P-wave Impedance Research Articles

Nonlinear inversion based on Metropolis sampling algorithm

Nonlinear inversion based on Metropolis sampling algorithm is formulated in the Bayesian framework. As one kind of Monte Carl non-linear inversions, it can effectively integrate high frequency information of well logging data, and obtain inversion results with a higher resolution. Firstly, we get the priori information through fast Fourier transform moving average (FFT-MA) and gradual deformation method (GDM). Second, we structure likelihood function. Then we apply Metropolis algorithm in order to obtain an exhaustive characterization of the posteriori probability density. FFT-MA is a kind of efficient simulation method. Combined with GDM, it can constantly modify reservoir model and keep the spatial structure unchanged until it matches the observed seismic data. According to the model trial and real data processing, we can conclude that nonlinear inversion based on Metropolis sampling algorithm provide reasonable elastic parameter information, especially it improves the resolution of P-wave velocity. Even when the signal noise ratio (SNR) is relatively low, it can still show reasonable elastic parameter information, which proves the effectiveness of the proposed method. The inversion resolution of P-wave and S-wave impedances is higher than elastic parameters inversion if we do not consider the noise. ©, 2015, Science Press. All right reserved.

Pore-scale modeling of elastic wave propagation in carbonate rocks

The relationship between P-wave velocity and porosity in carbonate rocks shows a high degree of variability due to the complexity of the pore structure. This variability introduces high uncertainties to seismic inversion, amplitude variation with offset analysis, porosity estimation, and pore-pressure prediction based on velocity data. Elastic wave propagation in porous media is numerically modeled on the pore scale to investigate the effects of pore structure on P-wave velocities in carbonate rocks. We built 2D models of porous media using pore structure information and the similarity principle. Then, we simulated normal incidence wave propagation using finite element analysis. Finally, the velocity was determined from received modeled signals by means of crosscorrelation. The repeatability and accuracy of this modeling process was verified carefully. Based on the modeling results, a simple formulation of Sun’s frame flexibility factor ([Formula: see text]), aspect ratio (AR, the ratio of the major axis to the minor axis), and pore density was developed. The numerical simulation results indicated that the P-wave velocity increases as a power function as the AR increases. Pores with small AR ([Formula: see text]) or large [Formula: see text] created softening effects that decrease P-wave velocity significantly. The P-wave velocity of carbonate rocks was dispersive; it depends on the ratio of the wavelength to pore size ([Formula: see text]). Such scale-dependent dispersion was more evident for carbonate rocks with higher porosity, lower AR, and/or lower P-wave impedance of pore fluids. The P-wave velocity of carbonate rocks with complicated pore geometries (low AR, high [Formula: see text], small [Formula: see text]) was much lower than that of rocks with simple pore geometries (high AR, small [Formula: see text], large [Formula: see text]) at low and high [Formula: see text]. The pore-scale modeling of elastic wave properties of porous rocks may explain the poor velocity-porosity correlation in carbonate rocks.

Seismic prediction of sweet spots in the Da'anzhai shale play, Yuanba area, the Sichuan Basin

Burial depth, thickness, total organic carbon (TOC) content, brittleness and fracture development of shale reservoirs are the main geologic indexes in the evaluation of sweet spots in shale gas plays. Taking the 2nd interval of Da'anzhai shale of the Lower Jurassic as the study object, a set of techniques in seismic prediction of sweet spots were developed based on special processing of seismic data and comprehensive analysis of various data based on these geologic indexes. First, logging and seismic responses of high quality shales were found out through fine calibration of shale reservoir location with seismogram, which was combined with seismic facies analysis to define the macroscopic distribution of the shale. Then, seismic impedance inversion and GR inversion were used to identify shale from limestone and sandstone. Based on statistical analysis of sensitive parameters such as TOC, the uranium log inversion technique was used to quantitatively predict TOC of a shale reservoir and the thickness of a high quality shale reservoir. After that, fracture prediction technique was employed to predict play fairways. Finally, the pre-stack joint P-wave and S-wave impedance inversion technique was adopted to identify shales with high brittleness suitable for hydraulic fracturing. These seismic prediction techniques have been applied in sorting out sweet spots in the 2nd interval of the Da'anzhai shale play of the Yuanba area, and the results provided a sound basis for the optimization of horizontal well placement and hydraulic fracturing.

Fracture filling fluids identification using azimuthally elastic impedance based on rock physics

Abstract Fracture filling fluids identification is an important aspect of fractured reservoirs description. It is well known that fracture weaknesses parameters (the normal and tangential weaknesses) are closely related to fracture parameters (fracture density, fracture aspect ratio and fracture fillings). Hence, the fracture filling fluids can be identified after the fracture weaknesses parameters being obtained. The efficient method, which is presented to estimate the fracture weaknesses parameters in this paper, is azimuthally elastic impedance (EI) inversion. We first derive a new azimuthal EI equation which contains fracture weaknesses parameters. Using the formula, we propose a method of seismic inversion for elastic parameters (P-wave and S-wave impedances) and fracture weaknesses parameters. The fluid factor, which is introduced to identify the fluids in fractures, can be estimated after the calculation of elastic and fracture weaknesses parameters. Tests on real data show that the method is more stable and reasonable by reducing the uncertainty for the estimation of elastic parameters and fracture weaknesses parameters. The inverted results are in good agreement with the results of well log data.

Dynamic elastic properties of the Wufeng–Longmaxi formation shale in the southeast margin of the Sichuan Basin

In spite of the growing interest in Late Ordovician to the Early Silurian Wufeng–Longmaxi black shale for gas production in the southeast of the Sichuan Basin, little data is available on the acoustic properties of these shale reservoirs. The dynamic elastic properties of a suite of shales from this formation with different organic matter content were measured using the ultrasonic transmission technique at a range of confining pressures. The mineralogical features and reservoir space types were studied with the goal of analyzing their influence on the acoustic properties of the shale samples. The TOC (total organic content) is found to have a positive correlation with the quartz content and a negative correlation with the clay content. Organic matter pores and inter-crystal micro-pores are the main pore types. Organic-rich shales show a low P-wave impedance (Ip) and Vp/Vs ratio due to relatively higher TOC and quartz content; nonetheless, high P-wave (Ip) is also observed when the quartz content is very high resulting from the variation of load-bearing grains. The velocities and anisotropy of different shale samples show varying pressure dependence. A strong positive correlation is found between the anisotropy and the clay content. Three different types of microfabric can be observed in the shale samples, giving a qualitative explanation for the correlation between the anisotropy and the clay content. The occurrence of preferential alignment of the clay minerals requires that the clay content exceeds a critical volume, and this value is about 25%–30% in this study.

Prestack seismic inversion versus neural-network analysis: A case study in the Scarab field offshore Nile Delta, Egypt

In clastic depositional systems such as those encountered in the Nile Delta Basin, simultaneous prestack seismic-amplitude inversion is an effective method for detecting and appraising gas-bearing sandstone reservoirs. However, the method has limitations concerning the requirement of a reliable set of wavelets, suitable wireline logs, and a sufficiently dense initial model. The neural-network analysis method is an alternative technique which sometimes can provide similar or better results and does not require significant volumes of data. Simultaneous prestack inversion was applied over the Scarab field, West Delta Deep Marine concession, offshore Egypt. The field comprises submarine channel-based gas reservoirs that extend laterally over 20 km2. Six wells were analyzed in a rock-physics study prior to performing inversion. Three angle gathers (near: 0–15°; mid: 15–30°; far: 30–45°) were inverted for P-wave impedance (ZP), S-wave impedance (ZS), P-wave velocity (VP), S-wave velocity (VS), VP/VS, and density (ρ) using the prestack inversion method. Neural-network analysis was performed using full-stack seismic data along with well logs in the training stage, followed by cross-validation of results and rendering of VP, VS, VP/VS, and density volumes. The VP/VS volumes produced from the two methods were used to infer water saturation (Sw). Direct comparisons were made between neural-network and prestack inversion results at a blind-well location to assess the relative quality of each method. Results suggest that application of the proposed neural-network method leads to reliable inferences. Hence, using the neural-network method alone or along with the prestack inversion method has a positive impact on reserves growth and increased production.

From qualitative to quantitative interpretation: An interpreter’s guide to fluid prediction in Pliocene to Turonian deepwater turbidites from West Africa to Asia Pacific

To mitigate exploration risk in deepwater settings, subsurface analysis increasingly has to rely on integration of qualitative with quantitative techniques. To predict pay in turbidite sandstones, proven statistical and analytical methods can routinely be run on well and seismic inversion data. However, quantitative interpretation (QI) should begin with a responsible audit of available well logs and seismic data, succeeded by data conditioning, proceeding with quality control, and placing elastic attribute responses within their geologic context. To address these issues, we evaluate geologic controls on porosity change as manifested by overpressure and compaction on calibration and analysis of elastic attributes. Following calibration of seismic inversion data, we provide tutorial-style interpretations of deepwater clastic reservoirs from the Gulf of Guinea, West Africa, to the Sabah trough, Borneo. Case study examples offer interpreters the potential to use workflows surrounding data mining in exploration or during field development. In our first example, a comparison of univariate statistics run on compressional- and shear-wave impedances and Poisson’s ratio is introduced to potentially data mine 3D seismic over turbidite fairways. Joint interpretation of P-wave and S-wave impedances is combined with innovative uses of bivariate statistical analysis for anomaly detection. Additionally, the geologic rationale of interpreting elastic relationships of calibrated attributes, such as Lambda Rho and Mu Rho, is discussed on the seismic scale of a single reservoir layer using a combination of statistical methods and rock physics. Here, qualitative interpretation, via application of principles from seismic stratigraphy and seismic geomorphology, ultimately unlocks ambiguity in rock-physics-driven, quantitative lithology determination, guiding application of QI routines toward correctly predicting the prevailing fluid type. Elastic calibration permits seismic lithofacies classification of Cretaceous turbidite sandstones deposited as middle to lower slope channels canyon-fill and basin-floor channel complexes.

Integration of crosswell seismic data for simulating porosity in a heterogeneous carbonate aquifer

Abstract A challenge for the geostatistical simulation of subsurface properties in mining, petroleum and groundwater applications is the integration of well logs and seismic measurements, which can provide information on geological heterogeneities at a wide range of scales. This paper presents a case study conducted at the Port Mayaca aquifer, located in western Martin County, Florida, in which it is of interest to simulate porosity, based on porosity logs at two wells and high-resolution crosswell seismic measurements of P-wave impedance. To this end, porosity and impedance are transformed into cross-correlated Gaussian random fields, using local transformations. The model parameters (transformation functions, mean values and correlation structure of the transformed fields) are inferred and checked against the data. Multiple realizations of porosity can then be constructed conditionally to the impedance information in the interwell region, which allow identifying one low-porosity structure and two to three flow units that connect the two wells, mapping heterogeneities within these units and visually assessing fluid paths in the aquifer. In particular, the results suggest that the paths in the lower flow units, formed by a network of heterogeneous conduits, are not as smooth as in the upper flow unit.

3D coupled acoustic-elastic migration with topography and bathymetry based on spectral-element and adjoint methods

In the context of the adjoint method, we considered 3D coupled acoustic-elastic migration in the presence of surface topography and/or bathymetry. Isotropic elastic imaging involves three primary kernels, related to mass density and shear and bulk moduli, and various secondary kernels, for example, related to P-wave impedance and compressional and shear-wave speeds. Similar to reverse-time migration, these kernels reflect the constructive interference between a forward wavefield generated by active sources and an adjoint wavefield triggered by simultaneously back propagating recorded reflections from all receivers. Forward and adjoint wavefields were simulated using a spectral-element method, which, due to its weak nature, captures free-surface topography in land surveys and bathymetry in marine acquisition. To avoid storing the entire 3D forward wavefield, required for calculating its interaction with the adjoint wavefield, we only saved information on domain boundaries and reconstructed the forward wavefield while simulating the adjoint wavefield. Their interactions were calculated and integrated on the fly, thereby eliminating storage issues but doubling memory and CPU requirements. Our 3D images confirmed a previous conclusion based on 2D simulations, namely, that the impedance kernel best highlights reflectors, whereas wave-speed kernels constrain large-scale structures, i.e., the background model.

Study of S-wave ray elastic impedance for identifying lithology and fluid

In this paper, we derive an approximation of the SS-wave reflection coefficient and the expression of S-wave ray elastic impedance (SREI) in terms of the ray parameter. The SREI can be expressed by the S-wave incidence angle or P-wave reflection angle, referred to as SREIS and SREIP, respectively. Our study using elastic models derived from real log measurements shows that SREIP has better capability for lithology and fluid discrimination than SREIS and conventional S-wave elastic impedance (SEI). We evaluate the SREIP feasibility using 25 groups of samples from Castagna and Smith (1994). Each sample group is constructed by using shale, brine-sand, and gas-sand. Theoretical evaluation also indicates that SREIP at large incident angles is more sensitive to fluid than conventional fluid indicators. Real seismic data application also shows that SREIP at large angles calculated using P-wave and S-wave impedance can efficiently characterize tight gas-sand.

Azimuthal reflectivity inversion

Seismic fracture prediction is becoming a more important exploration and development problem with the growing focus on unconventional reservoirs. A non-linear inversion technique is presented to estimate layer-based fracture parameters and velocities based on azimuthal reflectivity data. The earth model assumes a single set of vertical fractures per layer parameterized in terms of linear slip parameters - the normal and tangential fracture weaknesses - and fracture strike. In addition, the background P-wave and S-wave impedances are estimated. Either the exact Zoeppritz equation or some linearization thereof is used in a convolutional modelling scheme to estimate seismic amplitude data. The inverse problem is solved in a nonlinear fashion using simulated annealing. The new technique has several advantages over performing azimuthal amplitude versus angle analysis (AVAz). The reflectivity calculation used in the new technique is more theoretically correct, allowing for the symmetry plane to change as a function of layer. The 90 degree ambiguity in estimating the symmetry plane typical of the near offset approximation also disappears. Further, there is an improvement in the isotropic parameter estimates compared to isotropic inversion since the bias introduced by neglecting anisotropy has been removed by incorporating it into the forward model. The azimuthal inversion is demonstrated on both synthetic and real seismic data.

Resource assessment based on 4D seismic and inversion at Ringhorne Field, Norwegian North Sea

Time-lapse (4D) seismic data from Ringhorne Field in the North Sea are used to monitor water movement in both Paleocene- and Jurassic-age reservoir sands, improve existing geologic and simulation models, and enable more cost-effective field operations. The structural complexity of the reservoirs, their proximity to the high-impedance Cretaceous chalk, and a relatively small 4D response has required a significant effort in seismic acquisition and processing which resulted in highly repeatable surveys (Johnston et al., 2010). In addition to the 4D interpretation, VP/VS derived from simultaneous elastic inversion is diagnostic of sand and provides additional constraints on Ringhorne subsurface models. Connected volumes based on VP/VS correlate to areas of water sweep seen in the 4D data and reduce uncertainty in 4D interpretation. Relative P-wave impedance changes calculated from inversion are consistent with presurvey 4D predictions. The 4D seismic data and inversion help explain water breakthrough timing, improve our understanding of field production history, and have resulted in the identification of additional infill well opportunities.

AMPLITUDE VERSUS OFFSET (AVO) TECHNIQUE FOR LIGHT HYDROCARBON EXPLORATION: A CASE STUDY

AVO as a known methodology is used to identify fluid type and reservoir lithology in subsurface exploration. Method discussed in this paper, consists of three stages, including: Direct modeling, Inverse modeling and Cross plot interpretation. By direct modeling we can clarify lithology or fluid dependent attributes. Analysis performed using both P-P and P-Sv attributes. Inverse modeling deals with real data and is fed by the results of direct modeling to identify the light hydrocarbon (gas) zones. The main role of cross plot interpretation is to confirm the inverse modeling results and consequently increasing validity of performed analysis. Using Hodogram – cross plot, makes possible to identify hydrocarbon zone even in small scales. This methodology was applied in Gorgan Plain Southeast Caspian, northern Iran. It was concluded that: fluid factor, SIGN, and Poisson reflectivity are fluid dependent attributes. It was also defined that normal incidence reflectivity and P-wave impedance reflectivity are lithology dependent. Inverted sections of fluid-dependent attributes defined the existence two light hydrocarbon accumula- tion under the Tertiary-Cretaceous unconformity in the North Gorgan Plain. Two wet and gaseous zones are also confirmed by cross plot.

Spectral decomposition aids AVO analysis in reservoir characterization: A case study of Blackfoot field, Alberta, Canada

Blackfoot field, Alberta, Canada, has produced oil and gas from a Glauconitic compound incised valley-system. In this area channels can be filled with sands and/or shales. Differentiation of prospective channel sands and non-productive shales was always problematic due to the similarity in P-wave impedance of these two lithotypes. We study the spectral decomposition response to the hydrocarbons presence in the Glauconitic channel of Early Cretaceous age. From previous AVO analysis and modeling, a strong Class III AVO anomaly has been observed at the top of the porous sandstone in the upper valley, whereas shale had a very different AVO response. Furthermore, AVO inversion revealed additional information about lithology and fluid content in the channel. Our workflow starts from selecting a continuous horizon that was close and conforms to the channel interval; we then run spectral analyses for the channel area. Short Window Fourier Transform workflow could successfully image the channel's stratigraphic features and confirm results obtained from AVO analysis and inversion run on the data before being stacked. Additionally, the producing oil wells in the sand-fill channel were found to be correlating with high spectrum amplitude; while the dry wells in the shale-plugged channel fell in low amplitude anomaly.

4D Joint Stratigraphic Inversion of Prestack Seismic Data: Application to the CO2Storage Reservoir (Utsira Sand Formation) at Sleipner Site

Seismic monitoring is commonly used in the oil industry to follow the evolution of reservoir properties during production. We present a methodology of time-lapse (or 4D) stratigraphic inversion, which is able to provide an estimation of P- and S-wave impedance variations in the reservoir by inverting prestack time-lapse seismic data. The 4D inversion is implemented in the time domain and requires a time scaling law for each repeated seismic dataset in order to adjust the arrival times of homologous events observed in the so-called reference and monitor datasets. This operation is often referred to as the warping problem. The 4D inversion is a 3-step methodology. The first step consists in inverting each seismic vintage independently, thus providing as many P- and S-wave impedance distributions as datasets considered. The second step uses the available P-wave impedance information to solve the warping problem which is crucial to the third and final step: the joint inversion of all available seismic vintages.This 4D inversion sequence was applied to seismic datasets recorded on the Norwegian CO<sub>2<sub/> storage reservoir of Sleipner field located in the North Sea. The latter is becoming a reference industrial site for the long-term storage of carbon dioxide (CO<sub>2<sub/>) in a saline aquifer, the Utsira sand formation. We focused our 4D inversion study on the 1994 and 2006 vintages acquired two years before and ten years after the beginning of CO<sub>2<sub/> injection, respectively. The warping correction resulted in a time-scaling law with a maximum pushdown effect of about 45 ms at the base of the Utsira aquifer. The joint 4D inversion results show more consistency than the single 3D inversion results: the 4D inversion notably provides P-wave impedances for the CO<sub>2<sub/> -saturated sandstones which are close to the values derived from rock physics studies.

Subducted lithosphere beneath the Kuriles from migration of PP precursors

We seismically image both thermal and chemical heterogeneity of the mantle beneath the Kurile subduction zone using P-wave energy reflected from the underside of discontinuities, arriving as precursors to the seismic phase PP. We take advantage of new broadband seismic data provided by the High Lava Plains Seismic Experiment and EarthScope's USArray, collecting a dataset of 31 high-quality Sumatran earthquakes sampling beneath the Kuriles. We employ high-resolution array analysis techniques, including migration and vespagrams, to identify precursory arrivals and study lateral variations in discontinuity depth, sharpness, and impedance of the mantle transition zone. We find the 410 km boundary is at 395 km near the subducting Kurile slab, though the boundary is 410–425 km deep elsewhere. In regions away from subduction, we do not detect a laterally continuous underside reflection of P-waves from the 660 km discontinuity. However, in the vicinity of the subducting Kurile slab, we detect robust P660P reflections from interfaces near 620–670 km depth, signifying an increase in the impedance contrast at 660 km depth. We also detect deeper reflectors, down to 720 km depth, beneath the Kurile slab in a localized area. Cold, aluminum-depleted harzburgitic lithosphere residing at the base of the transition zone best explains the local enhancement of the 660 km discontinuity P-wave impedance contrast. Our new discontinuity measurements support the hypothesis of cold, depleted lithosphere stagnating at the 660 km discontinuity beneath the Kuriles subduction zone, and imply the 660 km boundary can locally impede mantle flow and produce chemical heterogeneity within the transition zone.

Preselection of Reservoir Models From a Geostatistics-Based Petrophysical Seismic Inversion

Summary A new geostatistics-based seismic-inversion method is introduced in this paper for determining reservoir models consistent with base seismic information. The proposed methodology entails two steps, with only the second being examined in this paper. First, cubes of acoustic velocities or impedances are derived from seismic inversion. Second, these data are incorporated into a matching process to identify reservoir models leading to acoustic responses close to the reference acoustic data. The parameterization of the facies and petrophysical properties populating the reservoir models is based upon the gradual-deformation method (GDM), which relies on geostatistical concepts. This particular feature makes it possible to change the spatial distribution of the property of interest from a few parameters while preserving its spatial variability. The matching process is driven from a global optimization algorithm known as the particle-swarm optimization (PSO). Such a global approach is reasonable for the problem considered because the forward modeling is very fast. A variant of the PSO algorithm is implemented to take advantage of the GDM properties. This approach yields reservoir models that honor the seismic data better than those derived from stochastic simulation only with seismic used as a secondary variable. A numerical experiment is then presented to stress the applicability of the proposed matching methodology: The GDM-based PSO approach is used to identify facies reservoir models and water/oil contact consistent with some reference acoustic P-wave impedances.

Effects of P-Wave and S-Wave Impedance Contrast on the Characteristics of Basin Transduced Rayleigh Waves

Different aspects of body wave amplifications in a basin have been studied in detail in the past. However, the study on amplification of basin-transduced surface waves is very limited, although surface waves are more damaging as compared to body waves. This paper presents the effects of P-wave and S-wave impedance contrast (IC) at the basin-edge on the spectral amplification and complex mode transformation of basin-transduced Rayleigh (BTR) waves. BTR-waves, the acronym for basin-transduced Rayleigh waves, is used in the manuscript. Analysis of simulated results reveals a complex mode transformation of Rayleigh wave after entering the basin. The less dispersed horizontally polarised first mode and highly dispersed vertically polarised fundamental mode of BTR-waves were inferred in the basin. The first mode of BTR-waves is developed in a frequency bandwidth and the frequency content in that is very much dependent on the Poisson’s ratio and fundamental frequency of soil in the basin. An increase of phase velocity of first mode of BTR-waves with Poisson’s ratio is obtained. It is concluded that spectral amplification of BTR-waves depends on both the P-wave IC and S-wave IC at the basin-edge. An increase of the largest and average spectral amplifications of the horizontal component of the BTR-wave is obtained with the increase of both the P-wave IC and S-wave IC. On the other hand, an increase of the largest and average spectral amplification of the vertical component of the BTR-wave is obtained with the increase of P-wave IC, but such a systematic and significant effect is not inferred with the increase of S-wave IC at the basin-edge.

AVA inversion of the top Utsira Sand reflection at the Sleipner field

Amplitude variation with angle (AVA) inversion is performed on the top Utsira Sand reflector at the Sleipner field, North Sea, Norway. This interface is of particular interest because of the accumulation of [Formula: see text] injected from a point deeper in the Utsira Sand. The focus is on the postmigration processing of angle gathers together with the actual inversion procedure. The processing treats amplitude extraction, offset-to-angle mapping, and global scaling in detail. Two algorithms are used for the inversion of AVA data, one that assesses uncertainties and one fast least-squares variant. Both are very suitable for this type of problem because of their covariance matrices and built-in regularization. In addition, two three-parameter approximations of the Zoeppritz equations are used. One is linear approximation and the other is quadratic. The results show significant signals for all three elastic parameters, but the substitution of brine by [Formula: see text] using Gassmann’s equation indicates that the contrasts in S-wave impedance and density are overestimated. For the contrasts in P-wave impedance the results are in agreement with the fluid substitution. A simple sensitivity analysis shows that the offset-to-angle mapping and the damping factor in the inversion are the most plausible explanations of the discrepancy.

Fast probabilistic nonlinear petrophysical inversion

We have developed an extension of the mixture-density neural network as a computationally efficient probabilistic method to solve nonlinear inverse problems. In this method, any postinversion (a posteriori) joint probability density function (PDF) over the model parameters is represented by a weighted sum of multivariate Gaussian PDFs. A mixture-density neural network estimates the weights, mean vector, and covariance matrix of the Gaussians given any measured data set. In one study, we have jointly inverted compressional- and shear-wave velocity for the joint PDF of porosity, clay content, and water saturation in a synthetic, fluid-saturated, dispersed sand-shale system. Results show that if the method is applied appropriately, the joint PDF estimated by the neural network is comparable to the Monte Carlo sampled a posteriori solution of the inverse problem. However, the computational cost of training and using the neural network is much lower than inversion by sampling (more than a factor of 104 in this case and potentially a much larger factor for 3D seismic inversion). To analyze the performance of the method on real exploration geophysical data, we have jointly inverted P-wave impedance and Poisson’s ratio logs for the joint PDF of porosity and clay content. Results show that the posterior model PDF of porosity and clay content is a good estimate of actual porosity and clay-content log values. Although the results may vary from one field to another, this fast, probabilistic method of solving nonlinear inverse problems can be applied to invert well logs and large seismic data sets for petrophysical parameters in any field.