. Moreover, uncertainty associated with the different predicted values (i.e., confidence interval and estimate of misclassification probability) must be provided as well, so that proper decisions can be made. Thus, it is evident that this involves interdisciplinary effort that includes rock physics, geologic interpretation, and seismic inversion technology. However, for quantitative description of reservoir properties, one must derive a way to quantify the errors and uncertainties associated with the process.

Fast 3D ultra shallow seismic reflection imaging using portable geophone mount

We present the results of three different seismic experiments designed to develop and evaluate the use of 3D Ultra Shallow Seismic Reflection for high-resolution near-surface imaging. A feasibility study and the first implementation of a 2D portable geophone mount for fast and cost-effective ultra-shallow 3D seismic data acquisition are discussed. The portable geophone mount is made out of an anelastic base with a frame and an array of 72 geophones spaced with an interval of 0.25m both in the inline and crossline direction. The array enables acquisition of very high-resolution 3D data cubes with bin size of 12.5 × 12.5cm and wavelets of 350Hz. The time for re-planting the 72-channels portable geophone mount is about 5min in the field. Thus, we show that high-resolution near-surface 3D images can be obtained fast and in a cost-effective manner. This has the potential of providing effective solutions for many geotechnical and geoenvironmental applications.

Liquefaction and dynamic poroelasticity in soft sediments

In this paper we present a model that can explain earthquake-induced dynamic liquefaction in unconsolidated sediments without the need for irreversible compaction. We study the behavior of a poroelastic layer subjected to a periodic cyclic stress using dynamic poroelasticity formulation. We show that in such a layer pore pressure may increase due to a resonant mode of Biots type II wave, an attenuated mode whose wavelength is short and can resonate inside a layer of few meters thickness. We show that in sediments such as sand, where the shear modulus is less than 0.3 GPa, pore pressure can exceed the total stress. This will cause unconsolidated material to liquefy. We also show that as the elastic coefficient of the sediment decreases, the pore pressure induced by Biots type II wave increases. Thus, in a material where the elastic moduli are pressure dependent (e.g., Hertzian material) the increased pore pressure reduces the stiffness and thus liquefaction is more likely to occur.

Model‐uncertainty quantification in seismic tomography: method and applications

Uncertainty is inherent in every stage of the oil and gas exploration and production (E&P) business and understanding uncertainty enables mitigation of E&P risks. Therefore, quantification of uncertainty is beneficial for decision making and uncertainty should be managed along with other aspects of business. For example, decisions on well positioning should take into account the structural uncertainty related to the non-uniqueness of a velocity model used to create a seismic depth image. Moreover, recent advances in seismic acquisition technology, such as full-azimuth, long-offset techniques, combined with high-accuracy migration algorithms such as reverse-time migration, can greatly enhance images even in highly complex structural settings, provided that an Earth velocity model with sufficient resolution is available. Modern practices often use non-seismic observation to better constrain velocity model building. However, even with additional information, there is still ambiguity in our velocity models caused by the inherent non-uniqueness of the seismic experiment. Many different Earth velocity models exist that match the observed seismic (and well) data and this ambiguity grows rapidly away from well controls. The result is uncertainty in the seismic velocity model and the true positions of events in our images. Tracking these uncertainties can lead to significant improvement in the quantification of exploration risk (e.g., trap failure when well-logging data are not representative), drilling risk (e.g., dry wells and abnormal pore pressure) and volumetric uncertainties. Whilst the underlying ambiguity can never be fully eradicated, a quantified measure of these uncertainties provides a valuable tool for understanding and evaluating the risks and for development of better risk-mitigation plans and decision-making strategies