Relative acoustic impedance from wavelet transform

Most deconvolution algorithms try to transform the seismic wavelet into spikes by designing inverse filters that attempts to remove an estimated seismic wavelet from seismic data. Considering that seismic trace singularities are associated with acoustic impedance contrasts, and can be characterized by wavelet transform modulus maxima lines (WTMML), we show how to improve seismic resolution by using the wavelet transform. Specifically, we apply complex Morlet continuous wavelet transform (CWT) to each seismic trace and compute the WTMML‟s. Then, we reconstruct the seismic trace with the inverse continuous wavelet transform (ICWT) from the computed WTMML‟s with a slightly different complex Morlet wavelet than that used in the forward CWT. As the reconstruction process preserves amplitude and phase along different scales, or frequencies, the result resembles a deconvolution process. Using synthetic and real seismic data we show the effectiveness of the methodology on detecting seismic events associated with acoustic impedance changes.

Conventional sparse spike deconvolution algorithms that are based on the iterative shrinkage-thresholding algorithm (ISTA) are widely used. The aim of this type of algorithm is to obtain accurate seismic wavelets. When this is not fulfilled, the processing stops being optimum. Using a recurrent neural network (RNN) as deep learning method and applying backpropagation to ISTA, we have developed an RNN-like ISTA as an alternative sparse spike deconvolution algorithm. The algorithm is tested with both synthetic and real seismic data. The algorithm first builds a training dataset from existing well-logs seismic data and then extracts wavelets from those seismic data for further processing. Based on the extracted wavelets, the new method uses ISTA to calculate the reflection coefficients. Next, inspired by the backpropagation through time (BPTT) algorithm, backward error correction is performed on the wavelets while using the errors between the calculated reflection coefficients and the reflection coefficients corresponding to the training dataset. Finally, after performing backward correction over multiple iterations, a set of acceptable seismic wavelets is obtained, which is then used to deduce the sequence of reflection coefficients of the real data. The new algorithm improves the accuracy of the deconvolution results by reducing the effect of wrong seismic wavelets that are given by conventional ISTA. In this study, we account for the mechanism and the derivation of the proposed algorithm, and verify its effectiveness through experimentation using theoretical and real data.

Comparison of spectral decomposition methods

<p>Seismic inversion method is widely used to characterize reservoirs and detect zones of interest, i.e., hydrocarbon-bearing zone in the subsurface by transforming seismic reflection data into quantitative subsurface rock properties. The primary aim of seismic inversion is to transform the 3D seismic section/cube into an acoustic impedance (AI) cube. The integration of this elastic attribute, i.e., AI cube with well log data, can thereafter help to establish correlations between AI and different petrophysical properties. The seismic inversion algorithm interpolates and spatially populates data/parameters of wells to the entire seismic section/cube based on the well log information. The case study presented here uses machine learning-neural network based algorithm to extract the different petrophysical properties such as porosity and bulk density from the seismic data of the Upper Assam basin, India. We analyzed three different stratigraphic  units that are established to be producing zones in this basin.</p><p> AI model is generated from the seismic reflection data with the help of colored inversion operator. Subsequently, low-frequency model is generated from the impedance data extracted from the well log information. To compensate for the band limited nature of the seismic data, this low-frequency model is added to the existing acoustic model. Thereafter, a feed-forward neural network (NN) is trained with AI as input and porosity/bulk density as target, validated with NN generated porosity/bulk density with actual porosity/bulk density from well log data. The trained network is thus tested over the entire region of interest to populate these petrophysical properties.</p><p>Three seismic zones were identified from the seismic section ranging from 681 to 1333 ms, 1528 to 1575 ms and 1771 to 1814 ms. The range of AI, porosity and bulk density were observed to be 1738 to 6000 (g/cc) * (m/s), 26 to 38% and 1.95 to 2.46 g/cc respectively. Studies conducted by researchers in the same basin yielded porosity results in the range of 10-36%. The changes in acoustic impedance, porosity and bulk density may be attributed to the changes in lithology. NN method was prioritized over other traditional statistical methods due to its ability to model any arbitrary dependency (non-linear relationships between input and target values) and also overfitting can be avoided. Hence, the workflow presented here provides an estimation of reservoir properties and is considered useful in predicting petrophysical properties for reservoir characterization, thus helping to estimate reservoir productivity.</p>

Seismic impedance inversion is a geophysical technique that transforms seismic data into quantitative subsurface properties, primarily acoustic impedance. This process enables the identification of rock boundaries, hydrocarbon reservoirs, and lithological variations, thus supporting informed drilling decisions and reducing exploration risks. However, conventional inversion methods face limitations such as noise sensitivity, low resolution, and reduced effectiveness in geologically complex areas, often resulting in oversimplified subsurface models. This study addresses these challenges by employing deep learning approaches, specifically LeNet, AlexNet, and conventional CNN architectures, to improve seismic resolution and synthetic seismogram generation. The methodology involves preprocessing seismic and well-log data, calculating acoustic impedance and reflection coefficients, and applying Continuous Wavelet Transform (CWT) for feature extraction. The models are trained using synthetic seismograms and validated against real seismic data. Among the models evaluated, AlexNet demonstrates superior performance in seismic data reconstruction, achieving the lowest MSE (0.0031), RMSE (0.0557), and MAE (0.052), along with the highest R2 score (0.993). The proposed technique demonstrates superior predictive accuracy, refined subsurface characterization, and reduced geological risk, thereby establishing a robust benchmark for advanced geophysical data analysis.

Summary The seismic data spectral inversion method, arisen in recent years, can improve the resolution of seismic data for obtaining reservoir characteristics. It does not rely on prior information such as well-logging data. By using partial spectrum information from the input seismic trace data, a sparse reflectivity series can be inverted. The inverted reflectivity series can be used to improve the resolution and impedance inversion for thin layer reservoir prediction. In this paper, we implement seismic spectral inversion based on a compressed sensing algorithm, which can solve the ill-posed problem of the inversion process. In the process of inversion, we introduce a quadratic spectrum method to calculate the spectrum of seismic wavelet in the frequency domain, which can stabilize the inversion and handle real field data. Synthetic and real field seismic data examples show that the proposed spectral inversion based on compressed sensing algorithm is stable and effective. Moreover, the real field data inversion results show a good signal-to-noise ratio (SNR) and lateral continuity.

We developed a sparse multichannel blind deconvolution (SMBD) method. The method is a modification of the multichannel blind deconvolution technique often called Euclid deconvolution, in which the multichannel impulse response of the earth is estimated by solving an homogeneous system of equations. Classical Euclid deconvolution is unstable in the presence of noise and requires the correct estimation of the length of the seismic wavelet. The proposed method, on the other hand, can tolerate moderate levels of noise and does not require a priori knowledge of the length of the wavelet. SMBD solves the homogeneous system of equations arising in Euclid deconvolution by imposing sparsity on the unknown multichannel impulse response. Trivial solutions to the aforementioned homogeneous system of equations are avoided by seeking sparse solutions on the unit sphere. We tested SMBD with synthetic and real data examples. Synthetic examples were used to judge the viability of the method in terms of noise. We found that SMBD gives reasonable estimates of the wavelet and reflectivity series for [Formula: see text]. The results clearly deteriorated when we tried to work on data that were severely contaminated by noise. A real marine data set was also used to test SMBD. In this case, the estimated wavelet was compared with a wavelet estimated by averaging first breaks. The estimated wavelet showed a noticeable resemblance to the average first break with normalized correlation coefficient of 0.92.

A technique is presented in order to quantitatively determine the geoacoustic parameters of the uppermost seafloor strata by model-based inversion of backscattered data obtained with a parametric sonar. The technique has been implemented by means of an inversion software package that has been named sirOb (Seafloor Identification by acoustic Remote sensing Of the Bottom). The parameters to be identified can be grouped in two classes: deterministic parameters (acoustic impedance, compressional wave attenuation) and stochastic parameters (bottom surface roughness, volume inhomogeneities). The BoRIS code, that relies on the Kirchhoff approximation and on the small perturbation theory, has been selected as the forward model. Field data are obtained with a parametric sonar instrument, having a peak difference frequency at 8 kHz and 4 kHz bandwidth (both sides). A specific wavelet transform has been defined to obtain a significative measure of discrepancy between the data and the model. This discrepancy is minimized as a function of the bottom parameters (deterministic and stochastic). A divide-and-conquer strategy has been implemented, by first recovering the surface-related parameters (acoustic impedance, surface roughness) and then recovering the subbottom parameters (changes in acoustic impedance, volume inhomogeneities, compressional wave attenuation). This artificial division is made possible by an appropriate weighting of the discrepancy measure. The technique has been tested on simulated data, and then it has been applied on field data collected in shallow water areas of the Mediterranean Sea, where independent ground truth data were available.

Deep learning has been applied to tackle the seismic inversion problem, bringing more efficiency and accuracy. However, bad spatial continuity and poor generalizability limit the practical application. To solve these problems, we propose a 2D end-to-end seismic inversion method based on domain adaption. Firstly, the proposed 2D network learns the inversion mapping of seismic data under the constraint of domain adaption layer, which can reduce the difference between the features of real seismic data and synthetic seismic data, improving the generalization ability on real seismic data. Then, the trained model is finetuned with well logging data. In the first process, the spatial continuity of the inversion result is guaranteed by the 2D training scheme. Meanwhile, due to the constraint of the domain adaption layer, our model not only performs well on the synthetic data but also has good generalization ability on the real seismic data. And we carefully discuss the mechanism of domain adaption layer. In the second process, finetuning introduces well logging information, which can further improve the ability to invert details. Moreover, in order to improve the inversion accuracy on real seismic data, we develop a new training data generation method that can generate the synthetic samples close to the real samples, and a 2.5D training strategy is adopted to improve the continuity of the 3D data. The experiments on both synthetic and real seismic data show that our method performs better than both the recursive inversion method and the 1D closed-loop CNN methods.

The coherence method is always used to describe the discontinuity and heterogeneity of seismic data. In traditional coherence methods, a linear correlation coefficient is always used to measure the relationship between two random variables (i.e., between two seismic traces). However, mathematically speaking, a linear correlation coefficient cannot be applied to describe nonlinear relationships between variables. In order to overcome this limitation of liner correlation coefficient. We proposed an improved concordance measurement algorithm based on Kendall’s tau. That mainly concern the sensitivity of the liner correlation coefficient and concordance measurements on the waveform. Using two designed numerical models tests sensitivity of waveform similarity affected by these two factors. The analysis of both the numerical model results and real seismic data processing suggest that the proposed method, combining information divergence measurement, can not only precisely characterize the variations of waveform and the heterogeneity of an underground geological body, but also does so with high resolution. In addition, we verified its effectiveness by the actual application of real seismic data from the north of China.

Scanning acoustic microscopy (SAM) is a useful observational tool in cellular study as non-invasive living observation is feasible, unlike in conventional optical microscopy. In a previous study, cell morphological changes were successfully visualized using acoustic impedance measurements. These acoustic impedance changes correspond to cell elasticity, mainly reflecting changes in the cytoskeleton. In this study, we evaluate the elastic changes in murine breast cancer cell C127I during mitosis. C127I cells were cultured to ∼75% confluency before measurement, using a transducer with a central frequency of 320 MHz. Dynamic changes during mitosis were successfully mapped using SAM and confirmed by laser confocal microscopy. Cells in prometaphase, anaphase, and telophase, which could previously only be confirmed through immunostaining, were successfully visualized using SAM. This suggests that SAM is capable of distinguishing cells in different mitotic phases based on the changes in acoustic impedance.

Various methods can characterize microstructural properties of reservoir rocks with the ultimate goal of relating microstructure to seismic properties. Scanning electron microscopy, transmission electron microscopy, and optical microscopy have traditionally been used for such studies. They have identified lithology, pore space, interconnectivity of pores, grain size, and cementation as the most important factors controlling seismic wave velocity and attenuation. However, these techniques provide qualitative descriptions only. The acoustic techniques presented here, scanning acoustic microscopy (SAM) and acoustic sounding (AS), can map and, more importantly, quantify microstructure as variations in acoustic impedance. Ultrasonic stress waves are sensitive to local variations in elastic properties and are therefore particularly suited for characterizing microstructural properties of reservoir rocks. Reflections from impedance boundaries in grains and between interfaces in the sample are used to construct the microstructural image. This paper will show that acoustic microscopy can be a powerful tool for studying internal structure and pore geometry of reservoir rocks. Acoustic microscopy's basic principle is almost identical to that of reflection seismology. Images of surface and subsurface microstructures are prepared on the basis of reflected acoustic waves—that is, on the impedance changes in the sample. Acoustic waves on a sample are mode converted, partly transmitted into the sample, and partly reflected. The reflection coefficient and with it the signal intensity received by the transducer are determined by the elastic constants of the material. Changes in acoustic impedance in the sample that influence wave reflection characteristics can be studied by mapping the reflected waves. Because the working frequency of the acoustic waves can be varied, their penetration depth into the sample and the resolution of microstructural features can be controlled. I will present results from high-frequency SAM (0.1–2 GHz) and low-frequency AS (25–100 MHz). The resolution of SAM is about 1 μm at 1 GHz; AS …

ABSTRACTAutomatic feature detection from seismic data is a demanding task in today's interpretation workstations. Channels are among important stratigraphic features in seismic data both due to their reservoir capability or drilling hazard potential. Shearlet transform as a multi‐scale and multi‐directional transformation is capable of detecting anisotropic singularities in two and higher dimensional data. Channels occur as edges in seismic data, which can be detected based on maximizing the shearlet coefficients through all sub‐volumes at the finest scale of decomposition. The detected edges may require further refinement through the application of a thinning methodology. In this study, a three‐dimensional, pyramid‐adapted, compactly supported shearlet transform was applied to synthetic and real channelised, three‐dimensional post‐stack seismic data in order to decompose the data into different scales and directions for the purpose of channel boundary detection. In order to be able to compare the edge detection results based on three‐dimensional shearlet transform with some famous gradient‐based edge detectors, such as Sobel and Canny, a thresholding scheme is necessary. In both synthetic and real data examples, the three‐dimensional shearlet edge detection algorithm outperformed Sobel and Canny operators even in the presence of Gaussian random noise.

Enhancing the detection of small coal structures by seismic diffraction imaging

The seismic image produced by pre-stack depth migration is more accurate and has clearer geological significance than the time image. However, the waveform of the depth-domain seismic image is affected not only by depth-dependent velocity variation but also by media attenuation, resulting in strong spectral variation of depth-domain seismic data. Therefore, depth-domain seismic inversion is still challenging. We propose a wavelet extraction method of attenuation media based on the generalized seismic wavelet, to address this issue. Then, the estimated depth-domain wavelets were applied to the direct acoustic impedance inversion. First, we investigated the effect of attenuation media on depth-domain source wavelets and derived an analytical formula for the depth-domain wavelets of attenuation media. Next, the time-domain generalized seismic wavelet was extended to the depth domain, which was utilized to study the feasibility of using the generalized seismic wavelet to characterize the seismic wavelet of the depth-domain attenuation media. Based on the orthogonal matching pursuit, we propose a method to extract the depth-domain generalized seismic wavelet directly from depth-domain seismic data. Finally, we applied this method to the depth-domain direct acoustic impedance inversion of a 3D field data example. Tests on the synthetic and 3D field datasets show that the proposed method can correctly extract the depth-domain seismic wavelet of attenuation media and attain direct inversion of the depth-domain acoustic impedance with high accuracy. Therefore, our method is effective and has robust potential in reservoir characterization, fluid prediction, and attribute extraction in the depth domain.