P-wave Reflection Research Articles

Effects of marine sediment on the response of a submerged floating tunnel to P-wave incidence

Submerged floating tunnels (SFTs) are a novel type of traffic structure for crossing long straits or deep lakes. To investigate the dynamic pressure acting on an SFT under compression (P) wave incidence, a theoretical analysis model considering the effect of marine sediment is proposed. Based on displacement potential functions, the reflection and refraction coefficients of P-waves in different media are derived. Numerical examples are employed to illustrate the effects of the thickness of the sediment layer, the incident P-wave angle, the tether stiffness and spacing, and the permeability of the sediment on the dynamic pressure loading on the SFT. The results show that the dynamic pressure is related to the saturation of the sediment and affected by its thickness. Partially saturated sediment will amplify the dynamic pressure loading on the SFT, and the resonance frequency increases slightly with fully saturated sediment. Besides, increasing the tether stiffness or decreasing the tether spacing will decrease the dynamic pressure. Locating the SFT at greater depth and reducing the permeability of the sediment are effective measures to reduce the dynamic pressure acting on the SFT.

Pre-stack AVA Inversion by Using Propagator Matrix Forward Modeling

Most existing amplitude variation with angle (AVA) inversions are based on the exact Zoeppritz equation or its approximations. These modeling methods, which are ray-tracing-based and describe P-wave primary reflections only, lead to exacting requirements for pre-processing of the input data. Current processing is inadequate to satisfy these demands, especially for removing the effects of transmission losses, P-wave multiples and various converted-wave modes. By using input data with processing errors, inversion results of primary-only methods are predictably not accurate enough. The propagator matrix (PM), like the reflectivity method, uses an analytical solution to the wave equation and considers full-wave propagation effects in horizontal or nearly horizontal multilayered earth models. The numerical examples verify that a PM can effectively estimate transmission losses, multi-reflections and the comprehensive responses of thin interbedded layers, and also has higher reflection sensitivities to P-wave and S-wave velocity and density, as compared with ray-tracing-based AVA modelling. A pre-stack AVA three-parameter inversion by using a PM as the forward engine is proposed. Following a Bayesian approach, the inversion is stabilized by including the correlation of P-wave velocity, S-wave velocity and density. For inversion accuracy, the limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) optimization method is used to solve the augmented function, and the generalized cross-validation (GCV) criterion (Huang et al. in J Geophys Eng 14(1):100–112, 2017) is introduced to adaptively acquire the regularization parameter. Theoretical model inversion analysis shows that the proposed inversion can make use of transmission losses, P-wave multiples and converted wave modes, which not only cost-effectively simplifies the pre-processing, but also generates reasonable inverted results for multilayered conditions. The proposed inversion is then applied to a set of real data, and a comparison with Zoeppritz equation-based inversion demonstrates that PM inversion is clearly superior to Zoeppritz equation-based inversion in terms of stability and accuracy.

Simultaneous seismic inversion to identify prospective areas in carbonate rocks of the southeastern part of the West Siberian Platform

This paper focuses on the description of a technology and results of identifying and mapping areas in Devonian carbonate rocks prospective for hydrocarbons and associated with increased fracture-cavern porosity in the southeastern part of the West Siberian Platform. The lack of wide-azimuthal seismic data and recording of only the vertical component in the study area did not allow the use of the direct indicators of fracture systems based either on azimuthal anisotropy of the amplitudes of pressure waves or on splitting converted waves into fast and slow. Instead, abnormally low values of the ratio of pressure-wave and shear-wave velocities derived by deterministic simultaneous pre-stack seismic inversion were used as an indirect indicator of increased fracturing. The choice of this seismic signature of fractures is substantiated by a brief review of publications on its successful use in the identification and delineation of highly fractured and cavernous zones in carbonate reservoirs. The behaviour of the indicator showed good agreement with well productivity in the study area and, therefore, made it possible to predict a number of perspective pay zones, presumably associated with in-creased fracturing. At the same time, however, well log estimates of the velocity ratio related to fractured reservoirs exhibited an opposite trend, which mismatched the facts observed in the study area and reported in the literature. This apparent discrepancy is explained by the impact of near-vertical natural macro-fracturing, which, due to different measurement scales, might substantially reduce seismic estimates while producing no impact on well log estimates. In order to describe this phenomenon quantitatively, the weak-anisotropy approximation of P-wave reflection coefficients at a horizontal boundary derived by Rüger for transversely isotropic media with a horizontal axis of symmetry was used. This equation was rewritten in terms of impedances and density and then was analyzed analytically. To express the impact of fractures in terms of fracture density, the simplest model of thin, isolated, penny-shaped fractures was used.

Image-domain wavefield tomography for VTI media

Processing algorithms for transversely isotropic (TI) media are widely used in depth imaging and typically bring substantial improvements in reflector focusing and positioning. Here, we develop acoustic image-domain tomography (IDT) for reconstructing VTI (TI with a vertical symmetry axis) models from P-wave reflection data. The modeling operator yields an integral wave-equation solution, which is based on a separable dispersion relation and contains only P-waves. The zero-dip NMO velocity ([Formula: see text]) and anellipticity parameter [Formula: see text] are updated by focusing energy in space-lag images obtained by least-squares reverse-time migration (LSRTM). Application of LSRTM helps mitigate aperture- and illumination-induced artifacts in space-lag gathers and improve the robustness of [Formula: see text]-estimation. The impact of the trade-off between [Formula: see text] and [Formula: see text] is reduced by a three-stage inversion algorithm that gradually relaxes the constraints on the spatial variation of [Formula: see text]. Assuming that the depth profile of the Thomsen parameter [Formula: see text] is known at two or more borehole locations, we employ image-guided interpolation to constrain the depth scale of the parameter fields and of the migrated image. Image-guided smoothing is also applied to the IDT gradients to facilitate convergence towards geologically plausible models. The algorithm is tested on synthetic reflection and borehole data from the structurally complicated elastic VTI Marmousi-II model. Although the initial velocity field is purely isotropic and substantially distorted, all three relevant parameters ([Formula: see text], [Formula: see text], and [Formula: see text]) are estimated with sufficient accuracy. The algorithm is also applied to a line from a 3D ocean-bottom-node data set acquired in the Gulf of Mexico.

Extended poroelastic impedance

Linearized approximations to the P-wave reflectivity as a function of the incidence angle (called amplitude variation with offset) involve the extraction of band-limited reflectivity terms that are a function of changes in the elastic constants of the earth across each lithologic interface. The most common of these extracted reflectivities are the intercept and gradient, usually labeled [Formula: see text] and [Formula: see text], respectively. The extended elastic impedance (EEI) method uses a rotation angle [Formula: see text] to map [Formula: see text] and [Formula: see text] into a new reflectivity corresponding to a particular elastic parameter. The success of EEI depends on finding an optimum value for the angle [Formula: see text]. This value is usually calculated by correlating the EEI result over a range of [Formula: see text] angles with various elastic parameters and then finding the best correlation coefficient. We have developed a new approach for the interpretation of the EEI method, which incorporates the Biot-Gassmann poroelastic theory and attaches a physical meaning to the [Formula: see text] angle. We call this method extended poroelastic impedance (EPI). The main advantage of the EPI method is that the [Formula: see text] angle is now interpreted as a parameter that is dependent on the dry-rock properties of the reservoir, rather than a parameter whose value is estimated empirically. The method is evaluated by numerical and synthetic seismic examples and by application to field data from a gas sand reservoir.

Prestack Stochastic Frequency-Dependent Velocity Inversion With Rock-Physics Constraints and Statistical Associated Hydrocarbon Attributes

Previous studies have demonstrated that P-wave velocity dispersion at seismic frequencies is often related to hydrocarbons, which results in frequency-dependent P-wave reflection coefficients. This effect is neglected in the conventional amplitude-versus-angle (AVA) inversion, or reduced in most AVA inversion involving seismic dispersion due to the linearization of either the forward modeling or the inversion objective function. As a consequence, there are times when nonnegligible error exists in the inverted dispersion-associated result, which is probably nonnegligible in some cases. In this letter, we adopt the propagator matrix forward modeling derived from the wave equation and the particle swarm optimization (PSO)-based inversion to solve the uncollapsed objective function to avoid any linearization operator at the cost of probably more computational complexity and inversion ill-posedness. To address the ill-posedness, in both the forward modeling and inversion, we introduce rock-physics constraints of frequency-independent S-wave velocity and limited variations of P-wave velocity with frequency. Furthermore, we statistically derive the average frequency-dependent P-wave velocity attribute, the P-wave velocity dispersion intensity attribute, and the characteristic frequency attribute corresponding to the maximum velocity dispersion gradient from multiple experimental inverted dispersive P-wave velocity results. These attributes can be directly applied to detect hydrocarbons. A synthetic data example and a real data example through a drilling well are used to demonstrate that PSO-based prestack stochastic inversion method with rock-physics constraints is effective, and that the statistical attributes derived from the multiple inverted dispersive P-wave velocities can be utilized to favorably indicate gas reservoirs.

AVAZ inversion for fracture weakness based on three-term Rüger equation

Fracture is one of the most important migration channels and accumulation spaces in hydrocarbon reservoirs. For unconventional hydrocarbon reservoirs, especially for shale reservoirs, the accurate prediction of fracture distribution can help improve the hydrocarbon production. With the development of seismic monitoring techniques, wide-azimuth acquisition and processing techniques are being increasingly used to describe the distribution of subsurface factures. The P-wave AVAZ inversion based on seismic anisotropy is one of the most important and commonly used methods for fracture prediction. In this paper, we develop an inversion algorithm to acquire the normal and tangential fracture weakness based on P-wave reflection anisotropy and wide-azimuth seismic data. The newly developed algorithm can effectively utilize the amplitude information of large offset data to retrieve the fracture weakness which is related to the fracture density and fluid fillings. Two synthetic data examples show that the fracture weakness can be accurately estimated by using the newly proposed AVAZ inversion method. Our inversion method can obtain reliable fracture identification results even when seismic data are contaminated by random noise, which demonstrates the reliability and noise resistance of the inversion method. Finally, the method is successfully applied to a 3-D physical model data with an equivalent area of 100 km2. The predicted fracture distribution result is consistent with the designed physical model and is highly related to the locally geological structures of the target reservoir. Through synthetic and physical model data studies, we demonstrate that the proposed inversion method is an effective approach to directly evaluate the fracture distribution in the reservoir.

OBS Data Analysis to Quantify Gas Hydrate and Free Gas in the South Shetland Margin (Antarctica)

The presence of a gas hydrate reservoir and free gas layer along the South Shetland margin (offshore Antarctic Peninsula) has been well documented in recent years. In order to better characterize gas hydrate reservoirs, with a particular focus on the quantification of gas hydrate and free gas and the petrophysical properties of the subsurface, we performed travel time inversion of ocean-bottom seismometer data in order to obtain detailed P- and S-wave velocity estimates of the sediments. The P-wave velocity field is determined by the inversion of P-wave refractions and reflections, while the S-wave velocity field is obtained from converted-wave reflections received on the horizontal components of ocean-bottom seismometer data. The resulting velocity fields are used to estimate gas hydrate and free gas concentrations using a modified Biot-Geertsma-Smit theory. The results show that hydrate concentration ranges from 10% to 15% of total volume and free gas concentration is approximately 0.3% to 0.8% of total volume. The comparison of Poisson’s ratio with previous studies in this area indicates that the gas hydrate reservoir shows no significant regional variations.

Reservoir Characterization Through Target-Oriented AVA-Petrophysical Inversions with Spatial Constraints

We apply three methods that use different regularization strategies to insert spatial constraints into the seismic-petrophysical inversion. The first method is what we call the structurally constrained inversion (SCI), which directly uses the structural information brought by the seismic stack image to insert geological (structural) constraints into the inversion. The second method is based on anisotropic Markov random field (AMRF) and uses the Huber energy function to reasonably model the spatial heterogeneity of petrophysical reservoir properties. Finally, the last method includes both geostatistical information (describing the lateral variability of reservoir properties) and hard data (i.e. well log data) constraints into the inversion kernel (GHDC inversion). For computationally feasibility, we apply a target-oriented inversion that uses the amplitude versus angle (AVA) responses extracted along the top reservoir reflections to infer the petrophysical properties of interest (i.e. porosity, water saturation and shaliness) for the target layer. In particular, an empirical, linear rock-physics model, properly calibrated for the investigated area, is used to rewrite the P-wave reflectivity equation as a function of the petrophysical contrasts instead of the elastic constants. This reformulation allows for a direct and a simultaneous estimation of petrophysical properties from AVA data. The implemented approaches are tested both on synthetic and field seismic data and compared against the standard method in which each AVA response is inverted independently (laterally unconstrained Bayesian inversion; LUBI). In the case of poor signal-to-noise ratio it turns out that the three considered spatially constrained methods achieve better delineations of reservoir bodies and provide more reliable results than the standard LUBI approach. More in detail, the AMRF recovers sharper geological boundaries than the SCI and GHDC algorithms. The SCI algorithms is more sensitive to data noise, whereas the key advantage of the GHDC consists in analytically providing posterior uncertainties for the model parameters. Finally, for what concerns the computational cost the GHDC and the SCI methods result the most and the least computationally demanding, respectively.

Impact of frequency-dependent anisotropy on azimuthal P-wave reflections

Seismic anisotropy has widely been used for the characterization of fractures in a reservoir. Recent work has demonstrated the effect of seismic dispersion on producing a frequency-dependent reflection coefficient, which can be important in fracture characterization since large fractures often lead to frequency-dependent anisotropy. In this paper, we examine the impact of anisotropic dispersion on P-wave reflections based on an HTI sand model overlaid by VTI shale. Although VTI in the overburden does not lead to azimuthal anisotropy, its effect on angle dependence could significantly affect the azimuthal AVO responses at far offsets. We show a modest effect on the amplitude and large effect on the phase, the latter of which could even be mistaken for azimuthal velocity variations. We present a Bayesian inversion based on a forward modelling technique aimed at recovering water saturation, fracture density and fracture length of a HTI sand. Our results show potential of using seismic dispersion in azimuthal AVO analysis to discriminate large-scale fractures from micro-scale cracks.

Direct reservoir property estimation based on prestack seismic inversion

Reservoir property estimation is an essential part for reservoir characterization. Most commonly-used estimation methods are implemented in two steps, seismic inversion and rock physics inversion. However, these indirect methods may increase the uncertainty and reduce the accuracy of estimation results. In this work, we propose a Bayesian inversion approach to estimate reservoir properties directly from prestack seismic data. Firstly, by combining the reflection coefficient equation and rock physics model, we derive a P-wave reflection approximation in terms of reservoir parameters, which establishes a direct link between seismic data and reservoir properties. Model examples illustrate the accuracy of the approximation comparing to the exact reflection coefficient equation, which satisfies the requirements of the prestack seismic inversion. Then in the framework of Bayesian inversion theory, a novel inversion method is presented to estimate porosity, mineral volume and water saturation directly from prestack seismic angle gathers. Direct estimation increases the stability and decreases the uncertainty. The synthetic test demonstrates the advantage of the proposed method on the accuracy and stability over indirect methods. The real data example verifies the feasibility of the proposed method in direct reservoir property estimation.

Two-stage and single-stage seismic-petrophysical inversions applied in the Nile Delta

We discuss two Bayesian seismic-petrophysical inversion techniques, the two-stage and single-stage approach, which estimate petrophysical properties from prestack seismic data. Both approaches are developed considering linear approximations and are applied for reservoir appraisal studies in the Nile Delta. The two-stage approach first uses an amplitude-variation-with-angle (AVA) inversion to infer P-wave velocity, S-wave velocity, and density. Then, a linear empirical rock-physics model, properly calibrated for the investigated area, is used to transform the estimated elastic parameters into the petrophysical properties of interest under the assumption of Gaussian mixture distributed petrophysical properties. The single-stage approach uses the linear rock-physics model to rewrite the time-continuous P-wave reflectivity equation as a function of the petrophysical contrasts instead of the elastic constants. This reformulation, together with the assumption of a Gaussian prior model, allows us to directly derive (in a single-stage inversion) the petrophysical properties from AVA data. Despite the differences in the forward-model parameterization and in the assumed a priori distribution for the petrophysical properties, the two inversion methods yield comparable predictions that are consistent with borehole data. For the investigated zone, this work demonstrates that, although neglecting the facies-dependent behavior of petrophysical properties, the a priori Gaussian assumption for the petrophysical properties can provide reliable predictions with a very limited computational effort. In addition, the good match between predicted and logged properties proves the suitability of the linear rock-physics model for reservoir characterization in the Nile Delta.

The accuracy of AVA approximations in isotropic media assessed via synthetic numerical experiments: Implications for the determination of porosity

Analyses of seismic amplitude vs. angle are widely used to estimate hydrocarbon reservoir properties. This paper investigates the accuracy of existing approximations based on the Zoeppritz equation, using synthetic numerical experiments that correlate P-wave reflectivity in isotropic media with reservoir porosity. An effective medium non-interacting approach (NIA) in rock physics modelling was used to compute the properties of fluid-saturated (water + gas) reservoir, which were then used in seismic modelling. In parallel, a Bayesian approach was used to estimate reservoir porosities from angle-dependent reflection coefficients and seismic amplitudes. A Maximum a posteriori solution of the Bayesian approach was also utilised to obtain an inverted porosity distribution in the reservoir model. The results of our forward models are important as they suggest that most of the approximations deviate from the exact Zoeppritz solutions with increasing angles of incidence of seismic waves. The results from the Bayesian inversion show that the Rüger and Bortfeld approximations agree with the exact Zoeppritz solutions to accurately estimate reservoir porosity. All the other approximations, except for Smith's, underestimate reservoir porosity and should be used in pre-stack inversion with caution. Smith's and Fatti's approximations failed to estimate reservoir porosity because of associated uncertainties.

Lithospheric discontinuities in Central Australia

Lithospheric discontinuities are elusive, with properties that are strongly frequency dependent. Results from a temporary deployment of broadband stations along a north-south transect through Central Australia, and the permanent arrays ASAR and WRA, are used to evaluate the spatial coherence of lithospheric features, particularly mid-lithospheric discontinuities. We exploit stacked station autocorrelograms that provide an estimate of P-wave reflectivity beneath stations, with imaging methods exploiting teleseismic arrivals. We use both common conversion point (CCP) stacking from Ps receiver functions and reflection point imaging using the autocorrelation of the P wavetrain. The results tie well for the Moho and have a good general correspondence for deeper levels. Although indications of mid-lithospheric discontinuities from changes in the frequency of reflectivity occur at similar depths, the spatial continuity of specific features at high frequency (around 2 Hz) is of the order of 10–15 km. Broader trends can be tracked across the profile, but no strong lithospheric interfaces can be mapped, except for a south dipping feature traversing the lithosphere on the southern part of the profile that is likely to be a former mantle detachment zone.

Reflection and Transmission of P-Waves in an Intermediate Layer Lying Between Two Semi-infinite Media

With a motivation to gain physical insight of reflection as well as transmission phenomena in frozen (river/ocean) situation for example in Antarctica and other coldest place on Earth, the present article undertakes the analysis of reflection and transmission of a plane wave at the interfaces of layered structured comprised of a water layer of finite thickness sandwiched between an upper half-space constituted of ice and a lower isotropic elastic half-space, which may be useful in geophysical exploration in such conditions. A closed form expression of reflection/transmission coefficients of reflected and transmitted waves has been derived in terms of angles of incidence, propagation vector, displacement vector and elastic constants of the media. Expressions corresponding to the energy partition of various reflected and transmitted waves have also been established analytically. It has been remarkably shown that the law of conservation of energy holds good in the entire reflection and transmission phenomena for different angles of incidence. A numerical examples were performed so to graphically portray the analytical findings. Further the deduced results are validated with the pre-established classical results.

A two-step inversion approach for seismic-reservoir characterization and a comparison with a single-loop Markov-chain Monte Carlo algorithm

We have evaluated a two-step Bayesian algorithm for seismic-reservoir characterization, which, thanks to some simplifying assumptions, is computationally very efficient. The applicability and reliability of this method are assessed by comparison with a more sophisticated and computer-intensive Markov-chain Monte Carlo (MCMC) algorithm, which in a single loop directly estimates petrophysical properties and lithofluid facies from prestack data. The two-step method first combines a linear rock-physics model (RPM) with the analytical solution of a linearized amplitude versus angle (AVA) inversion, to directly estimate the petrophysical properties, and related uncertainties, from prestack data under the assumptions of a Gaussian prior model and weak elastic contrasts at the reflecting interface. In particular, we use an empirical, linear RPM, properly calibrated for the investigated area, to reparameterize the linear time-continuous P-wave reflectivity equation in terms of petrophysical contrasts instead of elastic constants. In the second step, a downward 1D Markov-chain prior model is used to infer the lithofluid classes from the outcomes of the first step. The single-loop (SL) MCMC algorithm uses a convolutional forward modeling based on the exact Zoeppritz equations, and it adopts a nonlinear RPM. Moreover, it assumes a more realistic Gaussian mixture distribution for the petrophysical properties. Both approaches are applied on an onshore 3D seismic data set for the characterization of a gas-bearing, clastic reservoir. Notwithstanding the differences in the forward-model parameterization, in the considered RPM, and in the assumed a priori probability density functions, the two methods yield maximum a posteriori solutions that are consistent with well-log data, although the Gaussian mixture assumption adopted by the SL method slightly improves the description of the multimodal behavior of the petrophysical parameters. However, in the considered reservoir, the main difference between the two approaches remains the very different computational times, the SL method being much more computationally intensive than the two-step approach.

Effect of rotation and gravity on the reflection of P-waves from thermo-magneto-microstretch medium in the context of three phase lag model with initial stress

In this paper the linear theory of the thermoelasticity has been employed to study the effect the reflection of plane harmonic waves from a semi-infinite elastic solid under the effect of the magnetic field , rotation, initial stress and gravity. The medium under consideration is traction free, homogeneous, isotropic, as well as with three-phase-lag. The normal mode analysis is used to solve the resulting non-dimensional coupled equations. The expressions for the reflection coefficients, which are the relations of the amplitudes of the reflected waves to the amplitude of the incident waves, are obtained similarly, the reflection coefficient ratio variations with the angle of incident under different conditions are shown graphically. Comparisons are made with the results predicted by different theories Lord-Shulman theory (L-S), the Green-Naghdi theory of type III (G-N III) and the three-phase-lag model in the absence and presence of a magnetic field, rotation, initial stress and gravity. The results indicate that the effect of rotation, magnetic field, initial stress and gravity field are very pronounced.

The study of applicability of the geophysical exploration methods for the strike-slip fault (part 1; shallow P-wave seismic reflection and refraction survey, CSAMT survey, and gravity survey) : the case study of the Go-mura fault zone and Yamada fault zone

The study of applicability of the geophysical exploration methods for the strike-slip fault (part 1; shallow P-wave seismic reflection and refraction survey, CSAMT survey, and gravity survey) : the case study of the Go-mura fault zone and Yamada fault zone

AVA Simultaneous Inversion of Prestack Seismic Data Using Particle Swarm Optimization

A new prestack AVA simultaneous inversion using particle swarm optimization algorithm is proposed, which can obtain the elastic parameters such as P-wave and S-wave impedance from P-wave reflection data simultaneously. Compared with the conventional AVA inversion based on generalized linear technique, this method does not depend on the initial model and can reach the global minimum. In order to increase the stability of the inversion, low-frequency trends of P-wave and S-wave impedances are built into the inversion. This method has been successfully applied to synthetic and field data. The estimated P-wave and S-wave impedances can be combined to derive other elastic parameters, which are sensitive for lithology identification and fluid prediction.

High-resolution P- and S-wave Seismic Reflection Followed by Engineering Modeling for Geotechnical Site Characterization in Southern Illinois

A study was conducted to determine whether the structural failure of a house in a residential subdivision in southern Illinois was caused by the collapse of an old underground coal mine ( i.e. mine subsidence) or as a result of a landslide. The house was displaced approximately 5 m downhill towards an engineered lake behind it. To detect any old mines near the house, we acquired high-resolution S-wave seismic reflection profiles along the roads surrounding the subdivision and a series of high-resolution P-wave reflection profiles in the immediate vicinity of the house. The S-wave seismic reflection profiles imaged a strong shallow horizon that we interpreted as Pennsylvanian siltstone overlying the Mecca Quarry Shale and Colchester Coal, which had been previously mined in the area. Locally, this horizon showed no evidence of any recent mining activities. The high-resolution P-wave reflection profiles imaged a steeply dipping bedrock with a 20° dip at the house location. These results exclude mine subsidence from being the cause for the house failure. To investigate land sliding as a possible cause of the house failure, depths to bedrock from the seismic results together with the soil type information were used to model the soil materials with a Mohr-Coulomb stress-strain model. The engineering model demonstrated that a land slide is a more plausible cause for the house failure, which agrees with the seismic results.