Full Waveform Research Articles

Source wavefield reconstruction based on an implicit staggered-grid finite-difference operator for seismic imaging

Reverse time migration and full waveform inversion involve the crosscorrelation of two wavefields, propagated in the forward- and reverse-time directions, respectively. As a result, the forward-propagated wavefield needs to be stored, and then accessed to compute the correlation with the backward-propagated wavefield. Boundary-value methods reconstruct the source wavefield using saved boundary wavefields and can significantly reduce the storage requirements. However, the existing boundary-value methods are based on the explicit finite-difference (FD) approximations of the spatial derivatives. Implicit FD methods exhibit greater accuracy and thus allow for a smaller operator length. We develop two (an accuracy-preserving and a memory-efficient) wavefield reconstruction schemes based on an implicit staggered-grid FD (SFD) operator. The former uses boundary wavefields at M layers of grid points and the spatial derivatives of wavefields at one layer of grid points to reconstruct the source wavefield for a (2 M + 2)th-order implicit SFD operator. The latter applies boundary wavefields at N layers of grid points, a linear combination of wavefields at M – N layers of grid points, and the spatial derivatives of wavefields at one layer of grid points to reconstruct the source wavefield (0 ≤ N < M ). The required memory of accuracy-preserving and memory-efficient schemes is ( M +1)/ M and ( N +2)/ M times, respectively, that of the explicit reconstruction scheme. Numerical results reveal that the accuracy-preserving scheme can achieve accurate reconstruction at the cost of storage. The memory-efficient scheme with N = 2 can obtain plausible reconstructed wavefields and images, and the storage amount is 4/( M +1) of the accuracy-preserving scheme.

INFLUENCES OF DATA ACQUISITION AND LAYER PARAMETERS ON FUNDAMENTAL DISPERSION CURVE IN ACTIVE MULTICHANNEL ANALYSIS OF SURFACE WAVE (A-MASW) METHOD

Aktif ÇKYDA yönteminde, sığ yeraltının güvenilir bir S-dalgası hız-derinlik profilini elde etmek için en önemli aşamalarından biri, geniş frekans aralığında sürekli ve yüksek ayrımlı bir dispersiyon eğrisinin elde edilmesidir. Bu makalede, tabaka (S- ve P-dalga hızları, yoğunluk ve kalınlık) ve veri toplama (kaynak ofseti-X0, alıcı aralığı-dx ve sayısı-N, serim boyu-L=(N-1)*dx) parametrelerinin, yüzey dalga alanının temel mod dispersiyon eğrisi üzerindeki etkileri, yapay atış verilerinin analizi ile incelenmiştir. Yapay veriler, tabaka yansıma/iletim katsayısı tekniği ile hesaplanan dispersiyon eğrisi kullanılarak, her bir alıcıda harmonik mod toplama tekniği ile oluşturulmuştur. Buna göre, düşük S-dalga hızlı ara tabakalar dispersiyon eğrisinin düşük frekans bölgesinde düşük hızlara kaymasına, yüksek hızlı ara tabakalar ise, dispersiyon eğrisinin yüksek frekanslarda sürekliliğinin bozulmasına (zig-zag etkisi) ve yüksek mod etkisi yanılgısına neden olabileceği gözlenmiştir. Kaynak ofseti yüzey dalgalarının tam dalga formlarının oluşmasında etkin iken, ilk ve son alıcı arası uzaklık olan serim uzunluğunun ise, dispersiyon eğrisinin frekans bandını ve çözünürlüğünü etkilediği görülmüştür. Ayrıca, geniş alıcı aralıklarının, dispersiyon eğrisinin düşük frekans bölgesindeki güvenirliğinin arttırmasının yanında, yüksek frekans bölgesinde dalga sayısı katlanması nedeniyle dispersiyon eğrisinin sürekliliğini bozduğu görülmüştür. Sonuç olarak, farklı dalga hızlarına sahip yer modelleri için üretilen yapay veriler üzerinde yapılan analizler N

Source-Independent Waveform Inversion Method for Ground Penetrating Radar Based on Envelope Objective Function

For the full waveform inversion, it is necessary to provide an accurate source wavelet for forwarding modeling in the iteration. The source wavelet estimation method based on deconvolution technology can solve this problem to some extent, but we find that the estimated source wavelet is not accurate and needs to be manually corrected repeatedly in the iteration. This process is highly operator-intensive, and the update process is time-consuming and increases the potential for errors. We propose a source-independent waveform inversion (SIEWI) scheme for cross-hole GPR data, and use the envelope objective function combined with this method to effectively reduce the nonlinearity of inversion. The residual field used by SIEWI to construct the gradient inherits the characteristics of the envelope wavefield. Compared with full waveform inversion (FWI), SIEWI is more robust and less sensitive to frequency components and inaccurate source wavelet. To avoid cycle jumping, the multi-scale strategy effectively utilizes the properties of convolutional wavefields. In one iteration, the wavefield is decomposed into multiple frequency bands through multiple convolutions in the time domain to construct a multi-scale inversion strategy that preferentially inverts low-frequency information.

A Set of In-Well Receiver Array for Borehole Induced Polarization Detecting Technology in Deep Mine Exploration

With the rapid development of the economy, the demand for mineral resources has increased dramatically. Because it is difficult to explore new mines in deep and peripheral areas, new theories, technologies, methods, and equipment are needed. How to accurately and effectively carry out new mine exploration has become an urgent research topic. In this study, based on the requirements of mine exploration within a depth of 3000 m, an array receiver for borehole-induced polarization was developed. Each channel of the receiver array independently acquires data, and it is able to carry out full waveform acquisition in the dual voltage and voltage difference mode. The structure of the receiver array can be flexibly adjusted to obtain array observations of induced polarization in different ways. Experiments demonstrated that the device works well at a high temperature of 155 °C, its resolution reached 0.1 μV, and the error between the different channels was less than 3%. Its dynamic range is 180 db. Through experiments on induced polarization in a demonstration mining area, the apparent resistivity curve and the apparent polarization curve were determined to be consistent with the known well-logging information, and the interpretation results were in agreement with the stratum information.

A review of the use of optimal transport distances for high resolution seismic imaging based on the full waveform

This study is a review of recent applications to seismic imaging of optimal transport based numerical tools. Modern seismic imaging methods used in the industry rely on the interpretation of the full signal. The characterization of the subsurface mechanical properties is formulated as a PDE-constrained optimization problem, solved through local optimization strategies. The choice of the misfit function used to measure the distance between actual seismic recordings and those synthetized by the solution of wave propagation PDE is crucial. Indeed, the conventional least-squares distance function leads to a non-convex optimization problem whose solution through local optimization then strongly depends on the initial guess. Using an optimal transport distance is an interesting alternative from its convexity properties with respect to translation and dilation. Specific strategies need however to be implemented as seismic data are oscillatory, while the optimal transport theory has been developed for the comparison of positive measures. In this study we review two optimal transport based misfit functions, from their mathematical formulation to their application to field data through their numerical implementation. Advantages and drawbacks of both strategies are discussed. Numerical experiments show that they represent two interesting and complementary alternative to the classical least-squares misfit function, mitigating the dependency to the choice of the initial guess.

The connection of velocity and impedance sensitivity kernels with scattering-angle filtering and its application in full waveform inversion

Multi-scale strategies such as starting from the low-frequency and early-arrival part of recorded data are commonly used in full waveform inversion (FWI) to maneuver complex nonlinearity. An alternative way is to apply appropriate filtering and conditioning to the misfit gradient in the model domain. In acoustic constant-density media, we prove that velocity and impedance sensitivity kernels are equivalent to applying a high-pass and a low-pass scattering-angle filter to a conventional single-parameter velocity (CSV) kernel. The high-pass scattering-angle filter allows the velocity kernel to include low-wavenumber updates (tomography component). In contrast, the low-pass scattering-angle filter helps the impedance kernel to yield high-wavenumber updates (migration component). The velocity model can be updated using a hybrid gradient of two components combined with appropriate weights. This FWI scheme is able to overcome the potential nonlinearity and partially mitigate the cycle-skipping problem. Numerical examples for the SEG/EAGE overthrust model and the Marmousi model demonstrate that the hybrid gradient facilitates FWI to converge faster to the true model even in cases when conventional CSV-based FWI fails.

Wave-equation traveltime slope inversion by combining finite difference and cross-correlation methods

As an essential step in seismic inversion, velocity macromodel building provides a low-wavenumber background velocity model for seismic imaging and full waveform inversion. Defined as the first-order partial derivative of traveltime with regard to spatial coordinates, slope information has been directly or indirectly applied in ray-based geophysical inversion to retrieve models containing low and intermediate wavenumbers. In this study, to use slopes of locally coherent events in background velocity model building, we extend the slope inversion from ray theory to wave equation, which we name wave-equation traveltime slope inversion (WSI). Unlike traditional ray-based slope inversion, which relies on tedious picking of continuous horizons, we compute slope conveniently and robustly through cross-correlation and finite difference methods. Furthermore, we present the formulation of wave-equation traveltime slope inversion under the framework of wave-equation traveltime inversion. Traveltime and slopes are distinct data attributes that play different roles in reconstructing low-wavenumber background velocity models. Compared with the classic traveltime inversion, the wave-equation traveltime slope inversion is more sensitive to local velocity changes. Numerical examples demonstrate that the proposed method improves the horizontal resolution in velocity model building, which especially shows excellent potential in obtaining a higher lateral resolution of reconstruction for steeply dipping structures than traditional wave-equation traveltime inversion. What's more, this study makes the joint inversion of travel time and slope based on the wave equation possible, which can theoretically bring a higher resolution stabilized inversion.

SeisDeepNET: An extension of Deeplabv3+ for full waveform inversion problem

Determining velocity model in complex geology settings such as environments with a salt body, is one of the significant challenges in seismic data analysis. One highly accepted way to determine the seismic velocity model is full waveform inversion (FWI). FWI suffers from number of problems such as cycle skipping and high computational cost. In this paper we propose a deep network, so called SeisDeepNET, to provide high resolution velocity model. Since FWI is highly nonlinear and dimensions of the seismic field data (as input of the network) differ from the dimensions of velocity model (as output of the network), the proposed deep learning method requires an encoder-decoder network with efficient architecture in order to effectively approximate the inverse operator and estimate model details. The encoder section of the proposed network is in accordance with the encoder of the DeepLabv3+ network, but it has different architecture in the decoder section. In order to enlarge the size of image in the decoder section, we incorporated 2D transposed convolution and bilinear interpolation separately into the decoder of the proposed network and assessed their performances on 1600 simulated 2D velocity models. The results showed that 2D transposed convolution, due to its learnable parameters, preserved the model details better. New architecture enabled the network to generate superior velocity model than counterpart networks like Unet, even with less training data. We also evaluated the effect of MSE and MAE metrics on the estimated velocity models of the network in the presence of salt body.

Utility of the Full ECG Waveform for Stress Classification

The detection of psychological stress using the electrocardiogram (ECG) signal is most commonly based on the detection of the R peak—the most prominent part of the ECG waveform—and the heart rate variability (HRV) measurements derived from it. For stress detection algorithms focused on short-duration time windows, there is potential benefit in including HRV features derived from the detection of smaller peaks within the ECG waveform: the P, Q, S, and T waves. However, the potential drawback of using these small peaks is their smaller magnitude and subsequent susceptibility to noise, making them more difficult to reliably detect. In this work, we demonstrate the potential benefits of including smaller waves within binary stress classification using a pre-existing data set of ECG recordings from 57 participants (aged 18–40) with a self-reported fear of spiders during exposure to videos of spiders. We also present an analysis of the performance of an automated peak detection algorithm and the reliability of detection for each of the smaller parts of the ECG waveform. We compared two models, one with only R peak features and one with small peak features. They were similar in precision, recall, F1, area under ROC curve (AUC), and accuracy, with the greatest differences less than the standard deviations of each metric. There was a significant difference in the Akaike Information Criterion (AIC), which represented the information loss of the model. The inclusion of novel small peak features made the model times more probable to minimize the information loss, and the small peak features showed higher regression coefficients than the R peak features, indicating a stronger relationship with acute psychological stress. This difference and further analysis of the novel features suggest that small peak intervals could be indicative of independent processes within the heart, reflecting a psychophysiological response to stress that has not yet been leveraged in stress detection algorithms.

A consistent multiparameter Bayesian full waveform inversion scheme for imaging heterogeneous isotropic elastic media

SUMMARY The inversion of complete seismic waveforms offers new perspectives to better constrain the elastic properties of Earth’s interior. However, models of density and seismic velocities obtained from full waveform inversions are generally characterized by very different and uneven spatial resolutions. Because the 3-D structure of the Earth represents small deviations from average reference Earth models, the absolute values of density, VP and VS in the Earth are strongly correlated. Here, we exploit this strong correlation between model parameters as a priori information introduced into a new full waveform inversion algorithm, by considering a non-diagonal 3-D model covariance matrix in which the spatial correlations of elastic properties are described with an exponential covariance function. The inverse of such a model covariance matrix is easy to compute, and we thus have all the ingredients to construct a consistent Bayesian full waveform inversion scheme. We show that taking into account the correlations between density and seismic velocities can lead to dramatic improvements on the reconstructed models of density, seismic velocities and VP/VS ratio. This new imaging approach opens new perspectives for refining tomographic images of density and seismic velocities in the lithosphere and upper mantle on a regional scale by full waveform inversion of teleseismic body waves.

On the use of nonlinear anisotropic diffusion filters for seismic imaging using the full waveform

Nonlinear anisotropic diffusion filters have been introduced in the field of image processing for image denoising and image restoration. They are based on the solution of partial differential equations involving a nonlinear anisotropic diffusion operator. From a mathematical point of view, these filters enjoy attractive properties, such as minimum–maximum principle, and an inherent decomposition of the images in different scales. We investigate in this study how these filters can be applied to help solving data-fitting inverse problems. We focus on seismic imaging using the full waveform, a well known nonlinear instance of such inverse problems. In this context, we show how the filters can be applied directly to the solution space, to enhance the structural coherence of the parameters representing the subsurface mechanical properties and accelerate the convergence. We also show how they can be applied to the seismic data itself. In the latter case, the method results in an original low-frequency data enhancement technique making it possible to stabilize the inversion process when started from an initial model away from the basin of attraction of the global minimizer. Numerical results on a 2D realistic synthetic full waveform inversion case study illustrate the interesting properties of both approaches.

Explosive source signature determination: Two unequal shots in the same hole

AbstractBuried explosive charges generate seismic waves with unrivalled bandwidth. The source time function is not always repeatable and is difficult to measure, but is required for subsequent data processing including reverse time migration and full waveform inversion. I present a new method for estimating the explosive seismic source time function for every shot, using two unequal shots in the same shot hole. The measured data for each charge are deconvolved for the modelled monopole seismic source time function to recover estimated earth impulse responses or Green's functions. The source model parameters are adjusted to maximize the likeness of the estimated Green's functions from the two shots, applying physical constraints to obtain the prior probability density functions for each parameter. Ten parameters specify the two source models, but only five of these are independent and a grid search is used to find them. The method is tested on an experimental data set, obtained for a different purpose, consisting of a line of single geophones and three in‐line shot holes, each with two unequal charges, the larger one at twice the depth of the smaller. The method works well where the charge size ratio is at least 2: the estimated source time functions are recovered and the estimated Green's functions are more similar than the seismograms before deconvolution. To apply the method in practice, the smaller charge should be deeper than the larger. If the small charge is small enough, the vertical separation between the charges can be reduced to less than 1 m. The Green's functions for the two charges would then be almost identical for frequencies up to 250 Hz, and the differences in the measured data from the two charges would be caused principally by the differences in the two source time functions.

Enhancement of In-Plane Seismic Full Waveform Inversion with CPU and GPU Parallelization

Full waveform inversion is a widely used technique to estimate the subsurface parameters with the help of seismic measurements on the surface. Due to the amount of data, model size and non-linear iterative procedures, the numerical computation of Full Waveform Inversion are computationally intensive and time-consuming. This paper addresses the parallel computation of seismic full waveform inversion with Graphical Processing Units. Seismic full-waveform inversion of in-plane wave propagation in the finite difference method is presented here. The stress velocity formulation of the wave equation in the time domain is used. A four nodded staggered grid finite-difference method is applied to solve the equation, and the perfectly matched layers are considered to satisfy Sommerfeld’s radiation condition at infinity. The gradient descent method with conjugate gradient method is used for adjoined modelling in full-waveform inversion. The host code is written in C++, and parallel computation codes are written in CUDA C. The computational time and performance gained from CUDA C and OpenMP parallel computation in different hardware are compared to the serial code. The performance improvement is enhanced with increased model dimensions and remains almost constant after a certain threshold. A GPU performance gain of up to 90 times is obtained compared to the serial code.

Frequency-domain acoustic full waveform inversion with an embedded boundary method for irregular topography

In the implementation of full waveform inversion (FWI) to identify subsurface velocity distributions with land seismic data, which are often acquired in regions with irregular topography, wave equation-based modelling requires caution. In particular, when using the finite difference method (FDM), unwanted scattered waves are generated because irregular surfaces crossing a rectangular grid are discretized via a staircase approximation; hence, if the problems caused by this staircase approximation are disregarded, FDM-based FWI may fail due to the presence of undesirable wavefields. To resolve this problem, this study develops a 2D frequency-domain acoustic FWI technique using a 9-point FDM-based modelling scheme that includes an embedded boundary method (EBM). This study suggests a workflow for the whole EBM-based FWI process from the calculation of coefficients for the EBM-based 9-point FDM modelling to applying it to FWI for proper velocity updates. In numerical examples, using velocity models with a tilted surface and an arbitrarily fluctuating surface, we synthesize seismic data and verify the accuracy of EBM-based 9-point FDM modelling and its superiority over the conventional FDM by comparing it with wavefields derived from the spectral element method. Then, we show that our EBM-based FWI is able to estimate subsurface velocity distributions even though the model has irregular topography, which spoils the result of the conventional FWI.

A synthetic study of acoustic full waveform inversion to improve seismic modelling of firn

AbstractThe density structure of firn has implications for hydrological and climate modelling and for ice shelf stability. The firn structure can be evaluated from depth models of seismic velocity, widely obtained with Herglotz-Wiechert inversion (HWI), an approach that considers the slowness of refracted seismic arrivals. However, HWI is appropriate only for steady-state firn profiles and the inversion accuracy can be compromised where firn contains ice layers. In these cases, Full Waveform Inversion (FWI) can be more successful than HWI. FWI extends HWI capabilities by considering the full seismic waveform and incorporates reflected arrivals, thus offering a more accurate estimate of a velocity profile. We show the FWI characterisation of the velocity model has an error of only 1.7% for regions (vs. 4.2% with HWI) with an ice slab (20 m thick, 40 m deep) in an otherwise steady-state firn profile.

Comparison of the FWI-Adjoint and Time Reversal Methods for the Identification of Elastic Scatterers

The paper falls into the category of computational methods for inverse scattering techniques for the identification of scatterers. We consider a linear elastodynamic problem and compare two popular methods for identifying a scatterer in the domain. Finite elements are employed with each of the two methods for spatial discretization. One method considered is Full Waveform Inversion using a gradient-based optimization and the adjoint method. In the adjoint procedure for calculating the gradient, we use the variant of discretizing the unknown parameters from the outset while all other variables remain continuous. Gradient optimization is performed in the examples using a quasi-Newton method. The other method compared is the computational Time Reversal technique, which is used in combination with an augmentation procedure to enhance performance. advantages and limitations of the two methods are outlined, and their performance is compared through an example from geophysics.

Possibilities of Full Waveform Inversion as an imaging method in heterogeneous solids

Ultrasonic imaging of single objects in heterogeneous solids such as concrete is mainly performed using linearized methods that are limited to one wave type and neglect geometric reflections and mode conversions. This limits the reconstruction accuracy and can induce artifacts. By considering more information of the complete resulting wavefield, full waveform inversion (FWI) promises a more accurate imaging. The method compares the measured signals with the results of the forward calculation of the scattered field of the source signals. The distribution of all three isotropic material parameters is iteratively adjusted to minimize the difference between the calculated and measured signals. By using a viable forward model, no limiting assumptions about wave propagation are necessary. Since the problem is ill-posed, regularization techniques are used for stabilization. The paper explains the operation and possibilities of the model-based approach considering both synthetic and experimental measurement data. First results on idealized scatterer geometries in homogeneous and heterogeneous solids are presented. Beginning with synthetic measurement results for the identification of anomalies in the solid body, the method is then applied to laboratory experimental data in the ultrasonic frequency regime. In both cases the same concrete structure is adressed where a known inclusion made of extruded polystyrene foam (XPS) is representing the anomaly to be detected.

Full waveform inversion of common-offset ground-penetrating radar based on a special source wavelet and multiple integral wave-field transform

Ground-penetrating radar (GPR) can obtain the geological information by using the electrical difference between the abnormal body and the background field. Full waveform inversion (FWI) can process radar data and obtain a more accurate distribution of relative permittivity. However, when the electrical parameters between the anomalous body and the background field are quite different, the wavefield information is seriously disturbed. In that case, the FWI method can not obtain accurate physical parameters, which is worse for common-offset GPR because of the lack of illumination angles and of wavenumber coverage. To solve this problem, a novel GPR FWI method is proposed to improve the stability of inversion using a special source wavelet and multiple integral wave-field transform. The manuscript is composed as follows: first, a special wavelet is used to improve the gradient in FWI. Then the integral wave-field transform can provide low-frequency information of data. This process can make full use of the low-frequency components hidden in the original data, obtain the large-scale relative permittivity distribution structure, and reduce the instability of the full waveform inversion. Finally, three simulation examples and a practical example verify the effectiveness of the method. Especially when there is a large difference between the dielectric parameters of the abnormal body and the background field (more than ten times or even dozens of times), the proposed FWI algorithm can still obtain stable results.

Gradient-constrained model parametrization in 3-D compact full waveform inversion

SUMMARY Seismic full waveform inversion (FWI) can produce high-resolution subsurface models by using the complete information of the observed data, but its computational cost can be prohibitively large, particularly for realistically sized 3-D problems. Due to its relatively fast convergence rate, it would be beneficial when Gauss–Newton algorithms could be employed for such problems, but the approximate Hessian matrix required for Gauss–Newton schemes would be too large to be kept in computer memory. Therefore, compact FWI (CFWI) was introduced, with which the number of inversion model parameters can be reduced substantially, and thus the amenable properties of Gauss–Newton inversion schemes can be exploited. Here, we extend the CFWI technology to 3-D problems. Since the spatial coverage of sources and receivers is generally sparser in 3-D (compared with 2-D problems), the total number of model parameters can become very large, and adequate model parametrization is particularly important for 3-D problems. Furthermore, we introduce gradient constrained CFWI (GC-CFWI). This is a novel development that allows the number of model parameters to be further reduced significantly. CFWI employs hierarchical model parametrizations that can be, for example, based on spatial Fourier transforms or wavelet transforms. Only those parameters of such a hierarchical parametrization are retained that exhibit a sufficiently high formal resolution. With GC-CFWI, it is further checked which of these parameters are expected to be changed significantly during a single CFWI iteration. Only parameters with a potentially significant adjustment are retained in the inversion parameter space. We have performed numerical experiments to analyse the performance of CFWI and GC-CFWI for 3-D acoustic FWI problems. For that purpose, we have considered a crosshole geometry including four boreholes and a surface deployment of sources and receivers. As parametrizations, we have considered the Fourier-based Hartley transform and the Haar wavelet transform. For both set-ups, the number of inversion model parameters could be reduced to about 20 per cent for the crosshole model and to about 10 per cent for the surface-based acquisition using CFWI. With GC-CFWI, a further reduction of about 50 per cent for both experimental set-ups could be achieved. The different results for the crosshole and surface-based set-ups indicate that an optimal model parametrization is tightly coupled to the experimental layout.

In situ stress measurement method of deep borehole based on multi-array ultrasonic scanning technology

In order to improve the accuracy and efficiency of deep in-situ stress measurement, based on the wall collapse in deep borehole, a deep borehole in-situ stress measurement method based on multi-array ultrasonic scanning technology is proposed in this paper. The solution idea of using the combination of multiple elements for borehole contour scanning is put forward, and a multi-array ultrasonic scanning technology suitable for fine horizontal section scanning of deep geological borehole contour is formed. Through the analysis of the calculation principle of hole wall caving method and the derivation of multi-array element ultrasonic scanning solution algorithm, a multi-array ultrasonic scanning device is developed by using the effective fusion of multi-array ultrasonic full waveform scanning signals and the reconstruction of horizontal section contour. The measurement method of in-situ stress in deep borehole combined with hole wall caving method is studied. Finally, the feasibility and accuracy of this method are verified by physical experiments. The results show that: the effective fusion of multi-array ultrasonic full waveform scanning signals and horizontal section contour reconstruction can break through the limitations of conventional in borehole probe placement and in borehole medium sound velocity calibration, and improve the fine reconstruction and accurate measurement of 360° wall shape. The multi-array ultrasonic scanning technology can obtain the borehole shape data at any borehole depth, and then obtain the three-dimensional shape measurement of borehole wall, which can provide a new technical means for the three-dimensional detection of borehole wall and in-situ stress measurement.