Normal Incidence Reflection Coefficient Research Articles

Normal incidence reflection coefficient approximation at an isotropic–poroelastic interface

AbstractSeismic response from porous sediments can be used in reservoir characterization and fluid detection. Reflection coefficient at the isotropic/poroelastic interface is essential to reveal seismic response from the fluid‐saturated deposits. The exact normal incidence reflection coefficient is given by complex mathematic expression and not very clear relations with solid and fluid properties. Therefore, we derive the reflection coefficient approximate formula in series with respect to the square root of the imaginary unit multiplying by the ratio between angular frequency and the characteristic angular frequency. Compared to the exact reflection coefficient, the proposed approximate formula has a more concise mathematical form and clearer relationship with the moduli and densities. Meanwhile, there is no need to calculate the complex wavenumbers of poroelastic media from the dispersion equation as the exact reflection coefficient. When the frequency tends to zero, the approximate formula is consistent with reflection coefficient for the isotropic/isotropic interface. The proposed formula's applicability is verified through two models with an interface separating the mudstone and fully fluid‐saturated sandstone with pore fluids as water or carbon dioxide.

Normal incidence reflection coefficient measurements of layered sand-mud sediment and comparison to models

Depth-dependent variability in seabed acoustic and geophysical properties can be introduced by both physical and biogenic processes. An experiment was conducted near the mouth of Mobile Bay, Alabama to investigate spatial variability over a mud-sand gradient, where sediment properties showed lateral changes on the scales of tens of meters. Additionally, sediment layering on the scale of centimeters was evident in the top 20 cm of the seabed. Normal-incidence seabed reflection coefficient measurements (20–60 kHz) were acquired using a ship-mounted system to survey a 1.9 km2 area of the seabed, and diver cores were collected for direct analysis of near-surface seabed properties. The cores were acoustically logged to obtain vertical profiles of sound speed and attenuation (10–1000 kHz) and then analyzed for vertical profiles of sediment physical properties (porosity, grain size, organic matter content), infauna community composition, and tensile strength. Physical and acoustic profiles obtained from the cores were then used as inputs to model the n-layer reflection coefficient. Comparison of the modeled and measured reflection coefficients will be discussed. [Work supported by ONR.]

Norwegian Sea area Permo-Triassic organic-carbon-rich deposits from seismic

Seismic surveys of the Permo-Triassic successions in Norwegian Sea sub-basins have been studied to determine the distribution of organic-carbon-rich intervals in the deeper basinal areas. Upper Permian to Lower Triassic organic-carbon-rich deposits had been described in cores from the margins of the basin, but their distribution in the deeper parts of the basin was unknown. The distribution of the organic-carbon-rich deposits in the deeper basin areas has been determined using a combination of amplitude versus angle/offset (AVA/AVO) analysis and an assessment of strata-bound deformation structures. AVA/AVO anomaly class IV, which has a negative normal incident reflection coefficient that decreases with angle/offset, has been used to predict the presence of organic-carbon-rich rocks in this work. The intercept (I) and gradient (G) plots (IG-crossplots) together with the Near-Far angle amplitude comparison of the seismic surveys have been used to complement the interpretation. The IG cross-plotting was done by selecting small windows (data probes) along the intervals speculated to be organic-carbon-rich. Any data probe which displayed AVO class IV elements on the IG crossplots and exhibited amplitude dimming with angle has been considered to indicate an organic-carbon-rich layer. The results of this work show the presence of both Upper Permian and Middle Triassic organic carbon rich sediments in the deeper parts of sub-basins within the Froan and Helgeland basins in the Norwegian Sea area. Two and one organic-rich intervals are indicated in the Froan and Helgeland basins respectively. The distribution of these organic-rich rocks was partly tectonically controlled, resulting in spatially limited deposits in the compartmentalized Froan Basin but more extensive deposits in the Helgeland Basin. None of the Lower Triassic sections examined in this study showed AVA/AVO characteristics indicative of organic-carbon-rich sediments on IG crossplots.

A comparison of two reflectivity parametrizations in acoustic least-squares reverse time migration

ABSTRACTIn comparison with conventional reverse time migration (RTM), least-squares RTM (LSRTM) can improve imaging resolution and compensate irregular illumination caused by acquisition geometry and complex structures. Since proposed, as an advanced version of RTM, it has been applied a lot to improve resolution and balance amplitude in imaging. Generally, in LSRTM, there are two kinds of LSRTM reflectivity models: velocity perturbation related reflectivity model and normal-incidence reflection coefficient related reflectivity model. Each has its specific physical meaning and provides different inverted results. In this paper, we first give a brief review about the two different definitions. Then, we compare the differences of these two methods and build a mathematical relationship. In the definition related to reflection coefficient model, we rescale the defined reflectivity with background velocity. Also, in source wavefield reconstruction, we use an effective trick by moving file pointer to fetch data from disk to reduce the memory cost. Finally, we test these two LSRTM schemes using the Marmousi model. We observe that the two inverted reflectivities are different, although they both image the subsurface discontinuities well. We furthermore extract traces from the inversion results and compare them with the true reflectivity models, respectively, to verify the physical definitions of them.

Reflection dispersion signatures due to wave-induced pressure diffusion in heterogeneous poroelastic media

ABSTRACTWe have studied the reflection dispersion signatures of a heterogeneously patchy saturated reservoir exhibiting attenuation and velocity dispersion in a seismic range of frequency. A modified patchy saturation model is employed to predict velocity dispersion and intrinsic attenuation behaviour associated with wave-induced pressure diffusion due to the presence of both mesoscopic and microscopic heterogeneities. Understanding the combined effects of microscopic squirt flow and wave-induced fluid flow related to mesoscopic heterogeneities on wave attenuation and associated dispersion would be important for determining the relative contribution of both of the interdependent energy loss mechanisms. The acoustic properties from the modified patchy saturation model were then employed in combination with an approximate expression for the frequency-dependent normal-incidence reflection coefficient of a dispersive reservoir rock, to give insights into the impacts of attenuation (and its associated velocity dispersion) and acoustic impedance contrast on the reflection dispersion characteristics. Analysis of the results indicates that the dispersion attribute of reflection coefficients and the associated cross-plot are more sensitive to fluid saturation and porosity than the magnitude of the reflection coefficient, and hence provide a promising approach to characterise fluid saturation and porosity in heterogeneous hydrocarbon reservoirs.

Effects of benthic biology on normal-incidence reflection coefficient measurements

Normal-incidence reflection coefficient measurements have been shown to be sensitive to sediment type based on the structure and amplitude of the returned signal. In contrast to other sediment classification methods such as coring, these measurements can be done quickly and easily over a large area. This type of sediment classification scheme can also be integrated into surveys by single- and multi-beam echo sounders. However, benthic biology can substantially change the normal-incident acoustic return possibly confounding the sediment classification methods while simultaneously providing a method of assessing benthic eco-systems. In this study, a collection of normal-incidence measurements taken in a variety of underwater environments will be analyzed for the effects of benthic biology. The areas surveyed include the Chesapeake Bay, the Arctic, the Western Mediterranean, and Gulf Coast. Each of the datasets will be considered for the presence of benthic biology and its affect on geo-acoustic properties. [Work supported by ONR, Ocean Acoustics.]

An approximate least squares reflectivity inversion in the presence of density

Traditional least-squares reverse time migration (LSRTM) often aims to improve the quality of seismic imaging, such as removing the acquisition footprint, suppressing migration artifacts and enhancing resolution. In this paper, we find that the conventional reflectivity defined in the LSRTM is related to the normal-incident reflection coefficient and the background velocity. Compared with the defined reflectivity, our inverted result is relatively “true”. With reflected data, LSRTM is mainly sensitive to impedance perturbations. According to an approximate relationship between them, we reformulate the perturbation related system into a reflection-coefficient related one. Then, we seek the inverted image through linearized iteration. Moreover, with the assumption that the density varies more gradually than the migration velocity, only the knowledge of the latter is required, although the reflected waves are produced at impedance discontinuities. We test our method using the 2D Marmousi synthetic dataset.

Improving imaging quality using least-squares reverse time migration: application to data from Bohai basin

Least-squares reverse time migration (LSRTM) is a seismic imaging technique based on linear inversion, which usually aims to improve the quality of seismic images through removing the acquisition footprint, suppressing migration artifacts, and enhancing resolution. LSRTM has been shown to produce migration images with better quality than those computed by conventional migration. In this paper, our derivation of LSRTM approximates the near-incident reflection coefficient with the normal-incident reflection coefficient, which shows that the reflectivity term defined is related to the normal-incident reflection coefficient and the background velocity. With reflected data, LSRTM is mainly sensitive to impedance perturbations. According to an approximate relationship between them, we reformulate the perturbation related system into a reflection-coefficient related one. Then, we seek the inverted image through linearized iteration. In the proposed algorithm, we only need the migration velocity for LSRTM considering that the density changes gently when compared with migration velocity. To validate our algorithms, we first apply it to a synthetic case and then a field data set. Both applications illustrate that our imaging results are of good quality.

Reflection coefficient measurement using a finite-difference-injection technique

Experimentally determining the acoustic reflection properties of materials requires accurate knowledge of the incident and reflected wave field at the reflecting interface. Consequently, a number of methods have been proposed for measuring the reflection coefficient, but most are limited to measuring only the normal incidence reflection coefficient or assume plane wave conditions. Here, we derive the reflection coefficient from pressure measurements by using a finite-difference wave field injection technique, which is applicable for a wide range of incidence angles and does not rely on the common plane wave assumption. It requires measurements at three planes parallel to the reflector and addresses two key objectives, namely, (1) the recorded wave field is separated into its incident and reflected components without the need of time-windowing, and (2) the separated components are re-datumed to the reflecting interface. The latter step comprises a forward propagation in time of the incident wave and a time-reversed backward propagation of the reflected wave. We experimentally test the methodology on laboratory data of the reflection from the free surface recorded in water and demonstrate its applicability to accurately measure the reflection coefficient for incidence angles up to 60°.

Measuring in‐situ reflection coefficients due to road pavements at 5.9 GHz

Planning emerging radio systems, as vehicle-to-vehicle or vehicle to infrastructure links, needs deep knowledge on the electromagnetic behaviour of the different materials involved. This Letter describes a system for measuring in-situ reflection coefficients. Besides, it gives data related to asphalt and concrete, in both wet and dry conditions, in a band from 5.8 to 6.0 GHz. Normal incidence reflection coefficients resulted to be similar in magnitude for both materials in dry conditions, and they experiment an increase of 65% after soaking the pavement. This indicates the strong influence of moisture on the electromagnetic behaviour of common road surfaces.

Quantification of signal and noise in two-way transmitted wavefields to improve well ties in Cooper Basin, Australia

Permian coal beds at 2400–2900 m depth in Cooper Basin, Australia have normal-incident reflection coefficient values as large as [Formula: see text]. If internal multiples are included in synthetic seismograms, excellent correlations exist between the synthetic seismogram and seismic, even when more than 50 coal beds are present. However, neither the synthetic seismogram nor the seismic tie the well-log lithologic boundaries because the incident wavefield that strikes a lithologic boundary and returns to the surface contains a signal wavelet followed by high-amplitude noise, which are interbed multiple reflections. Because the spectra of the signal and noise coda at a given two-way time normally do not overlap, time-varying Gaussian filters applied to the near-offset stack enhance the signal and suppress the noise coda. After filtering, the apparent time delay of reflections introduced by the coal beds is removed with variable time shifts (time compression), based on the estimated time-varying signal wavelets. The two-step process of low-pass filtering and compression yields seismic events that successfully tie the lithologic boundaries in the borehole, although with limited resolution. Our preliminary tests on a seismic line indicate that the horizon event associated with the base of a 500-m-thick coal sequence is more coherently imaged with our processing than with conventional processing.

Modeling and analysis of seismic wave dispersion based on the rock physics model

Seismic wave attenuation and dispersion are largely related to the fluid content in reservoirs, which has been verified by rock physics models, numerical modeling and some field case studies. The main mechanism of seismic wave dispersion is wave-induced fluid flow due to the heterogeneity at different scales, including ‘macroscopic’, ‘microscopic’ and ‘mesoscopic’. Recently, studies on dispersion have focused on mesoscopic rock. Previous studies have shown that there are many factors influencing seismic wave dispersion and attenuation, and amongst all the parameters, gas saturation is a very important one. Based on the White model, in this paper we firstly model the seismic wave dispersion and attenuation characteristics with varying gas saturation and porosity, and then analyze the velocity and normal-incidence (NI) reflection coefficient using three sandstone models. The results show that the frequency-dependent reflection coefficient (FDRC) is influenced by gas saturation, which corresponds to the frequency-dependent velocity characteristic. Finally, we derive approximate FDRC expressions using the NI reflection coefficient method, which can be used to estimate the dispersion characteristic. Analysis of the cross-plots of NI and dispersion indicates that dispersion and attenuation are more sensitive to gas saturation and porosity. Therefore, dispersion and NI cross-plots provide a potential way to predict the gas saturation. The modeling results of different consolidated sandstone reservoirs also indicate that there is a critical gas saturation point at which the dispersion magnitude reaches maximum value. Based on the critical point, the cross-plot can be divided into two parts and we can predict the gas saturation in either of them.

Petrophysical analysis of a mid-crustal reflector in the IBERSEIS profile, SW Spain

The origin of strong crustal reflectors in vertical incidence reflection seismic data is generally attributed to either rock layering, deformation fabrics in shear zones, fluids, or igneous intrusions. The IBERSEIS normal incidence reflection and wide-angle seismic profiles in SW Spain imaged a large, high velocity, subhorizontal reflector in the middle crust (the IBERSEIS Reflective Body) whose origin has been attributed to a mafic intrusion. In order to test this hypothesis, in this paper we present laboratory measurements of Vp, Vs, and density from 17 samples of mafic igneous and metamorphic rocks, and metasediments that are thought to be equivalent to the proposed IBERSEIS Reflective Body. These measurements are then corrected to 400°C at 600MPa and used to calculate Poisson's ratio and to compare it, Vp, and Vs to values measured in situ by wide-angle data. Finally, normal incidence reflection coefficients are calculated to test if the measured lithologies could reproduce the reflectivity imaged in the vertical incidence reflection seismic data for the IBERSEIS Reflective Body. Our physical property measurements are very similar to those modeled from the wide-angle data, and our reflection coefficients are sufficiently high to cause strong mid-crustal reflectivity. Our data indicate, therefore, that previous interpretations of the IBERSEIS Reflective Body as a mafic sill are quite reasonable.

Impact of fluid saturation on the reflection coefficient of a poroelastic layer

The impact of changes in saturation on the frequency-dependent reflection coefficient of a partially saturated layer was studied. Seismic attenuation and velocity dispersion in partially saturated (i.e., patchy saturated) poroelastic media were accounted for by using the analytical solution of the 1D White’s model for wave-induced fluid flow. White’s solution was applied in combination with an analytical solution for the normal-incidence reflection coefficient of an attenuating layer embedded in an elastic or attenuating background medium to investigate the effects of attenuation, velocity dispersion, and tuning on the reflection coefficient. Approximations for the frequency-dependent quality factor, its minimum value, and the frequency at which the minimum value of the quality factor occurs were derived. The approximations are valid for any two alternating sets of petrophysical parameters. An approximation for the normal-incidence reflection coefficient of an attenuating thin (compared to the wavelength) layer was also derived. This approximation gives insight into the influence of contrasts in acoustic impedance and/or attenuation on the reflectivity of a thin layer. Laboratory data for reflections from a water-saturated sand layer and from a dry sand layer were further fit with petrophysical parameters for unconsolidated sand partially saturated with water and air. The results showed that wave-induced fluid flow can explain low-frequency reflection anomalies, which are related to fluid saturation and can be observed in seismic field data. The results further indicate that reflection coefficients of partially saturated layers (e.g., hydrocarbon reservoirs) can vary significantly with frequency, especially at low seismic frequencies where partial saturation may often cause high attenuation.

Modelling sound propagation in the Southern Ocean to estimate the acoustic impact of seismic research surveys on marine mammals

Modelling sound propagation in the ocean is an essential tool to assess the potential risk of air-gun shots on marine mammals. Based on a 2.5-D finite-difference code a full waveform modelling approach is presented, which determines both sound exposure levels of single shots and cumulative sound exposure levels of multiple shots fired along a seismic line. Band-limited point source approximations of compact air-gun clusters deployed by R/V Polarstern in polar regions are used as sound sources. Marine mammals are simulated as static receivers. Applications to deep and shallow water models including constant and depth-dependent sound velocity profiles of the Southern Ocean show dipole-like directivities in case of single shots and tubular cumulative sound exposure level fields beneath the seismic line in case of multiple shots. Compared to a semi-infinite model an incorporation of seafloor reflections enhances the seismically induced noise levels close to the sea surface. Refraction due to sound velocity gradients and sound channelling in near-surface ducts are evident, but affect only low to moderate levels. Hence, exposure zone radii derived for different hearing thresholds are almost independent of the sound velocity structure. With decreasing thresholds radii increase according to a spherical 20 log10 r law in case of single shots and according to a cylindrical 10 log10 r law in case of multiple shots. A doubling of the shot interval diminishes the cumulative sound exposure levels by −3 dB and halves the radii. The ocean bottom properties only slightly affect the radii in shallow waters, if the normal incidence reflection coefficient exceeds 0.2.

Poroelastic analysis of amplitude-versus-frequency variations

Although significant advancement has occurred in the interpretation of seismic amplitude-variation-with-offset (AVO) anomalies, a theory is lacking to guide the interpretation of frequency-dependent seismic anomalies. Using analytic equations and numerical modeling, we have investigated characteristics of the normal-incident reflection coefficient (NI) as a function of frequency at an interface between a nondispersive medium and a patchy-saturated dispersive medium. Because of velocity dispersion, the variation of NI magnitude is divided into three general classes. These classes are (1) low-frequency dim-out reservoirs, in which NI magnitude decreases toward lower frequencies; (2) phase-shift reservoirs, in which NI is a small negative value at low frequencies but becomes positive at higher frequencies; and (3) low-frequency bright-spot reservoirs, in which NI magnitude increases toward lower frequencies. This classification could provide insight for frequency-dependent seismic interpre-tation.

Measurements of sound speed, attenuation, and normal-incidence reflection coefficient in water-saturated glass beads as a function of porosity.

Sound propagation in water‐saturated granular sediments is known to depend on the sediment porosity, but few data in the literature address both its frequency and porosity dependency. To address this deficiency, a method to control porosity [Argo et al. J. Acoust. Soc. Am. 124, 2469 (2008)] was used to prepare artificial sediments composed of water‐saturated glass spheres (130, 265, and 530 μm diameters) with porosities ranging from 0.37 to 0.43. Through‐transmission measurements were performed for frequencies from 250 to 800 kHz to determine the sound speed and attenuation. Pulse‐echo measurements for frequencies from 0.25 to 7.5 MHz were performed to determine the normal‐incidence reflection coefficient. For both classes of measurements, the Fourier phase technique was used to analyze the data. Measurement results will be presented and compared to existing models. A Biot‐based model was found to qualitatively describe the porosity dependence of the sound speed and attenuation, but a transition to a scattering‐dominated regime was observed. [Work supported by NSF, ONR, and the Welch Foundation.]

Subglacial seismic reflection strategies when source amplitude and medium attenuation are poorly known

AbstractSeismic reflection techniques are a powerful way to probe physical properties of subglacial strata. Inversion of seismic data for physical properties may be hampered, however, by lack of knowledge of the source amplitude as well as lack of knowledge of the compressional and shear attenuation in the ice. New methods are described to measure the source signature that require no a priori knowledge of the ice attenuation profile. Another new method is described to obtain the angular dependence of the subglacial bed reflection coefficient that is relatively insensitive to knowledge of the ice attenuation. Finally, a correction is provided to a long-standing error in the literature regarding measurement of the bed normal incidence reflection coefficient.

Thin oil-film thickness distribution measurement using ultrasonic arrays

This paper describes an approach for calculating the oil-film thickness distribution in machine elements using an ultrasonic array, based on the measurement of normal and oblique incidence reflection coefficients. An experimental system is described in which a high-precision digital piezoelectric translator (DPT) is used to controllably displace the surfaces in a steel–oil–steel system and hence alter the oil-film thickness by a known amount. This three-layer system was chosen to be representative of a typical lubricated contact found in various machine elements such as bearings, gears and seals. In such lubricated systems the oil-film thickness typically ranges from 0.1 to 100 μm and this paper explores the range 2–9 μm experimentally. In the measurements described, reflection coefficients were obtained from transmitter–receiver pairs of an ultrasonic array. In this way, each reflection coefficient measurement corresponds to a point on the oil-film and is related to a specific incidence angle. The oil-film thickness distributions were then extracted from these reflection coefficients via a multi-layer model. The measured oil-film thicknesses are shown to be in good quantitative agreement with the known displacements. This demonstrates the potential of this approach for the measurement of oil-film thickness distribution in lubricated contacts.

Laser Doppler vibrometer-based acoustical measurement of reflection coefficient up to 20 kHz

The well‐established two‐microphone technique for determining the acoustic reflection of a material in an impedance tube has physical limitations that hinder the measurement of this quantity at high frequencies. Tube geometry, microphone spacing, and perturbation of the sound field by measurement instruments make the determination of normal incidence reflection coefficients above 10 kHz difficult, if not impossible, using microphones and the traditional impedance tube methods. In a recent work, an extended impedance tube technique utilizing a scanning laser doppler vibrometer (SLDV) was presented [Vanlanduit et al., J. Acoust. Soc. Am. 3 (2005)]. In this study, a method using a single point laser Doppler vibrometer (LDV) is used to study the limitations and merits of acousto−optic sensing in impedance tubes. Foams of various thicknesses are measured using the transfer function method in a transparent impedance tube. Results are presented that convey the potential usage of these acousto−optic techniques in the measurement of acoustic reflection properties of materials up to 20 kHz and beyond.