Unilateral Alignment: An interpretable machine learning method for geophysical logs calibration

Most of the existing machine learning studies in logs interpretation do not consider the data distribution discrepancy issue,so the trained model cannot well generalize to the unseen data without calibrating the logs.In this paper,we formulated the geophysical logs calibration problem and give its statistical explanation,and then exhibited an interpretable machine learning method,i.e.,Unilateral Alignment,which could align the logs from one well to another without losing the physical meanings.The involved UA method is an unsupervised feature domain adaptation method,so it does not rely on any labels from cores.The experiments in 3 wells and 6 tasks showed the effectiveness and interpretability from multiple views.

Seismic noise attenuation using nonstationary polynomial fitting

We propose a novel method for seismic noise attenuation by applying nonstationary polynomial fitting （NPF）, which can estimate coherent components with amplitude variation along the event. The NPF with time-varying coefficients can adaptively estimate the coherent components. The smoothness of the polynomial coefficients is controlled by shaping regularization. The signal is coherent along the offset axis in a common midpoint （CMP） gather after normal moveout （NMO）. We use NPF to estimate the effective signal and thereby to attenuate the random noise. For radial events-like noise such as ground roll, we first employ a radial trace （RT） transform to transform the data to the time-velocity domain. Then the NPF is used to estimate coherent noise in the RT domain. Finally, the coherent noise is adaptively subtracted from the noisy dataset. The proposed method can effectively estimate coherent noise with amplitude variations along the event and there is no need to propose that noise amplitude is constant. Results of synthetic and field data examples show that, compared with conventional methods such as stationary polynomial fitting and low cut filters, the proposed method can effectively suppress seismic noise and preserve the signals.

A unified poroviscoelastic model with mesoscopic and microscopic heterogeneities

The wave-induced fluid flow(WIFF) is considered to be the main cause of dispersion and attenuation of seismic waves in fluid-saturated porous media. Among numerous theories, the mesoscopic and microscopic heterogeneities are considered to be the primary mechanisms causing the WIFF. Furthermore,in most rocks, the mesoscopic and microscopic heterogeneities exist simultaneously and can cause obvious transitions of the fast P-wave velocity, which means it is necessary to consider the influence of the two mechanisms on the dispersion and attenuation simultaneously. Numerous results have shown that the dispersions and attenuations caused by these two mechanisms can be approximated in terms of the Zener model. To combine the two mechanisms into a unified model, we introduce a new generalized Zener model into the Biot poroelasticity theory to obtain a new poroviscoelastic model. Comparisons between the numerical results and two groups of experimental data further confirm the validity of our new model.

Applying accurate gradients of seismic wave reflection coefficients (SWRC) to the inversion of seismic wave velocities

Through solving the Zoeppritz's partial derivative equations, we have obtained accurate partial derivatives of reflected coefficients of seismic wave with respect to Pand S-wave velocities.With those partial derivatives, a multi-angle inversion is developed for seismic wave velocities.Numerical examples of different formation models show that if the number of iterations goes over 10, the relative error of inversion results is less than 1%, whether or not there is interference among the reflection waves.When we only have the reflected seismograms of P-wave, and only invert for velocities of P-wave, the multi-angle inversion is able to obtain a high computation precision.When we have the reflected seismograms of both P-wave and VS-wave, and simultaneously invert for the velocities of P-wave and VS-wave, the computation precisions of VS-wave velocities improves gradually with the increase of the number of angles, but the computation precision of P-wave velocities becomes worse.No matter whether the reflected seismic waves from the different reflection interface are coherent or non-coherent, this method is able to achieve a higher computation precision.Because it is based on the accurate solution of the gradient of SWRCs without any additional restriction, the multi-angle inversion method can be applied to seismic inversion of total angles.By removing the difficulties caused by simplified Zoeppritz formulas that the conventional AVO technology struggles with, the multiangle inversion method extended the application range of AVO technology and improved the computation precision and speed of inversion of seismic wave velocities.

A wave propagation model with the Biot and the fractional viscoelastic mechanisms

Energy loss in porous media containing fluids is typically caused by a variety of dynamic mechanisms.In the Biot theory,energy loss only includes the frictional dissipation between the solid phase and the fluid phase,resulting in underestimation of the dispersion and attenuation of the waves in the low frequency range.To develop a dynamic model that can predict the high dispersion and strong attenuation of waves at the seismic band,we introduce viscoelasticity into the Biot model and use fractional derivatives to describe the viscoelastic mechanism,and finally propose a new wave propagation model.Unlike the Biot model,the proposed model includes the intrinsic dissipation of the solid frame.We investigate the effects of the fractional order parameters on the dispersion and attenuation of the P-and S-waves using several numerical experiments.Furthermore,we use several groups of experimental data from different fluid-saturated rocks to testify the validity of the new model.The results demonstrate that the new model provides more accurate predictions of high dispersion and strong attenuation of different waves in the low frequency range.

Jacobian matrix for the inversion of P-and S-wave velocities and its accurate computation method

The optimization inversion method based on derivatives is an important inversion technique in seismic data processing,where the key problem is how to compute the Jacobian matrix.The computation precision of the Jacobian matrix directly influences the success of the optimization inversion method.Currently,all AVO(Amplitude Versus Offset) inversion techniques are based on approximate expressions of Zoeppritz equations to obtain derivatives.As a result,the computation precision and application range of these AVO inversions are restricted undesirably.In order to improve the computation precision and to extend the application range of AVO inversions,the partial derivative equation(Jacobian matrix equation(JME) for the P-and S-wave velocities inversion) is established with Zoeppritz equations,and the derivatives of each matrix entry with respect to Pand S-wave velocities are derived.By solving the JME,we obtain the partial derivatives of the seismic wave reflection coefficients(RCs) with respect to P-and S-wave velocities,respectively,which are then used to invert for P-and S-wave velocities.To better understand the behavior of the new method,we plot partial derivatives of the seismic wave reflection coefficients,analyze the characteristics of these curves,and present new understandings for the derivatives acquired from in-depth analysis.Because only a linear system of equations is solved in our method,the computation of Jacobian matrix is not only of high precision but also is fast and efficient.Finally,the theoretical foundation is established so that we can further study inversion problems involving layered structures(including those with large incident angle) and can further improve computational speed and precision.

An Improved Method of Laser Particle Size Analysis and Its Applications in Identification of Lacustrine Tempestite and Beach Bar：An Example from the Dongying Depression

Grain size analysis is a common method in the study of sedimentology. For the consolidated sedimentary rocks, the traditional methods are rock slice observation and image analysis. In recent years, laser particle size analyzer is used widely in particle size analysis of sedimentary rock. Unlike the pretreatment of loose samples, the rock samples must be crushed, added acid to wipe out cement, and washed. However, in the step of washing, most of the fines component（less than 63 μm） in the suspended state should be inevitably lost. It will significantly affect the accuracy of particle size analysis, especially for siltstone. This paper presents a siltstone sample pretreatment method which core step is washing acid by centrifuge. Compared with traditional decantation method, the results show that the median particle size reduced 33.2 μm on average. Compared with the precipitation method which is commonly used for handling loose samples, the change of solid-liquid separation time is from 12 h to 10 min, while the average reduction of median particle size is about 15 μm. The grain size value corresponded to the cumulative volume of 10%/90% reduced 2.5 μm/20.3 μm on average. The percentage of the clay component less than 2 μm increased 2.88% on average. The fine particle（2–4 μm） and silt component（4–63 μm） increased 1.71% and 5.56% on average. Based on this method, two kinds of similar lacustrine siltstone were analyzed. They are tempestite and beach bar which are difficult to identify in the Lijin sub-depression, Dongying depression, Shengli oilfield, China. The final grain-size probability plot of tempestite is the type of “one saltation component and three suspension components”. The content of suspension components can reach to 80%–90%. The beach bar is the type of “one saltation component and two suspension components”. The content of suspension components can reach to 40%–45%. They both have the characteristics of high slope which means well sorting. But they can be distinguished based on the suspension sedimentary characteristics which were preserved by maximum degree in this kind of sample pretreatment method.

Flume Tank Simulation on Depositional Mechanism and Controlling Factors of Beach-Bar Reservoirs

The beach-bar reservoir has become an important exploration target in China, but its depositional mechanism and controlling factors have not yet been fully modeled. They have become an inhibitory factor for the exploration and development of beach-bar reservoirs. The depositional mechanism of beach-bars and their controlling factors have been studied by means of a flume experiment including seven runs under controlled boundary conditions which were the water level（Run 1, Run 2 and Run 3）, wave parameters（Run 1, Run 4 and Run 5） and initial slope（Run 1, Run 6 and Run 7）. The experiment revealed that the development of beach-bar was controlled by water level, wave parameters and initial slope. The deposited locations of distal bar and nearshore bar were controlled by the water level. Two beach-bars were migrated downward when the water level falls（Run 1, Run 2 and Run 3）. The width and thickness of distal bar and nearshore bar were controlled by wave parameters, especially the wave height. They increased with the scale of wave. But, the maximum thickness is limited by the water level（Run 1, Run 4 and Run 5）. The distance between distal bar and nearshore bar was controlled by the initial slope. It became shorter with the steeper slope. Distal bar and nearshore bar changed into one bar when the initial gradient was greater than 1/20（Run 1, Run 6 and Run 7）. The results suggest formative mechanism and controlling factors related to beach-bars.

The Goos-Hnchen shift of wide-angle seismic reflection wave

The partial derivative equations of Zoeppritz equations are established and the derivatives of each matrix entry with respect to wave vectors are derived in this paper.By solving the partial derivative equations we obtained the partial derivatives of seismic wave reflection coefficients with respect to wave vectors,and computed the Goos-Hnchen shift for reflected P-and VS-waves.By plotting the curves of Goos-Hnchen shift,we gained some new insight into the lateral shift of seismic reflection wave.The lateral shifts are very large for glancing wave or the wave of the incidence angle near the critical angle,meaning that the seismic wave propagates a long distance along the reflection interface before returning to the first medium.For the reflection waves of incidence angles away from the critical angle,the lateral shift is in the same order of magnitude as the wavelength.The lateral shift varies significantly with different reflection interfaces.For example,the reflected P-wave has a negative shift at the reflection interface between mudstone and sandstone.The reflected VS-wave has a large lateral shift at or near the critical angle.The lateral shift of the reflected VS-wave tends to be zero when the incidence angle approaches 90°.These observations suggest that Goos-Hnchen effect has a great influence on the reflection wave of wide-angles.The correction for the error caused by Goos-Hnchen effect,therefore,should be made before seismic data processing,such as the depth migration and the normal-moveout correction.With the theoretical foundation established in this paper,we can further study the correction of Goos-Hnchen effect for the reflection wave of large incidence angle.

Lithology Classification Based on Set-Valued Identification Method

Lithology classification using well logs plays a key role in reservoir exploration.This paper studies the problem of lithology identification based on the set-valued method(SV),which uses the SV model to establish the relation between logging data and lithologic types at a certain depth point.In particular,the system model is built on the assumption that the noise between logging data and lithologic types is normally distributed,and then the system parameters are estimated by SV method based on the existing identification criteria.The logging data of Shengli Oilfield in Jiyang Depression are used to verify the effectiveness of SV method.The results indicate that the SV model classifies lithology more accurately than the Logistic Regression model(LR)and more stably than uninterpretable models on imbalanced dataset.Specifically,the Macro-F1 of the SV models(i.e.,SV(3),SV(5),and SV(7))are higher than 85%,where the sandstone samples account for only 22%.In addition,the SV(7)lithology identification system achieves the best stability,which is of great practical significance to reservoir exploration.

Estimation of Elastic Parameters Using Two-Term Fatti Elastic Impedance Inversion

Elastic impedance （EI） inversion has been widely used in industry to estimate kinds of elastic parameters to distinguish lithology or even fluid. However, it is found that conventional three-term elastic impedance formula is unstable even with slight random noise in seismic data, due to the m-conditioned co- efficient matrix of elastic parameters. We presented two-term Fatti elastic impedance inversion method, which is more robust and accurate than conventional three-term elastic impedance inversion. In our method, density is ignored to increase the robustness of inversion matrix. Besides, P-impedance and S-impedance, which are less sensitive to random noise, are inverted instead of Vp and Vs in conventional three-term elastic impedance. To make the inversion more stable, we defined the range of K value as a con- straint. Synthetic tests claim that this method can obtain promising results with low SNR （signal noise ratio） seismic data. With the application of the method in a 2D line data, we achieved λp, μp and Vp/Vs sections, which matched the drilled well perfectly, indicating the potential of the method in reservoir prediction.