Crosshole Seismic Data Research Articles

Characteristics of shallow buried karst and its safety distance to tunnel in wuxi city, China

Subway tunneling construction in shallow buried karst region is a common challenge. Survey boreholes and cross-hole seismic CT data showed that 29 karst caves exist at elevation of −17 m to −37 m in Si–He section of the Wuxi Metro Line 4, which are consisted of 18 filled caves and 11 empty caves and constitute substantial dangers to the stability and quality of metro construction projects. Based on their size, position, and type of filling, we divided these shallow karst caves into four types. Aimed at exploring the instability of the tunnel after excavation, numerical analyses have been developed by using the Finite difference method. Both the effects of the distance between tunnel and karst caves and the effects of the filling of the cavities on the overall stability of the rock mass around the tunnel have been investigated. According to the design criteria, safety distance between tunnel and karst caves was determined. The monitoring data of tunnel during excavation proved the rationality and accuracy of the analysis results. The research results can provide technical reference for the design and construction of other proposed tunnels that are located in the regions of shallow buried karst in Jiangsu Province.

High-resoultion shallow anomaly characterization using cross-hole P- and S-wave tomography

Cross-hole seismic tomography is a high-precision method that can obtain the velocity structure between boreholes. At present, single-component geophones are mainly used for P-wave velocity estimation. However, S waves have a shorter wavelength than P waves, incurring a high-resolution tomography image. In this paper, we apply three-component cross-hole seismic tomography to shallow geological survey. First, three-component geophone is used to collect cross-hole seismic data. Secondly, the apparent velocity polarization method is used to separate the P and S wavefields from the recorded three-component waveform data. Then, a damped least-squares traveltime tomography is used to calculate the cross-hole P- and S-wave velocity structures. Finally, the distribution of Poisson's ratio between the boreholes is derived from the inverted P- and S-wave velocities. Numerical model experiments show that this method can solve some typical shallow subsurface problems, such as the detection of karst features and boulders. The proposed method is used to detect an underground air-raid shelter located in Hangzhou, Zhejiang Province, China, and the P- and S-wave velocities and the Poisson's ratio are obtained with high precision. The tomography image of the air-raid shelter agrees well with its known location. and the calculated Poisson's ratio distribution shows that the air-raid shelter may be partially filled with mucky clay. Three-component cross-hole seismic tomography achieves a high data acquisition efficiency and can simultaneously obtain shallow subsurface stratum velocities and Poisson's ratio with high precision. Thus, this technique can be used for shallow-subsurface surveys.

Visco-acoustic data modeling using optimum layer approximation technique: greenwood oil field example, USA

It is desirable to use Finite Element (FE) or Finite Difference (FD) method to simulate elastic data for cross-hole seismic surveys. But FE and FD are computationally intensive and time-expensive for full wave-field modeling of large cross-hole survey. The computation cost – space and time- of elastic data modeling inhibits the use of synthetic data for providing solution to cross-hole geophysics problems .On the other hand, acoustic synthetic data require less computation time but lacks some of seismic arrivals seen in the field data. In this study a recursive reflectivity method incorporating P and S wave properties and attenuation effects is formulated to model cross-hole seismic data. The model is tested using a set of field data acquired in Green Wood field, USA. The visco-acoustic data modeled by the recursive reflectivity method show improvement over the acoustic data and gave a perfect match to the elastic and field data. The visco-acoustic data featured the different seismic arrivals seen in the field and elastic synthetic data. The data simulation method is stable, efficient, and fast. The inclusion of a scheme for determining the optimum layer model further reduced the computation time without compromising the quality of the results: only about one-eight of the time require for elastic data is needed to produce the equivalent visco-acoustic data. Because of its low computation cost, the study highlights the strong potentials for solving the problem of inefficient algorithm for processing and imaging cross-hole data, with a consequence of using cross-hole technology as a routine in oil and gas industry.Keywords: Cross-hole seismic survey; synthetic data; acoustic wave simulation; visco-acoustic

Comparison of deterministic and stochastic approaches to crosshole seismic travel-time inversions

The Bayesian inversion method is a stochastic approach based on the Bayesian theory. With the development of sampling algorithms and computer technologies, the Bayesian inversion method has been widely used in geophysical inversion problems. In this study, we conduct inversion experiments using crosshole seismic travel-time data to examine the characteristics and performance of the stochastic Bayesian inversion based on the Markov chain Monte Carlo sampling scheme and the traditional deterministic inversion with Tikhonov regularization. Velocity structures with two different spatial variations are considered, one with a chessboard pattern and the other with an interface mimicking the Mohorovicic discontinuity (Moho). Inversions are carried out with different scenarios of model discretization and source–receiver configurations. Results show that the Bayesian method yields more robust single-model estimations than the deterministic method, with smaller model errors. In addition, the Bayesian method provides the posterior probabilistic distribution function of the model space, which can help us evaluate the quality of the inversion result.

Anisotropic full-waveform inversion of crosshole seismic data: A vertical symmetry axis field data application

Anisotropic waveform tomography (AWT) uses anisotropic traveltime tomography followed by anisotropic full-waveform inversion (FWI). Such an approach is required for FWI in cases in which the geology is likely to exhibit anisotropy. An important anisotropy class is that of transverse isotropy (TI), and the special case of TI media with a vertical symmetry axis (VTI) media is often used to represent elasticity in undeformed sedimentary layering. We have developed an approach for AWT that uses an acoustic approximation to simulate waves in VTI media, and we apply this approach to crosshole data. In our approach, the best-fitting models of seismic velocity and Thomsen VTI anisotropy parameters are initially obtained using anisotropic traveltime tomography, and they are then used as the starting models for VTI FWI within the acoustic approximation. One common problem with the acoustic approach to TI media is the generation of late-arriving (spurious) S-waves as a by-product of the equation system. We used a Laplace-Fourier approach that effectively damps the spurious S-waves to suppress artifacts that might otherwise corrupt the final inversion results. The results of applying AWT to synthetic data illustrate the trade-offs in resolution between the two parameter classes of velocity and anisotropy, and they also verify anisotropic traveltime tomography as a valid method for generating starting models for FWI. The synthetic study further indicates the importance of smoothing the anisotropy parameters before proceeding to FWI inversions of the velocity parameter. The AWT technique is applied to real crosshole field gathers from a sedimentary environment in Western Canada, and the results are compared with the results from a simpler (elliptical) anisotropy model. The transversely isotropic approach yields an FWI image of the vertical velocity that (1) exhibits a superior resolution and (2) better predicts the field data than does the elliptical approach.

Joint acoustic full-waveform inversion of crosshole seismic and ground-penetrating radar data in the frequency domain

Integrating crosshole ground-penetrating radar (GPR) with seismic methods is an efficient way to reduce the uncertainty and ambiguity of data interpretation in shallow geophysical investigations. We have developed a new approach for joint full-waveform inversion (FWI) of crosshole seismic and GPR data in the frequency domain to improve the inversion results of both FWI methods. In a joint objective function, three geophysical parameters (P-wave velocity, permittivity, and conductivity) are effectively connected by three weighted cross-gradient terms that enforce the structural similarity between parameter models. Simulation of acoustic seismic and scalar electromagnetic problems is implemented using 2D finite-difference frequency-domain methods, and the inverse problems of seismic FWI and GPR FWI are solved using a matrix-free truncated Newton algorithm. The joint inversion procedure is performed in several hierarchical frequencies, and the three parameter models are sequentially inverted at each frequency. The joint FWI approach is illustrated using three numerical examples. The results indicate that the joint FWI approach can effectively enhance the structural similarity among the models, modify the structure of each model, and improve the accuracy of inversion results compared with those of individual FWI approaches. Moreover, joint inversion can reduce the trade-off between permittivity and conductivity in GPR FWI, leading to an improved conductivity model in which artifacts are significantly decreased.

Crosshole seismic CT data field experiments and interpretation for karst caves in deep foundations

Foundations at karstic terrains often cause instability problems for the supporting piles of upper buildings, resulting in uneven settlement and/or rock failure. Borehole investigation of the study site showed that the limestone cavities existed from 77.0m to 100.1m below the surface with the mean dimension of 1.52m and maximum of 8.0m. However, it is difficult to characterize these deeply buried karst caves accurately and completely. In this study, we used crosshole seismic CT techniques to image the P-wave velocities of the limestone stratum. Field experiments were designed to acquire seismic data from 44 boreholes and 113 survey lines at depths of >75m. The inverted P-wave velocities were iterated by combining the shortest path raytracing method and the damped least-square QR decomposition (LSQR) method on the basis of the initial model. Issues including the inverted velocities, uncertainty, stability and resolution of the results, and ray coverage were evaluated from the synthetic model. As bases for the interpretation of cavities, fractures and fillings, the quantitative relationship between P-wave velocities and geological anomalies was consequently obtained through correlating the results of field tomography and ultrasonic tests to the borehole data and limestone samples from karst foundations, respectively. Representative P-wave velocity maps were shown and the interpreted cavities were projected onto horizontal planes. Two sampling boreholes and in-situ water injection/pumping tests verified the interpretations. Regarding the number and scale of cavities, each area was divided into three engineering geological zones providing references for the grouting proposals of different zones.

Crosshole seismic tomography with cross-firing geometry

We have developed a case study of crosshole seismic tomography with a cross-firing geometry in which seismic sources were placed in two vertical boreholes alternatingly and receiver arrays were placed in another vertical borehole. There are two crosshole seismic data sets in a conventional sense. These two data sets are used jointly in seismic tomography. Because the local sediment is dominated by periodic, flat, thin layers, there is seismic anisotropy with different velocities in the vertical and horizontal directions. The vertical transverse isotropy anisotropic effect is taken into account in inversion processing, which consists of three stages in sequence. First, isotropic traveltime tomography is used for estimating the maximum horizontal velocity. Then, anisotropic traveltime tomography is used to invert for the anisotropic parameter, which is the normalized difference between the maximum horizontal velocity and the maximum vertical velocity. Finally, anisotropic waveform tomography is implemented to refine the maximum horizontal velocity. The cross-firing acquisition geometry significantly improves the ray coverage and results in a relatively even distribution of the ray density in the study area between two boreholes. Consequently, joint inversion of two crosshole seismic data sets improves the resolution and increases the reliability of the velocity model reconstructed by tomography.

The development and testing of a 2D laboratory seismic modelling system for heterogeneous structure investigations

Lateral velocity variations and low velocity near-surface layers can produce strong scattered and guided waves which interfere with reflections and lead to severe imaging problems in seismic exploration. In order to investigate these specific problems by laboratory seismic modelling, a simple 2D ultrasonic model facility has been recently assembled within the Wave Propagation Lab at ETH Zurich. The simulated geological structures are constructed from 2mm thick metal and plastic sheets, cut and bonded together. The experiments entail the use of a piezoelectric source driven by a pulse amplifier at ultrasonic frequencies to generate Lamb waves in the plate, which are detected by piezoelectric receivers and recorded digitally on a National Instruments recording system, under LabVIEW software control.The 2D models employed were constructed in-house in full recognition of the similitude relations. The first heterogeneous model features a flat uniform low velocity near-surface layer and deeper dipping and flat interfaces separating different materials. The second model is comparable but also incorporates two rectangular shaped inserts, one of low velocity, the other of high velocity. The third model is identical to the second other than it has an irregular low velocity surface layer of variable thickness. Reflection as well as transmission experiments (crosshole & vertical seismic profiling) were performed on each model. The two dominant Lamb waves recorded are the fundamental symmetric mode (non-dispersive) and the fundamental antisymmetric (flexural) dispersive mode, the latter normally being absent when the source transducer is located on a model edge but dominant when it is on the flat planar surface of the plate.Experimental group and phase velocity dispersion curves were determined and plotted for both modes in a uniform aluminium plate. For the reflection seismic data, various processing techniques were applied, as far as pre-stack Kirchhoff migration. The irregular surface layer and the anomalous velocity block inserts can destroy the coherence of the reflections. Migration was able to resolve the two main buried interfaces when the surface layer was flat but for the variable irregular surface layer the imaging result is inferior. First-arrival tomography was applied to the crosshole seismic data set and yielded the correct velocity distributions.Numerical modelling was also carried out to replicate the laboratory data and to identify the arrivals. The numerical seismograms are of superior quality to the physical model data and yield improved images of the structures.

The Research of Reverse-Time Migration for Cross-Hole Seismic

Cross-hole seismic is the leading technology of development seismology, which is still developing and improving. With the development of down-hole acquisition equipment, cross-hole seismic acquisition technology is getting mature, providing better data for imaging. According to the features of cross-hole survey and cross-hole data, we put forward a reverse-time migration method which is suitable for the wave equation for cross-hole seismic data. We propose finite difference scheme of higher order, and then derive its stability condition in cross-hole seismic. The frequency dispersion problem in cross-hole seismic wave field extrapolation is also discussed. Cross correlation imaging condition is used to realize migration, and Laplace filter is applied to remove low-frequency noise from migration section. Thus finite-difference reverse-time migration method for cross-hole seismic is established. Finally, we build geological models with anomalous ellipsoids, and apply cross-hole seismic wave field simulation and migration to them, thus our method proves its effectiveness. When dealing with real cross-hole seismic data with this method, high-resolution migration sections can be achieved. Key words : Cross-hole seismic; Reverse-time migration; Model test

Time-lapse joint inversion of crosswell DC resistivity and seismic data: A numerical investigation

Time-lapse joint inversion of geophysical data is required to image the evolution of oil reservoirs during production and enhanced oil recovery, [Formula: see text] sequestration, geothermal fields during production, and to monitor the evolution of contaminant plumes. Joint inversion schemes reduce space-related artifacts in filtering out noise that is spatially uncorrelated, and time-lapse inversion algorithms reduce time-related artifacts in filtering out noise that is uncorrelated over time. There are several approaches that are possible to perform the joint inverse problem. In this work, we investigate the structural crossgradient (SCG) joint inversion approach and the crosspetrophysical (CP) approach, which are appropriate for time-lapse problems. In the first case, the inversion scheme looks for models with structural similarities. In the second case, we use a direct relationship between the geophysical parameters. Time-lapse inversion is performed with an actively time-constrained (ATC) approach. In this approach, the subsurface is defined as a space-time model. All the snapshots are inverted together assuming a regularization of the sequence of snapshots over time. First, we showed the advantage of combining the SCG or CP inversion approaches and the ATC inversion by using a synthetic problem corresponding to crosshole seismic and DC-resistivity data and piecewise constant resistivity and seismic velocity distributions. We also showed that the combined SCG/ATC approach reduces the presence of artifacts with respect to individual inversion of the resistivity and seismic data sets, as well as with respect to the joint inversion of both data sets at each time step. We also performed a synthetic study using a secondary oil recovery problem. The combined CP/ATC approach was successful in retrieving the position of the oil/water encroachment front.

Crosshole traveltime tomography using particle swarm optimization: A near-surface field example

Particle swarm optimization (PSO) is a relatively new global optimization approach inspired by the social behavior of bird flocking and fish schooling. Although this approach has proven to provide excellent convergence rates in different optimization problems, it has seldom been applied to inverse geophysical problems. Until today, published geophysical applications mainly focus on finding an optimum solution for simple, 1D inverse problems. We have applied PSO-based optimization strategies to reconstruct 2D P-wave velocity fields from crosshole traveltime data sets. Our inversion strategy also includes generating and analyzing a representative ensemble of acceptable models, which allows us to appraise uncertainty and nonuniqueness issues. The potential of our strategy was tested on field data collected at a well-constrained test site in Horstwalde, Germany. At this field site, the shallow subsurface mainly consists of sand- and gravel-dominated glaciofluvial sediments, which, as known from several boreholes and other geophysical experiments, exhibit some well-defined layering at the scale of our crosshole seismic data. Thus, we have implemented a flexible, layer-based model parameterization, which, compared with standard cell-based parameterizations, allows for significantly reducing the number of unknown model parameters and for efficiently implementing a priori model constraints. Comparing the 2D velocity fields resulting from our PSO strategy to independent borehole and direct-push data illustrated the benefits of choosing an efficient global optimization approach. These include a straightforward and understandable appraisal of nonuniqueness issues as well as the possibility of an improved and also more objective interpretation.

Crosshole seismic tomography including the anisotropy effect

Velocity anisotropy caused by fine layering has a strong effect on the travel paths at large vertical offsets in crosshole seismic data. This effect must be considered in seismic waveform tomography, so that the inversion procedure can match the waveforms in real data. In this paper, we propose to properly take into account this anisotropic effect in two stages. First, we invert for the anisotropy parameter simultaneously with the (horizontal) velocity in travel time tomography. Then we incorporate this estimated anisotropy parameter model in the waveform simulation during waveform tomography, to refine the velocity image. When considering this anisotropic effect, far-offset data are properly used in the inversion, then both travel time and waveform tomography may have a better ray coverage, producing a velocity image with a higher resolution.

Anisotropic seismic inversion using a multigrid Monte Carlo approach

We propose a new approach for the inversion of anisotropic P-wave data based on Monte Carlo methods combined with a multigrid approach. Simulated annealing facilitates objective minimization of the functional characterizing the misfit between observed and predicted traveltimes, as controlled by the Thomsen anisotropy parameters (ɛ, δ). Cycling between finer and coarser grids enhances the computational efficiency of the inversion process, thus accelerating the convergence of the solution while acting as a regularization technique of the inverse problem. Multigrid perturbation samples the probability density function without the requirements for the user to adjust tuning parameters. This increases the probability that the preferred global, rather than a poor local, minimum is attained. Undertaking multigrid refinement and Monte Carlo search in parallel produces more robust convergence than does the initially more intuitive approach of completing them sequentially. We demonstrate the usefulness of the new multigrid Monte Carlo (MGMC) scheme by applying it to (a) synthetic, noise-contaminated data reflecting an isotropic subsurface of constant slowness, horizontally layered geologic media and discrete subsurface anomalies; and (b) a crosshole seismic data set acquired by previous authors at the Reskajeage test site in Cornwall, UK. Inverted distributions of slowness (s) and the Thomson anisotropy parameters (ɛ, δ) compare favourably with those obtained previously using a popular matrix-based method. Reconstruction of the Thomsen ɛ parameter is particularly robust compared to that of slowness and the Thomsen δ parameter, even in the face of complex subsurface anomalies. The Thomsen ɛ and δ parameters have enhanced sensitivities to bulk-fabric and fracture-based anisotropies in the TI medium at Reskajeage. Because reconstruction of slowness (s) is intimately linked to that ɛ and δ in the MGMC scheme, inverted images of phase velocity reflect the integrated effects of these two modes of anisotropy. The new MGMC technique thus promises to facilitate rapid inversion of crosshole P-wave data for seismic slownesses and the Thomsen anisotropy parameters, with minimal user input in the inversion process.

Seismic first-arrival tomography with functional description of traveltimes

A two-dimensional smoothness-constrained least-squares inversion scheme was applied to seismic first-arrival time data. The inversion scheme was based on the functional description of traveltimes; thus, it did not require a step of ray tracing, and traveltimes were obtained by a finite-difference eikonal solver. The Laplacian difference of cell slownesses was used for the smoothness constraint. Model velocities were obtained by matrix inversion including the QR decomposition and iterative LSQR method. The Jacobian matrix of the partial derivatives was constructed by a finite-difference approximation based on the perturbation of the cell slowness. Since the construction of the Jacobian matrix was the most time-consuming step of the inversion scheme, Broyden's update was used for this matrix, and it was replaced by its numerical approximation obtained from Broyden's method after the third iteration and for all subsequent iterations to expedite the inversion process. This significantly improved the computational performance of the scheme by reducing the computer time for the calculation of the Jacobian matrix. The algorithm was tested by using a number of synthetic and field data sets. The test studies included both surface seismic refraction and crosshole seismic data acquisition configurations. Also image appraisal analyses were performed for the solutions obtained from both surface and crosshole field data sets by calculating model covariance and model resolution matrices. The presented algorithm yielded satisfactory results during the test studies. The stability and fast convergence rate were the main characteristics of the algorithm.

Inversion of crosshole seismic data in heterogeneous environments: Comparison of waveform and ray-based approaches

High-resolution tomographic imaging of the shallow subsurface is becoming increasingly important for a wide range of environmental, hydrological and engineering applications. Because of their superior resolution power, their sensitivity to pertinent petrophysical parameters, and their far reaching complementarities, both seismic and georadar crosshole imaging are of particular importance. To date, corresponding approaches have largely relied on asymptotic, ray-based approaches, which only account for a very small part of the observed wavefields, inherently suffer from a limited resolution, and in complex environments may prove to be inadequate. These problems can potentially be alleviated through waveform inversion. We have developed an acoustic waveform inversion approach for crosshole seismic data whose kernel is based on a finite-difference time-domain (FDTD) solution of the 2-D acoustic wave equations. This algorithm is tested on and applied to synthetic data from seismic velocity models of increasing complexity and realism and the results are compared to those obtained using state-of-the-art ray-based traveltime tomography. Regardless of the heterogeneity of the underlying models, the waveform inversion approach has the potential of reliably resolving both the geometry and the acoustic properties of features of the size of less than half a dominant wavelength. Our results do, however, also indicate that, within their inherent resolution limits, ray-based approaches provide an effective and efficient means to obtain satisfactory tomographic reconstructions of the seismic velocity structure in the presence of mild to moderate heterogeneity and in absence of strong scattering. Conversely, the excess effort of waveform inversion provides the greatest benefits for the most heterogeneous, and arguably most realistic, environments where multiple scattering effects tend to be prevalent and ray-based methods lose most of their effectiveness.

Rapid Method for Acoustic Wave‐Equation WTW Inversion of Crosshole Seismic Data

AbstractWTW is a hybrid inversion method of wave‐equation traveltime inversion (WT) and waveform inversion. Wave function is used to calculate the traveltime and derivative (perturbation of traveltime with respect to velocity) in WT. Unlike traditional ray‐based travetime inversion, WT has many advantages. No ray tracing or traveltime picking and no high frequency assumption is necessary and good result can be got while starting model is far from real model. Comparing with waveform inversion, WT has low resolution. Complementary to WT, waveform inversion has high resolution, but easily sticks in local minima when starting model is far from real model. So WTW is a good hybrid inversion method. Traditional WTW is to first reconstruct the smooth characters of model with WT inversion being primary and then reconstruct the detailed characters of model with waveform inversion being primary. But the computation time and memory using of this method are twice of that of WT inversion or waveform inversion. So a simplified method is used actually. That is to first use WT singly and then waveform inversion singly. Advantages and disadvantages of two inverse methods are not sufficiently complement for iterations with simplified method, this affects the inverse result. This paper proposes a new method to implement WTW and computation time and memory using are same with that of WT or waveform inversion. Model calculation shows the new method has better convergence.

Integration of diverse physical-property models: Subsurface zonation and petrophysical parameter estimation based on fuzzy c -means cluster analyses

Inversions of an individual geophysical data set can be highly nonunique, and it is generally difficult to determine petrophysical parameters from geophysical data. We show that both issues can be addressed by adopting a statistical multiparameter approach that requires the acquisition, processing, and separate inversion of two or more types of geophysical data. To combine information contained in the physical-property models that result from inverting the individual data sets and to estimate the spatial distribution of petrophysical parameters in regions where they are known at only a few locations, we demonstrate the potential of the fuzzy [Formula: see text]-means (FCM) clustering technique. After testing this new approach on synthetic data, we apply it to limited crosshole georadar, crosshole seismic, gamma-log, and slug-test data acquired within a shallow alluvial aquifer. The derived multiparameter model effectively outlines the major sedimentary units observed in numerous boreholes and provides plausible estimates for the spatial distributions of gamma-ray emitters and hydraulic conductivity.

Crosshole seismic inversion with normalized full‐waveform amplitude data

We investigate a simple scheme for full‐waveform amplitude spectrum inversion of crosshole seismic data with an unknown source wavelet. The method is based on our 2D/2.5D finite‐element method of acoustic‐wave modeling. The normalized amplitude data, defined as the spectral ratio of the original trace amplitude to the average amplitude for the entire common shot gather, are used for full‐waveform inversion in the frequency domain. In essence, the normalization of amplitudes removes the source wavelet and is easily carried out in the time domain or frequency domain from crosshole seismic surveying. Two synthetic models, simulating, respectively, a dipping fracture model and a complicated sedimentary structure, are examined with the inversion scheme. The numerical results show that clear images of the targets can be obtained by using the single‐ and multiple‐frequency data. For comparison, two other amplitude inversion schemes in which the source signatures are known and estimated with an iterative procedure were carried out for the same models. The results show that the iteratively source‐estimated procedure also produces satisfactory images of the velocity structure and yields an approximate amplitude of the source wavelet. With the multifrequency data, three such schemes yield very competitive results.

Porosity of fluid-saturated porous media from measured seismic wave velocities

This paper presents a novel procedure for determining porosity in fluid-saturated porous media from measured shear and dilatational wave velocities. The method is developed using the theory of linear poroelasticity in the low-frequency limit, which is equivalent to considering the fluid-saturated porous medium as a closed (un-drained) system with the pore fluid moving in phase with the soil skeleton. The new procedure for the in-situ measurement of porosity has been applied at two sites in Italy using cross-hole seismic data. The results obtained are in excellent agreement with independent laboratory data gathered from undisturbed soil specimens.