Compressional Wave Attenuation Research Articles

Seismic wave attenuation (1/Qp) in the crust underneath the Eastern and eastern Southern Alps (Europe): imaging effects of faults, fractures, and fluids

We present a novel three-dimensional model of compressional wave attenuation (1/QP) for the Eastern and eastern Southern Alps in Europe that includes the eastern part of the Adriatic indenter, termed here the Dolomites Sub-Indenter. Our approach employed waveform data from the SWATH-D network, a dense temporary network operational between 2017 and 2019, as well as selected stations of the larger AlpArray Seismic Network. A spectral inversion method using frequency-independent quality factor QP, was applied to derive 3578 path-averaged attenuation values (t*) from 126 local earthquakes. These were then inverted using the damped least square inversion (local earthquake tomography) for the attenuation structure. The resulting QP model, which builds on and complements a previously calculated 3-D velocity model (VP and VP/VS), exhibits good resolution down to ~ 20 km depth. Several anomalies can be correlated with the distribution of other physical parameters (VP and VP/VS) and regional tectonic features. Notably, the Friuli-Venetian region exhibits the highest attenuation (lowest QP) anomaly, coinciding with low VP values and increased VP/VS. This anomaly is likely associated with a high density of faults and fractures, as well as the presence of fluid-filled sediments along the active thrust front in the eastern segment of the Southern Alps. Another intriguing observation is the low attenuation (high QP) anomaly along the northwestern edge of the Dolomites Sub-Indenter (NWDI), located south of the Periadriatic fault and east of the Giudicarie fault, where seismicity is notably absent. This anomaly coincides with Permian magmatic rocks at the surface and may be a measure of their strength at depth.Graphical

Effects of Pore Geometry and Saturation on the Behavior of Multiscale Waves in Tight Sandstone Layers

AbstractGeometric heterogeneities in tight reservoir rocks saturated with a fluid mixture may exhibit different scale distribution characteristics. Conventional models of rock physics based on poroelasticity, which usually consider single‐scale pore structure and fluid patches, are inadequate for describing elastic wave responses. A major challenge is to establish the relationship between the wave response at different spatial scales and frequencies. To address this problem, three sets of observational data over a wide frequency range were obtained from a tight oil reservoir in the Ordos Basin, China. Ultrasonic measurements were made on eight sandstone samples at partial oil‐water saturation at 0.55 MHz. Data from six borehole measurements and seismic profiles were acquired and analyzed at about 10 kHz and 30 Hz, respectively. Analysis of the cast thin sections shows that dissolution pores and microcracks generally develop, with fractal dimensions of the pores ranging from 2.45 to 2.67 for the samples with porosities between 5.1% and 10.2%. Compressional wave velocity and attenuation were estimated from the observed data. The results show that the velocity dispersion from seismic to ultrasonic frequencies is 10.02%, mostly occurring between sonic and ultrasonic frequencies. The attenuation is stronger at higher oil saturation. The relationships between velocity, attenuation, and wavelength were established and can be used for further forward modeling and seismic interpretation studies. A partial saturation model has been derived based on effective differential medium theory and a double double‐porosity model, assuming that the medium contains fractal cracks and fluid patches. The effects of scale and saturation on wave responses are prevalent. Modeling results consistent with observed data show that the radii of cracks and fluid patches range from 0.1 μm to 2.8 mm, affecting ultrasonic, acoustic, and seismic attenuation. The multiscale data and proposed model quantify the relationship between fracture and fluid distributions and attenuation and could be useful for upscaling to the reservoir scale. The study helps improve the understanding of seismic wave propagation in partially saturated rocks, which has potential applications in seismic exploration, hydrocarbon production in reservoirs, and CO2 sequestration in aquifers.

Geoacoustic inversion of wide-angle reflection-coefficient data to estimate sediment shear properties

This paper considers Bayesian geoacoustic inversion of broadband, wide-angle reflection-coefficient data including shear parameters in the seabed model to investigate the ability to estimate these parameters as well as effects on the estimation of other geoacoustic parameters, particularly compressional-wave attenuation. The seabed parameterization is based on the viscous grain-shearing (VGS) sediment-acoustic model, including the grain-to-grain shear modulus as an unknown parameter. VGS sediment parameters are transformed to density and frequency-dependent compressional- and shear-wave speeds and attenuations. Data prediction involves spherical-wave reflection-coefficient calculations. Trans-dimensional inversion, which samples probabilistically over the number of layers in the seabed model, is applied to combine quantitative model selection with parameter/uncertainty estimation. The inversion is applied to reflection-coefficient data sets collected on the New England Mud Patch, and inversion results are compared to those obtained under the common assumption of negligible shear effects (i.e., inverting for a fluid sediment model).

Estimation of sediment compressional and shear properties in the New England Mud Patch using acoustic pressure and particle velocity data

New England Mud Patch was the site of the Seabed Characterization Experiment in multiple years (2017, 2021, and 2022). This site is characterized by a layer of very fine grained surficial sediment layer over sand. Analysis of broadband data measured on the ocean bottom recorders (OBXs) and hydrophones will be discussed. OBX is a geophone–hydrophone system which measures three components (two orthogonal horizontal components and a vertical component) in addition to acoustic pressure. Five OBXs were deployed on the seabed and four hydrophones were configured as a tetrahedral array on the bottom mounted Geosled. Data from these sensors will be analyzed and different arrivals corresponding to compressional, shear and interface wave (Scholte and love waves) presence will be examined. Inversion schemes will be implemented to estimate the compressional and shear wave speeds and attenuation. A priori information from seismic surveys and sediment cores will be incorporated into the inversion schemes. Outputs of these inversions will be compared with inversion results from other investigators based on different inversion techniques and using data from the same location. [Work Supported by Office of Naval Research.]

Manifestations of the weak shear rigidity of marine sediments in amplitudes and travel times of acoustic normal modes and lateral waves

Compressional-to-shear wave conversion at interfaces within unconsolidated marine sediments and interference of shear waves within thin sediment layers have been found to make significant contributions to sound attenuation [O. A. Godin, J. Acoust. Soc. Am. 149, 3586–3598 (2021)] and produce unexpectedly strong perturbations in the normal mode group speed even when the shear speed is small compared to the compressional wave speed. This paper extends the previous analysis to the lateral waves and their applications to characterize the compressional wave speed and attenuation in the seabed. Shear wave-induced contributions to horizontal refraction of normal modes over horizontally inhomogeneous seabed are modeled to characterize the bearing and travel time errors that arise in the fluid-bottom approximation. The acoustic travel time and amplitude effects of the shear waves are found to accumulate at different rates with the propagation range depending on the stability of the shear wave interference within the seabed. The ways to distinguish between the manifestations in acoustic observables of the weak shear rigidity in the seabed and the other environmental uncertainties are discussed for range-independent, range-dependent, and horizontally inhomogeneous shallow-water waveguides. [Work supported by ONR.]

In situ measurements of sediment shear wave speed from the New England Mud Patch and shelf break areas using the acoustic coring system

The acoustic coring system (ACS) is a probe-equipped gravity corer that provides in situ measurements of compressional and shear wave speed and attenuation. During an April 2022 coring survey, the ACS was deployed at 36 locations within the New England Mud Patch and New England Shelf Break areas. Data from these measurements will be presented to characterize the depth-dependent structure of the geoacoustic seabed properties as well as their spatial variability. The in situ measurements will be interpreted in the context of stratigraphic layering measured by a seismic survey. Historically, in situ shear speed measurements of the seabed have proved difficult to obtain. From the 2022 survey, depth-dependent (up to 4 meters) shear speed profiles at 800 and 1200 Hz were produced from a subset of the 36 deployments. These results, along with methods for analysis, challenges in the measurements, and supplemental laboratory experiments will be discussed. The results will also be compared to measurements from previous experiments. [Work sponsored by ONR.]

Shear and Scholte wave measurements on surficial intertidal mudflat sediments using medical sonoelastography techniques

In low-energy environments, the water–sediment interface often contains a dynamic fluffy transition layer (FTL) of suspended organic and inorganic matter, which is transformed by complex physical, biological, and chemical processes. The FTL mechanical properties are important for understanding carbon cycle dynamics and for robust sediment acoustic characterization, but erodibility and size make it difficult to study non-invasively and at sufficient resolution. In medical ultrasound sonoelastography, shear waves are excited within the body either using the acoustic radiation force (ARF) or via external vibration at the skin surface. Sub-micrometer displacements are measured remotely by subsequent ultrasound imaging at up to 10 kHz frame rate with approximately 0.5 μm spatial resolution. In this study, sediment cores were extracted from the intertidal mudflats from the Great Bay Estuary, USA. Compressional wave speed and attenuation measurements were performed using a core logger. Shear and Scholte waves were excited in the FTL using ARF- and external-vibration-based techniques and the motion detected with clinical ultrasound imaging arrays. Upward refraction of the shear wave was observed, and shear and Scholte wave speed and attenuation were measured. Finally, scanning electron microscopy was used to image the microstructure. Comparison between wave properties and microstructure will be discussed.

In situ acoustic coring systems for investigating the acoustic and physical properties of mud

In situ measurements of compressional and shear wave speed and attenuation provide direct characterization of marine sediment acoustic properties at near ambient conditions, as opposed to measurements that are conducted on samples removed from the seabed. Probe-based acoustic measurement techniques utilize piezoelectric sources and receivers that penetrate the seabed to obtain spatially localized depth-dependent records of compressional and shear waves in the sediment. When such measurements are coupled with conventional coring techniques, sediment samples can be collected from the propagation path between probes, allowing for comparison between the in situ acoustic records and quantities obtained from ex situ core analyses, such as porosity, grain size, or organic matter. Two acoustic coring measurement systems have been developed to investigate the acoustic, physical, and biological properties of soft sediment—the acoustic coring system, a gravity-corer-based platform capable of penetrating the seabed up to several meters, and the acoustic multi-corer, a seabed lander that samples the upper tens of centimeters of sediment near the water-seabed interface. The design and operation of these measurement platforms will be described, along with their capabilities and limitations. Some representative results from field deployments of these systems will be presented. [Work sponsored by ONR.]

Wave equations for porous media described by the Biot model

Single-mode equivalent space-time representations of the acoustic wave propagating in a Biot poroelastic medium have previously been found only for asymptotic cases: In the low frequency regime, where the viscous skin depth is greater than the characteristic pore size, the time domain equivalent is represented with integer order temporal and spatial loss terms, whereas in the high frequency regime, it is represented with fractional order temporal and spatial loss terms. In the current work, a time domain representation in terms of a partial differential equation is proposed for all three wave solutions of the Biot model across all frequencies, and it is derived from the material response function of the Biot poroelastic medium with suitable approximations for the compressional modes and the dynamic permeability. The dynamic permeability in the time domain is represented by a fractional pseudo-differential operator. Optimal correction factors are introduced into the wave equation to compensate for the discrepancies in the compressional wave dispersion and attenuation. Additionally, the method for incorporating the squirt flow mechanism into the wave equation via the Extended Biot poroviscoelastic model is described. The proposed wave equation has a physical basis and satisfies the passivity criterion.

Inversion for Parameters of Mud as a Porous Medium

In this article, the seven input parameters of a porous medium model for mud are defined and inverted for the New England Mud Patch. One distinguishing feature is that the skeletal frame may contain adsorbed water, and the pore water may contain suspended solid material. This means that the effective properties of the skeletal frame and pore water are different from that of the pure solid and pure seawater, and the effective porosity is not the same as the bulk water fraction. The model contains two loss mechanisms: creep and viscous loss due to relative motion between skeletal frame and pore water. It is demonstrated that the input parameters could be inverted from the wave speeds, attenuations, and reflection. The inversion from reflection loss exclusively is more difficult due to the relative insensitivity to shear properties. A partial solution is obtained by using a regression relationship to constrain the shear speed. A connection between the assumed shear speed and the inverted compressional wave attenuation is consistent with a recent finding by Godin. Regarding reflection loss from a half-space, for frequencies less than about 10 kHz, a homogeneous medium model is indistinguishable from a porous medium model, and for shear speeds less than 50 m/s, a fluid model would be adequate. The porous medium model does not suffer from these restrictions.

Compressional wave propagation in saturated porous media and its numerical analysis using a space-time conservation element and solution element method.

Compressional waves in saturated porous media are relevant to many fields from oil exploration to diagnostic of human cancellous bone and can be used to interpret physical behaviors of materials. In this work, based on Biot's theory in the low frequency range, a key finding is that there exists a critical frequency of Biot's theory in the low frequency range, which determines the coincidence of the properties of Biot waves of the first and second kinds. Furthermore, we have investigated the dispersion and attenuation of the coalescence of the first and second compressional waves in the low frequency range. The coalescence of the first and second waves is strongly attenuated with a moderate phase velocity and shows the in-phase feature. In addition, acoustic wave propagation has been calculated numerically using the space-time conservation element and solution element (CESE) method. The CESE-simulated results are compared to the experimental data and to those of the classical transfer function approach. We show that the CESEscheme preserves the local and global flux conservations in the solution procedure of Biot's theory. It is found that the CESEmethod provides more accurate predictions of high dispersion and strong attenuation of compressional waves in the low frequency range and is well suitable for predicting compressional wave fields in saturated porous media.

Biogeoacoustic sediment properties along a horizontal sand-mud gradient

Whether deposited from the water column or generated by benthic infauna, interstitial organic matter is a ubiquitous constituent of marine sediment and is particularly prevalent in sediments with significant silt/clay fractions. Interstitial organic matter suspends silt and clay particles in the sediment matrix, adsorbs onto mineral surfaces, and resides between mineral contacts, all of which are hypothesized to alter geoacoustic properties. However, the extent to which interstitial organics alter geoacoustic properties is understudied and warrants further investigation. To address this, diver cores were collected along a horizontal sand-mud gradient in Mobile Bay, Alabama. The sediment was subsequently processed in the laboratory, where compressional wave speed (10 kHz to 1 MHz), compressional wave attenuation (100 kHz to 1 MHz), density, porosity, grain-size distribution, and organic carbon and nitrogen content were measured. In addition, physics-based geoacoustic models, such as VGS(λ) and mCREB, were fit to the wide range of sediment types. Measured geoacoustic properties and fit parameters inherent to each sediment acoustics model are compared with organic sediment properties. The extent to which organics control sediment geoacoustic properties and considerations to include organics in future modeling efforts will be discussed. [Work sponsored by ONR.]

Estimation of seabed attenuation in the New England Mud Patch

Measurements of acoustic pressure and particle velocity were made during the Seabed Characterization Experiment (SBCEX-2017) in the New England Mud Patch south of Cape Cod in about 70 m of water. This experimental location is characterized by a “soft” layer of surficial sediment consisting of mud. University of Rhode Island and Woods Hole Oceanographic Institution deployed the “geosled” with a four-element geophone array, a tetrahedral array of four hydrophones, and several hydrophone receive units (SHRUs) as data acquisition packages. In addition, a new low frequency source, interface Wave Sediment Profiler (iWaSP) was deployed to excite interface waves (Scholte waves). The geophone array was localized using the known locations of the acoustic sources and noise from the research vessel. Modal arrivals from broadband sources on geophones and hydrophones were used to invert for compressional and shear wave speeds and attenuation in the mud layer and the underlying sand layer. Effect of shear conversion effects on the modal attenuation estimates and it’s frequency dependence will be explored. The role of shear conversion along the mud-sand interface will be discussed. [Work supported by the Office of Naval research, code 322 OA.]

Compressional and shear wave attenuations from walkway VSP and sonic data in an offshore Abu Dhabi oilfield

Seismic attenuation was estimated from compressional (P) and shear (S) waves carefully extracted from three-component vertical seismic profiling (VSP) data. A high sensitivity of attenuation to fluid content was noticed, which shows the advantage of its use as a seismic attribute for reservoir studies. Contrary to most observations in fully saturated sandstones, the magnitude of P to S wave attenuation in the studied carbonate reservoir zones is higher than one. This disagreement is most probably because the fluid flow models developed to describe the attenuation mechanisms in sandstones are not valid for carbonate rocks due their complex texture. Moreover, the magnitude of seismic attenuation in the reservoir zones is controlled by the saturation of pore fluids and clay content. Furthermore, the attenuation magnitudes obtained at sonic and VSP frequencies are of the same order, and compressional and shear attenuations show similar variation at both frequencies. This indicates frequency-independent attenuations in the studied oilfield.

Compressibility, stiffness and electrical resistivity characteristics of sand–diatom mixtures

The engineering characteristics of ocean sediments are significantly affected by fine particles such as diatoms. The objective of this study is to investigate experimentally the compressibility, small-strain stiffness and electrical resistivity of sand–diatom mixtures by way of oedometer tests. Sand–diatom mixtures are prepared at a fixed density with varying diatom contents ranging from 0 to 20% by weight. The vertical displacements are monitored during oedometer tests, and shear wave, compressional wave and electrical resistance are measured using bender elements, piezo-disc elements and an electrical resistance probe, respectively, at the end of each loading step. The test results show that the compression index increases, whereas the swelling index and shear and compressional wave velocities decrease with increasing diatom content because of the small and crushable diatom particles. The attenuation of shear and compressional waves increases continuously, while the shear and compressional wave velocities decrease with an increase in the diatom content due to weak inter-particle contact and a soft soil skeleton. In addition, the sand specimens with a lower compression index, Cc, a higher swelling index, Cs, a higher shear wave factor, α, and a lower shear wave exponent, β, gradually change to clay-like soils, which exhibit a higher Cc, a lower Cs, a lower α and a higher β as the diatom content increases. This study suggests that diatoms may affect the compressibility, small-strain stiffness and electrical resistivity of soil.

On compressional wave attenuation in muddy marine sediments.

A method for measuring in situ compressional wave attenuation exploiting the spectral decay of reflection coefficient Bragg resonances is applied to fine-grained sediments in the New England Mud Patch. Measurements of layer-averaged attenuation in a 10.3 m mud layer yield 0.04 {0.03, 0.055} dB/m/kHz (braces indicate outer bounds); the attenuation is twice as large at a site with 3.2 m mud thickness. It is shown that both results are heavily influenced by a ∼1 m sand-mud transition interval created by geological and biological processes that mix sand (at the base of the mud) into the mud. Informed by the observations, it appears that the spatial dependence of mud layer attenuation across the New England Mud Patch can be predicted by accounting for the transition interval via simple scaling. Further, the ubiquity of the processes that form the transition interval suggests that the scaling may be applied to any muddy continental shelf. In principle, attenuation predictions in littoral environments could be substantively improved with a modest amount of geologic and biologic information.

Compressional wave attenuation in muddy sediments at the New England Mud Patch

A new method for measuring in situ compressional wave attenuation exploiting the spectral decay of Bragg resonances is applied to sediments at the New England Mud Patch. Measurements of layer-averaged attenuation in a 10.3 m mud layer yield 0.04 {0.03 0.055} dB/mi kHz (braces indicate outer bounds); the attenuation is twice as large at a site with 3.2 m mud thickness. Both results are strongly influenced by a ∼1 m sand-mud transition interval, created by geological and biological processes which mix sand (at the base of the mud) into the mud. Above the transition interval, homogeneous mud exhibits an attenuation 0.01–0.02 dB/m kHz, lower than that in the sand-mud transition interval by a factor of 10. Informed by these and additional observations, mud attenuation in and above the transition interval appears to be roughly spatially invariant across the area, explaining the factor of two in attenuation between the two sites by simple depth scaling. Further, the ubiquity of the processes that form the transition interval suggests that the scaling may be broadly applied to other muddy continental shelves. In principle, attenuation predictions in shallow water could be substantively improved with a modest amount of geologic and biologic information. [Research supported by ONR Ocean Acoustics.]

An overview of seabed characterization experiment

An overview of the Spring 2021 component of the Seabed Characterization Experiment will be presented. The project is focused on the acoustics of fine-grained ocean bottom sediments. The study site is the New England Shelf, south of Martha’s Vineyard, MA, USA. The goals of the project are (1) understand the physical mechanisms that control acoustic propagation in fine-grained sediments, (2) quantify uncertainties in the estimation of seabed parameters, (3) correlate the observed horizontal variations in the acoustical field with the measured horizontal variability of the seabed and (4) assess the performance of the resulting geoacoustic models, and inversion and statistical inference methods. These goals have been pursued by obtaining direct measurements and/or inferring the values of the following parameters over a wide frequency band: compressional wave speed and attenuation, shear wave speed and attenuation, and seabed layering and gradients. Oceanographic data were collected to support both forward and inverse modeling efforts. A major part of this effort was completed in 2017 and a follow-on effort is planned for 2021 and 2022. This presentation provides an overview of the project, a summary of past results, and a discussion of the most recent work. [Work supported by ONR.]

Estimation of bottom parameters in the New England Mud Patch using geophone and hydrophone measurements

Measurements of acoustic pressure and particle velocity were made during the Seabed Characterization Experiment (SCEx) in the New England Mud Patch south of Cape Cod in about 70 m of water. The University of Rhode Island and Woods Hole Oceanographic Institution deployed the “geosled” with a four-element geophone array, a tetrahedral array of four hydrophones, and Several Hydrophone Receive Units (SHRUs) as data acquisition packages. In addition, a recently developed low frequency source, the interface Wave Sediment Profiler (iWaSP), was deployed to excite interface waves (Scholte waves) on the seabed. The geophone array was localized using the known locations of the small explosive sources and noise from the research vessel. Modal arrivals from broadband sources on geophones and hydrophones were used to invert for compressional and shear wave speeds and attenuation in the mud layer and the underlying sand layer. The Scholte wave arrivals from the iWaSP source measured by the geophone array also provided estimates for these parameters. The inversion results are compared to modeling using the viscous grain shearing (VGS) theory. [Work supported by the Office of Naval Research, Code 322 OA.]

Squirt flow in porous media saturated by Maxwell-type non-Newtonian fluids.

Mechanical waves, which are commonly employed for the noninvasive characterization of fluid-saturated porous media, tend to induce pore-scale fluid pressure gradients. The corresponding fluid pressure relaxation process is commonly referred to as squirt flow and the associated viscous dissipation can significantly affect the waves' amplitudes and velocities. This, in turn, implies that corresponding measurements contain key information about flow-related properties of the probed medium. In many natural and applied scenarios, pore fluids are effectively non-Newtonian, for which squirt flow processes have, as of yet, not been analyzed. In this work, we present a numerical approach to model the attenuation and modulus dispersion of compressional waves due to squirt flow in porous media saturated by Maxwell-type non-Newtonian fluids. In particular, we explore the effective response of a medium comprising an elastic background with interconnected cracks saturated with a Maxwell-type non-Newtonian fluid. Our results show that wave signatures strongly depend on the Deborah number, defined as the relationship between the classic Newtonian squirt flow characteristic frequency and the intrinsic relaxation frequency of the non-Newtonian Maxwell fluid. With larger Deborah numbers, attenuation increases and its maximum is shifted towards higher frequencies. Although the effective plane-wave modulus of the probed medium generally increases with increasing Deborah numbers, it may, however, also decrease within a restricted region of the frequency spectrum.