Velocity Imaging Research Articles

Spray characteristics of different regions downstream of a swirl cup

The spray characteristics of different regions downstream of swirl cups play a critical role in cold start and re-ignition of gas turbines. The spray measurements were performed at the fuel pressures of 0.5, 0.8, 1.0, 1.5, and 2.0 MPa and the fuel temperatures of −23, −13, −3, 7, 17 and 27 ℃, respectively. The droplet size, droplet velocity, droplet number, and instantaneous spatial spray image of sprays from an aviation kerosene Jet-A were measured using a two-component phase Doppler particle analyzer and a digital off-axis holography system. As the fuel pressure and temperature increase, the Sauter Mean Diameter (SMD) and spray non-uniformity of the Spray Shear Layer (SSL) gradually decrease. As the fuel pressure increases, the SMD and spray non-uniformity of the Central Toroidal Recirculation Zone (CTRZ) gradually decrease, and the slopes of these curves both decrease. As the fuel pressure increases, the SMD and spray non-uniformity of the CTRZ rapidly decrease at the fuel temperature of −23 ℃, while slightly decrease at the fuel temperature of 27 ℃. The droplets in the CTRZ come from 3 different sources: simplex nozzle, venturi, and outside the CTRZ. As the fuel pressure increases, the proportion of droplets recirculated from outside the CTRZ decreases. This study proposed the concept of the “pressure critical point” for the swirl cups. As the fuel temperature decreases, the proportion of droplets recirculated from outside the CTRZ increases below the critical pressure, while decreases above the critical pressure. In addition, through the models of liquid film formation and breakup on the curved cylindrical wall, a semi-theoretical model was established to predict the SMD of SSL for swirl cups. The prediction uncertainty of this model is less than 6% for all 14 conditions in this paper.

The N+ Formation Mechanism of Vibrationally Selected N2O+ Ions in the C2Σ+ State: A TPEPICO Imaging Study.

The N-NO bond fission of N2O+(C2Σ+) ions can produce two major fragment ions, NO+ or N+. In contrast to the dominant NO+ fragment ion, the N+ formation mechanism remains unclear to date. Here, dissociative photoionization of N2O via the C2Σ+ ionic state has been reinvestigated using a combined approach of threshold photoelectron-photoion coincidence (TPEPICO) velocity imaging and quantum chemical calculations. Accompanying the N+(3P) formation, the NO(X2Π) neutral fragment with low and high vi-rotational distributions was identified, based on the N+ speed and angular distributions derived from the TPEPICO images. In particular, the excitation of the symmetric stretching ν1+ mode promotes the formation of high rotational components, while the asymmetric stretching ν3+ mode shows the exact opposite effect. According to our calculated multistate potential energy surfaces, intersystem crossing from C2Σ+ to 14Π exclusively provides feasible decomposition pathways to produce the N+ fragment. In a slightly bent geometry, spin-orbit couplings between C2Σ+ and two substates of 14Π, 14A' or 14A″, play a crucial role in the N+ formation from vibrationally selected N2O+(C2Σ+) ions. The mechanism also provides new insights into the charge transfer reaction of N+ + NO → N + NO+.

Uncovering the progressive failure process of primary coal-rock mass specimens: Insights from energy evolution, acoustic emission crack patterns, and visual characterization

The failure and instability of deep coal-rock mass structures, which are influenced by mining disturbances, are major contributors to disasters like rock bursts. This study involved conducting indoor experiments using uniaxial loading test and acoustic emission (AE) experiments on indigenous primary coal-rock mass (PCRM). We utilize chaotic bifurcation based on strain energy to characterize the progressive damage stages of PCRM, demonstrating the chaotic characteristics of energy evolution during the gradual destruction process. The degree of damage resulting from PCRM failure was evaluated by jointly applying P-wave velocity tomography and AE event localization. Additionally, the classification of crack patterns in PCRM was conducted using the RA-AF correlation analysis method. The segmentation boundaries of crack classification patterns were then redefined using the Gaussian mixture model (GMM) algorithm. The research findings indicate that the chaotic bifurcation model of strain energy classifies stress into four stages: the stable region (Ⅰ), the metastable region (Ⅱ), the bifurcation region (Ⅲ), and the chaotic region (Ⅳ). The presence of a low-velocity zone in P-waves may indicate crack accumulation and damage within the system. Additionally, areas with abnormal P-wave velocities exhibit numerous AE events. The crack classification patterns of the four stages undergo an evolution from predominantly tensile cracks to a mixture of tensile and shear cracks, and the GMM algorithm successfully identifies the optimal separation path for crack classification boundaries. We propose an adaptive kernel density estimation (AKDE) algorithm to quantify the spatial distribution of AE events, thus offering a visual representation of the damage patterns at various stages.

3D shear wave velocity imaging of the subsurface structure of granite rocks in the arid climate of Pan de Azúcar, Chile, revealed by Bayesian inversion of HVSR curves

Abstract. Seismic methods are emerging as efficient tools for imaging the subsurface to investigate the weathering zone. The structure of the weathering zone can be identified by differing shear wave velocities as various weathering processes will alter the properties of rocks. Currently, 3D subsurface modelling of the weathering zone is gaining increasing importance as results allow the identification of the weathering imprint in the subsurface not only from top to bottom but also in three dimensions. We investigated the 3D weathering structure of monzogranite bedrock near the Pan de Azúcar National Park (Atacama Desert, northern Chile), where the weathering is weak due to the arid climate conditions. We set up an array measurement that records seismic ambient noise, which we used to extract the horizontal-to-vertical spectral ratio (HVSR) curves. The curves were then used to invert for 1D shear wave velocity (Vs) models, which we then used to compile a pseudo-3D model of the subsurface structure in our study area. To invert the 1D Vs model, we applied a transdimensional hierarchical Bayesian inversion scheme, allowing us to invert the HVSR curve with minimal prior information. The resulting 3D model allowed us to image the granite gradient from the surface down to ca. 50 m depth and confirmed the presence of dikes of mafic composition intruding the granite. We identified three main zones of fractured granite, altered granite, and the granite bedrock in addition to the mafic dikes with relatively higher Vs. The fractured granite layer was identified with Vs of 1.4 km s−1 at 30–40 m depth, while the granite bedrock was delineated with Vs of 2.5 km s−1 and a depth range between 10 and 50 m depth. We compared the resulting subsurface structure to other sites in the Chilean coastal cordillera located in various climatic conditions and found that the weathering depth and structure at a given location depend on a complex interaction between surface processes such as precipitation rate, tectonic uplift and fracturing, and erosion. Moreover, these local geological features such as the intrusion of mafic dikes can create significant spatial variations to the weathering structure and therefore emphasize the importance of 3D imaging of the weathering structure. The imaged structure of the subsurface in Pan de Azúcar provides the unique opportunity to image the heterogeneities of a rock preconditioned for weathering but one that has never experienced extensive weathering given the absence of precipitation.

Ion Velocity Map Imaging Study of the Reactive Collisions between Carbon Dioxide and Helium Ion.

The reactive collision between He+ and CO2 plays an important role in substance evolutions of the planetary CO2-rich atmosphere. Using a three-dimensional ion velocity map imaging technique, we investigate the low-energy ion-molecule reactions He+ + CO2 → He + CO2+/He + CO+ + O/He + CO + O+. The velocity images of the products CO+ and O+ of dissociative charge-exchange reactions are distinctly different from those of charge-exchange product CO2+. The remarkable features of stereodynamics are observed in the dissociative charge-exchange reaction and are attributed to the spatial alignment of the initially random target CO2 during the He+ approach. Branching ratios of different channels of dissociative charge exchange are further obtained with the Doppler kinematics model, indicating a high preference for the energy-resonant channel.

Ethraid: A Simple Method for Characterizing Long-period Companions Using Doppler, Astrometric, and Imaging Constraints

We present ethraid, an open-source Python package designed to measure the mass (m c ) and separation (a) of a bound companion from measurements covering a fraction of the orbital period. ethraid constrains m c and a by jointly modeling radial velocity, astrometric, and/or direct imaging data in a Bayesian framework. Partial orbit data sets, especially those with highly limited phase coverage, are represented well by a few method-specific summary statistics. By modeling these statistics rather than the original data, ethraid optimizes computational efficiency with minimal reduction in accuracy. ethraid uses importance sampling to efficiently explore the often broad posteriors that arise from partial orbits. The core computations of ethraid are implemented in Cython for speed. We validate ethraid's performance by using it to constrain the masses and separations of the planetary companions to HD 117207 and TOI-1694. We designed ethraid to be both fast and simple, as well as to give broad, “quick look” constraints on companion parameters using minimal data. ethraid is pip installable and available on Zenodo and GitHub.

A Frequency Domain Methodology for Quantitative Evaluation of Diffuse Wavefield With Applications to Seismic Imaging

AbstractAmbient Noise Imaging (ANI) of subsurface structures relies on seismic interferometry of diffuse seismic wavefields. However, the lack of effective methods to quantify and identify highly diffuse waves hampers applications of ANI, particularly in evaluating seismic attenuation and monitoring structural changes with high temporal resolution. Conventional ANI approaches require data normalization, which effectively suppresses the non‐diffuse component with large amplitude but also results in significant loss of amplitude and phase information in the continuous seismic records. In this study, we propose a frequency domain method to quantitatively evaluate the degree of diffuseness of seismic wavefields by analyzing their statistical characteristics of modal amplitudes for stationarity and randomness. Tests on synthetic waveform and field nodal records show that the proposed method can effectively distinguish between diffuse and non‐diffuse waveforms for either single‐ or three‐component data. As an application, we identify a 60‐s‐long diffuse coda of a local M 2.2 earthquake recorded by a dense nodal array on the San Jacinto Fault Zone, and successfully extract high‐quality dispersion curve and Q‐value without performing data normalization. These results are consistent with those obtained by conventional methods that assess the correlation between coherency and the Green's function, and by modeling ballistic waves generated by road traffic. Our proposed method can advance the imaging of subsurface velocity and attenuation structures as well as monitoring temporal changes for scientific studies and engineering applications.

The 3D Crustal Structure in the Epicentral Region of the 1980, Mw 6.9, Southern Apennines Earthquake (Southern Italy): New Constraints From the Integration of Seismic Exploration Data, Deep Wells, and Local Earthquake Tomography

AbstractWe present the first 3D crustal model of the epicentral region of the 1980, Mw 6.9, normal‐faulting Irpinia earthquake (southern Italy) determined by jointly interpreting the CROP‐04 deep seismic profile, a grid of commercial seismic lines, deep exploration wells, and a high‐resolution Local Earthquake Tomography. Despite numerous seismotectonic surveys and source studies of the background seismicity recorded by dense networks, a complete 3D geological model of the mid‐upper crust was still lacking in the region. The architecture of the Neogene fold‐and‐thrust belt is also debated, with competing thin‐ and thick‐skinned tectonic interpretations. We use the 3D geological model derived from subsurface exploration data to interpret the upper crustal tomographic velocities in terms of rock physical properties, while Vp and Vp/Vs anomalies provide inferences on the deep structural setting down to 12 km depth. We find that a thick‐skinned deformation style allows explaining the geometry of Pliocene fold‐and‐thrust systems deforming the Apulian carbonates but also deeper Permo‐Triassic metasediments and the Paleozoic crystalline femic basement. Inherited compressional structures and lithological heterogeneities control background seismicity occurring at two crustal levels. Fluid‐driven shallow seismicity (<4–6 km) concentrates in a high‐Vp/Vs wedge of fractured, brine‐saturated Mesozoic stiff rocks delimited by the 1980 earthquake faults. Deep seismicity (9–14 km) clusters instead within the low‐Vp/Vs crystalline basement underneath the Apulian carbonate ramp‐anticlines. Commercial seismic data allow us to identify the Irpinia Fault, the main fault ruptured by the 1980 earthquake, reinforcing its previous interpretations as an immature structure with subtle geological and geophysical evidence.

Tomographic imaging of South Rewa basin, Central India: Implications of Gondwana rifting and Late Cretaceous volcanism

We have imaged thick (3.0–5.0 km) sub-trappean Gondwana sediments deposited in a typical rift-environment of the south Rewa basin in Central India masked by the Deccan basalts. The basalts intrude through the basin forming several dykes, sills, and other intrusions along with large-scale undulations of the basement showing complex geology and tectonic settings due to Late Cretaceous volcanism (∼65 Ma). To delineate complex subsurface geological structures and understand the tectonic settings, we use long-offset seismic reflection data along the N-S trending 127 km Kuvari-Shahdol profile of the basin. The conventional stack and pre-stack time migration techniques fail to image the complex subsurface structures dominated by steeply dipping faults. The steeply dipping faults with small-scale structures are influenced by strong lateral and vertical velocity variations that cause problems in imaging the basin. Hence, a robust tomographic inversion with pre-stack depth migration technique is adopted to image fine-scale subtle subsurface geological structures with smooth velocity variations. The tomographic velocity model and pre-stack depth migration seismic image could decipher basaltic trap thickness, numerous dyke intrusions, alternate horsts and grabens with deposition of thick hydrocarbon-bearing sub-trappean Gondwana rocks along with the basement configuration. The deep basinal faults with highly distorted basement structures represent the intense tectonic activity of this Gondwana rift-basin. The deep-seated hydrocarbon reservoir is discovered with an excellent trapping mechanism forming both pre-rift and syn-rift settings of the rift-basin. The seismic image is further constrained and corroborated by the inversion of residual Bouguer gravity anomaly data to obtain corresponding density model derived from tomographic velocity model. The large basement faults, horsts and grabens, several intrusives like dyke, sill, laccolith, and thick sub-trappean Gondwana formations with Deccan trap cover indicate complex geology and tectonic settings of south Rewa basin forming the Late Cretaceous Volcanic Province of India.

Inverting the rock mass P-wave velocity field ahead of deep buried tunnel face while borehole drilling

Imaging the wave velocity field surrounding a borehole while drilling is a promising and urgently needed approach for extending the exploration range of the borehole point. This paper develops a drilling process detection (DPD) system consisting of a multifunctional sensor and a pilot geophone installed at the top of the drilling rod, geophones at the tunnel face, a laser rangefinder, and an onsite computer. A weighted adjoint-state first arrival travel time tomography method is used to invert the P-wave velocity field of rock mass while borehole drilling. A field experiment in the ongoing construction of a deep buried tunnel in southwestern China demonstrated the DPD system and the tomography method. Time-frequency analysis of typical borehole drilling detection data shows that the impact drilling source is a pulse-like seismic exploration wavelet. A velocity field of the rock mass in a triangular area defined by the borehole trajectory and geophone receiving line can be obtained. Both the borehole core and optical image validate the inverted P-wave velocity field. A numerical simulation of a checkerboard benchmark model is used to test the tomography method. The rapid convergence of the misfits and consistent agreement between the inverted and observed travel times validate the P-wave velocity imaging.

Ultrasound Shear Elastography With Expanded Bandwidth (USEWEB): A Novel Method for 2D Shear Phase Velocity Imaging of Soft Tissues.

Ultrasound shear wave elastography (SWE) is a noninvasive approach for evaluating mechanical properties of soft tissues. In SWE either group velocity measured in the time-domain or phase velocity measured in the frequency-domain can be reported. Frequency-domain methods have the advantage over time-domain methods in providing a response for a specific frequency, while time-domain methods average the wave velocity over the entire frequency band. Current frequency-domain approaches struggle to reconstruct SWE images over full frequency bandwidth. This is especially important in the case of viscoelastic tissues, where tissue viscoelasticity is often studied by analyzing the shear wave phase velocity dispersion. For characterizing cancerous lesions, it has been shown that considerable biases can occur with group velocity-based measurements. However, using phase velocities at higher frequencies can provide more accurate evaluations. In this paper, we propose a new method called Ultrasound Shear Elastography with Expanded Bandwidth (USEWEB) used for two-dimensional (2D) shear wave phase velocity imaging. We tested the USEWEB method on data from homogeneous tissue-mimicking liver fibrosis phantoms, custom-made viscoelastic phantom measurements, phantoms with cylindrical inclusions experiments, and in vivo renal transplants scanned with a clinical scanner. We compared results from the USEWEB method with a Local Phase Velocity Imaging (LPVI) approach over a wide frequency range, i.e., up to 200-2000 Hz. Tests carried out revealed that the USEWEB approach provides 2D phase velocity images with a coefficient of variation below 5% over a wider frequency band for smaller processing window size in comparison to LPVI, especially in viscoelastic materials. In addition, USEWEB can produce correct phase velocity images for much higher frequencies, up to 1800 Hz, compared to LPVI, which can be used to characterize viscoelastic materials and elastic inclusions.

Analysis of the shear wave velocity structure of a soft-hard interlayered rock slope based on surface wave and microtremor survey

The information regarding the layered structure is pivotal to the stability analysis of soft-hard interlayered rock slopes. The variation in the shear wave velocity offers insights into the characteristics of the strata structure within a rock slope. In this study, a joint analysis method that combines the multichannel analysis of surface waves (MASW) and the microtremor surface method (MSM) was used to identify the layered structure of a soft-hard interlayered rock slope located in the Shandong Province, China. The survey lines were positioned on slope crests. For the MASW, the receivers were placed in line with an active seismic source. The MSM method uses a concentric circular array comprising seven receivers. Fundamental-mode dispersion data were extracted from the active and passive microtremor sources. The 1D velocity models were then inverted from the combined dispersion curves using a surrogate optimization algorithm. A 2D velocity profile of the investigated slope was constructed through linear interpolation, and it exhibited distinct characteristics of high- and low-velocity interlayers, consistent with the borehole data. Our results demonstrate that the joint analysis method provides a complementary approach to image velocity profiling of slopes, thus contributing to enhanced investigation depth and resolution in shallow layers owing to the wider frequency range of the dispersion curves.

Three-dimensional density model of the mantle beneath the Ukrainian shield

Purpose. Mantle density models are key tools for understanding the fundamental geological and physical processes occurring within the Earth and are essential to our scientific and applied understanding of the planet. Methodology. The tasks were solved by a complex research method, including analysis and generalization of literary and patent sources, analytical, experimental studies, using computer and mathematical modelling methods. Findings. One-dimensional models simplify the mantle density distribution by assuming that it is uniform only in the vertical direction. This limitation does not allow for horizontal variations in mantle density, which may be important on a regional scale. 3D models are more complex and require more data and computational resources, so their use may be limited. In this study, we present a quasi-three-dimensional model of mantle density beneath the Ukrainian Shield. This 3D model is obtained using a basic set of one-dimensional seismic tomographic velocity models calculated for 21 mantle domains in the depth range from 50 to 2,600 km. The process of converting the P-wave velocity model into a density model includes the following stages: 1) determining seismic boundaries in the mantle based on P-wave velocity curves for each mantle domain; 2) creating a synthetic mantle model beneath the Ukrainian Shield for the P,S-wave velocity curves; 3) solving the Adams-Williamson equation for each domain, considering polynomial corrections to extract heterogeneities during its solution; 4) analysing existing models by comparing the calculated gravitational potential at the central point of the Ukrainian Shield as the standard reference for selecting one of 5 reference models. Here, we focus on the final stages of constructing the mantle density model by: 1) balancing the mass of the upper and lower mantle for each domain when determining density using the Adams-Williamson equation and introducing polynomial corrections; 2) calculating densities for each of the 21 mantle domains and their 3D integration. Originality. The obtained mantle-density model of the Ukrainian Shield aligns well with the division of the mantle into three main layers: lithosphere, upper mantle, and lower mantle. Each of the mantle’s structural layers has its representation pattern in density heterogeneities. Anomalies of decreased density in the lithosphere of the Ukrainian Shield correlate with thermal anomalies, whereas anomalies of increased density correspond to tectonic zones dividing its megablocks. Practical value. Regions of increased density gradient are associated with mantle thrust faults, which in some cases can be boundaries between different petrological formations and serve as channels for magma ascent into the Earth’s crust at certain stages of geological development of the Ukrainian shield and, in turn, be sources of minerals.

On the singularity point in acoustic orthorhombic media

Abstract The acoustic orthorhombic model is widely used in seismic modeling and processing of P-wave data. However, the anisotropic acoustic models have so called S-wave artifacts (1 artifact in transversely isotropic acoustic medium and two artifacts in orthorhombic acoustic medium). I show that S-wave artifacts can have one singularity point that results in complications in polarization field and the group velocity surface. The conditions of the existence of this point are defined in terms of anellipticity parameters. This singularity point and its group velocity image are the objects of my analysis.

Synchronized measurement method of burning rate and combustion temperature of a solid propellant specimen

To characterize the combustion properties of solid propellants, the synchronized measurement method of burning rate and combustion temperature is proposed combined shadow imaging and radiation imaging. Using spectroscopic and filtering imaging, shadow and radiation images of a solid propellant specimen are obtained synchronously. Burning rate is calculated by burning surface movement velocity of shadow images, and combustion temperature is calculated by radiation image thermometry. Measurement accuracies of burning rate and combustion temperature of the solid propellant specimen are validated by other independent measurement methods. On this basis, the synchronized measurements of burning rate and combustion temperature of different formulations of solid propellant specimens under different working conditions are carried out. The results show that the influence on burning rate and combustion temperature of pressure and formulas is different. Therefore, the synchronized measurement of burning rate and combustion temperature can provide more direct data support for the evaluation of solid propellant combustion performance.

Observation via Particle Image Velocity (PIV) Technology of Seepage Features in Replicas of Rock Fractures

Observation via Particle Image Velocity (PIV) Technology of Seepage Features in Replicas of Rock Fractures

A global SS precursor method for imaging discontinuities: the Moho and beyond

SUMMARY Imaging seismic velocity discontinuities within the Earth's interior offers important insight into our understanding of the tectonic plate, associated mantle dynamics, and the evolution of the planet. However, imaging velocity discontinuities in locations where station coverage is sparse, is sometimes challenging. Here we demonstrate the effectiveness of a new imaging approach using deconvolved SS precursor phases. We demonstrate its effectiveness by applying it to synthetic seismograms. We also apply it to ∼1.6 M SS precursor waveforms from the global seismic database (1990–2018) for comparison with CRUST1.0. We migrate to depth and stack the data in circular 6° bins. The synthetic tests demonstrate that we can recover Moho depths as shallow as 20 km. Globally, the Moho is resolved at 21–67 km depth beneath continental regions. The Moho increases in depth from 21 km ± 4 km beneath the continental shelf to 45–50 km beneath the continental interiors and is as deep as 67 ± 4 km beneath Tibet. We resolve the Moho in 77 percent of all continental bins, within 10 km of CRUST1.0, with all outliers located in coastal regions. We also demonstrate the feasibility of using this method to image discontinuities associated with the mantle transition zone with both synthetic and real data. Overall, the approach shows broad promise for imaging mantle discontinuities.

An iterative Kalman filter-based method for traveltime tomography

Abstract In addition to directly determining the inverted velocity, it is crucial to assess the uncertainty (or confidence) of the relevant velocity imaging results. This is especially true when dealing with time-lapse seismic data, which play a crucial role in detecting changes in fluid movement in petroleum reservoirs. In this study, we developed an iterative Kalman filter-based method to monitor time-lapse changes in the subsurface using traveltime tomography. Our approach considers the uncertainty of the results. We successfully verified the validity of our proposed method through synthetic crosshole and time-lapse tests. Our iterative Kalman filter-based method provides reasonable reconstruction results suitable for accessing uncertainties, and the algorithm can be used to monitor changes in the subsurface medium.

Osteochondroma of the distal humerus: A rare location

Osteochondroma of the medial condyle of the humerus is rare; hence, diagnosis can be challenging as it may be confused with other causes of swelling around the elbow joint. This can lead to compression of neurovascular structure. We present a case of left medial condyle humerus osteochondroma with ulnar nerve involvement and conduct a literature review of this rare condition. A 25-year-old male patient presented with swelling around the left elbow joint for 1 year and tingling and numbness along ulnar nerve distribution for the last 3 months. He underwent an X-ray, magnetic resonance imaging, electromyography, and nerve conduction velocity that confirmed the diagnosis of an osteochondroma with ulnar nerve involvement. An excisional biopsy was subsequently done. In conclusion, the case is an atypical location of osteochondroma. The history, clinical presentation, diagnostic imaging, and management outlined may help in the early identification and management of this rare but complicated condition.

Reconstruction method considering the electrostatic signal waveform of velocity distribution in flame based on EST

The velocity distribution of flame is an important combustion dynamic parameter that is used to analyze the stability, heat transfer and propagation of combustion. Digital particle image velocimetry and laser Doppler velocimetry are commonly used to measure the velocity distribution of flame. However, these methods work by adding tracer particles into the flame. A dual-section electrostatic tomography (EST) system is designed to detect the induction signal of the charged particles generated by the ionization process of combustion. The velocity distribution of flame is reconstructed through the electrostatic direct velocity tomography (EDVT) method. However, the different distance between the movement trajectory of the charged particles and a pair of electrodes for the cross-correlation calculation causes the difference in the induced signal waveform. It leads to an error in the cross-correlation velocity calculation. By analyzing the influence of the single charge induction signal waveform on the calculation of cross-correlation velocity, the reason for this error is clarified. Therefore, an electrostatic signal-waveform-based direct velocity tomography (ESDVT) method is proposed. The experimental results from a belt-type electrostatic device show that the average value of the L2-norm error of the ESDVT method is reduced by 40.9% compared with the EDVT method. Finally, using the method proposed in this paper, the velocity distribution at different sections of the Meker flame is reconstructed without adding tracer particles.