71 results about "Sonic logging" patented technology

The invention relates to the technical field of oil exploration logging data processing, and discloses a far exploration sound wave migration imaging data three-dimensional well trajectory correction method and related device.The method comprises the steps that horizontal well logging data are collected, coordinates of a well trajectory in space are obtained through calculation according to the horizontal well logging data, and the coordinates of the well trajectory are calculated according to the coordinates; the well track is drawn according to the coordinates of the well track in the space; generating migration imaging data in different directions according to the remote exploration acoustic logging data, and generating a migration imaging picture by using a color code according to the migration imaging data; the migration imaging picture is cut into a plurality of narrow strip pictures in the direction perpendicular to the well axis, all the narrow strip pictures are sequentially drawn into designed grids, migration imaging pictures generated by migration imaging data in different directions are sequentially drawn into a three-dimensional space, and horizontal well three-dimensional well trajectory correction of the migration imaging data is completed. According to the method, the accuracy of depicting the spatial relationship of geological reflectors such as stratum interfaces, faults and cracks near a horizontal well shaft by far-detection sound waves is improved.

The invention belongs to the technical field of geophysical exploration and oil and gas reservoir evaluation, and particularly relates to a heterogeneous dolomite reservoir fractal rock physical modeling method. The method comprises the following steps: data acquisition and processing: acquiring ultrasonic velocity and attenuation data, and acquiring acoustic logging data and post-stack seismic data of a target layer; constructing a fractal rock physical model; generating a multi-band rock physical drawing board; drawing board correction and reservoir parameter quantitative prediction. The fractal dimension serves as a clear and predictable key parameter to be introduced into the dolomite rock physical model for the first time, the limitation that a traditional model can only predict the pore volume (porosity and fracture content) but cannot describe the pore structure form is broken through, the precision and dimension of reservoir physical property prediction are improved, and the reservoir physical property prediction accuracy is improved. By combining an infinite heavy pore medium model with a fractal theory, the established model can simulate propagation of waves in an actual complex porous medium more truly, spanning from two dimensions to three dimensions is realized, and multiplicity of reservoir prediction is greatly reduced.

This invention relates to a wave impedance inversion method, comprising the following steps: Step 1, collecting post-stack seismic data, sonic logging curves, density logging curves, lithology-representing curves, and reservoir interpretation results within the work area; Step 2, calculating wave impedance curves based on sonic logging and density logging curves; Step 3, assigning values ​​to various types of reservoirs to obtain formation identification codes; and reconstructing the wave impedance curves using the formation identification codes to obtain reconstructed wave impedance curves; Step 4, performing intersection analysis using the lithology-representing curves and the reconstructed wave impedance curves; Step 5, performing wave impedance inversion on the post-stack seismic data using the reconstructed wave impedance curves. This invention can directly identify effective energy storage with high accuracy.

The application discloses a kind of based on deep learning's seismic brine reservoir response feature identification method, by fusing induction logging data and seismic inversion result, break through the technical limitation that brine reservoir feature response is weak to traditional acoustic logging, improve the accuracy of reservoir identification;Improved UNET++ network structure utilizes dense skip connection and channel attention mechanism, effectively integrates multi-scale geological features, enhances the capture ability of thin layer brine weak reflection signal, improves the accuracy of boundary identification;Introduce bidirectional LSTM and spatial feature alignment technology, realize the depth fusion of logging vertical feature and seismic horizontal profile, optimize horizon matching relationship, effectively reduce the risk of misjudgment caused by velocity anomaly;Based on deep supervision mechanism and joint training strategy, generate three-dimensional reservoir spatial distribution model, realize the description of deep pore-fracture type brine reservoir, greatly improve exploration efficiency, provide reliable technical support for brine resource positioning under complex geological conditions.

The application discloses a kind of InSAR and acoustic fusion's goaf left coal pillar stability comprehensive evaluation method, belong to the field of mine safety evaluation, including selecting SAR satellite suitable for mining area, obtaining SAR satellite image data of mining area, then carry out time series deformation analysis, obtain the deformation rate and cumulative deformation diagram of mining area, identify the subsidence abnormal area of mining area;Drilling is carried out in the coal pillar area of mining area, and ultrasonic logging device, interwell acoustic tomography system and acoustic emission monitor are laid out;Comprehensive analysis is carried out to all the data obtained, and a coal pillar stability evaluation model is constructed;Through coal pillar stability evaluation model, the coal pillar stability is classified, and the coal pillar instability risk is predicted.The application provides a kind of InSAR and acoustic fusion's goaf left coal pillar stability comprehensive evaluation method, which realizes high-precision evaluation of coal pillar stability by combining surface deformation monitoring and deep coal pillar structure detection.

This invention relates to the field of well logging data processing technology, and particularly to a method, system, and apparatus for improving the resolution of well logging data in thin sand layers. The method includes the following steps: S1, acquiring well logging data from thin sand layers in the area to be analyzed; S2, performing data preprocessing; S3, using wavelet transform technology for multi-resolution analysis to extract characteristic signals of the thin sand layers and enhance their resolution; S4, using a chart correction method to improve accuracy; S5, evaluating whether the characteristic signals of the thin sand layers processed in step S4 are acceptable. If the evaluation is unacceptable, steps S1-S5 are iteratively performed until the evaluation is acceptable. When the evaluation is acceptable, it indicates that the characteristic signals of the thin sand layers processed in step S4 represent well logging data with improved resolution. This achieves rapid and accurate high-resolution processing of acoustic logging data.

The application relates to the technical field of geological exploration, improves the problem that a probe rod cannot be conveniently and stably detected from the middle part of a drilling well, and discloses a sonic logging instrument which comprises a host computer, a cable and a probe rod, one end of the cable is connected to the probe rod, the other end of the cable is connected to a controller, a supporting mechanism is further connected to the cable, the supporting mechanism comprises an adjusting seat matched with the cable and a plurality of telescopic rods arranged along the circumference of the adjusting seat; the telescopic rod comprises a first rod connected with the adjusting seat and a second rod slidably connected with the first rod along the length direction; the bottom of the probe rod is connected with a counterweight mechanism, and the counterweight mechanism comprises a counterweight movably connected with the probe rod. The supporting mechanism is erected on the well mouth through the telescopic rod, the length of the second rod is adjusted so that the probe rod is located at the position of the middle part of the drilling well for detection, and the operation is convenient and fast; the adjusting seat and the counterweight can reduce the possibility of swinging and twisting of the cable and the probe rod, the counterweight can also make the swinging probe rod quickly return to the original position, and the detection accuracy of the probe rod is improved.

The application discloses a method for predicting natural fracture line density based on interval quantization random function, and provides an effective method for predicting natural fracture line density without the aid of third-party software and with low artificial workload when imaging logging data and core data are less. The method comprises the following steps: obtaining core data, conventional logging data, array sonic logging data and imaging logging data of a drilling well in a target layer system; calculating dynamic rock mechanics parameters of the drilling well according to the array sonic logging data and the conventional logging data; calculating natural fracture line density according to the core data or the imaging logging data; quantitatively studying the sectional correlation between the dynamic rock mechanics parameters and the natural fracture line density; and establishing an interval quantization random function model and predicting the natural fracture line density. The application is free from the limitations of great fitting difficulty and low reliability of parameters and natural fracture line density.

This invention discloses a method and system for measuring the performance indicators of an acoustic logging transducer, belonging to the field of geophysical logging technology. The method derives an admittance circle measurement method using an equivalent lumped system of the transducer; an admittance circle measurement system is constructed based on this method; the electrical parameters of the transducer are measured using this system to obtain the transducer admittance curve and admittance circle diagram; and the transducer's performance indicators are calculated based on these diagrams. This invention provides more accurate measurement results and simplifies the operation of testing the admittance circle and performance indicators of the transducer.

This application discloses a rapid positioning device for sonic logging tubes in pile foundations, comprising a pile hole, a reinforcing cage disposed within the pile hole, the reinforcing cage including a plurality of vertical main bars spaced circumferentially and a plurality of outer stirrups welded to the outside of the vertical main bars at vertical intervals, and further including: a plurality of inner stirrups welded to the inside of the vertical main bars at vertical intervals; a positioning member connected to the inner stirrups to position the sonic logging tube; and a connecting member, one end of which is welded to the inner stirrup, and the other end of which is welded to the positioning member. The inner and outer stirrups work together to form a double constraint, thereby enhancing the overall rigidity and shape stability of the reinforcing cage. The connecting member, as a rigid connecting arm, together with the positioning member, ensures that the sonic logging tube maintains a constant preset distance from the main body of the reinforcing cage in the vertical direction, which is beneficial for the effective transmission of ultrasonic signals and for improving the quality of the final bridge pile body.

The invention relates to the field of oil and gas resource exploration, and discloses a fracturing design method based on shale content three-dimensional geological modeling, which comprises the following steps: determining geological characteristics of a research area, integrating earthquake, logging and core data, analyzing reservoir deposition characteristics and shale content distribution, and combining porosity and permeability to establish a correlation model of a reservoir and shale content; the method comprises the following steps: establishing a shale content three-dimensional geologic model by adopting a sequential Gaussian simulation method by taking well data as hard data and seismic inversion data as soft data through petri l software, constructing a reservoir three-dimensional geologic model according to porosity, permeability and reservoir thickness, and fitting the shale content three-dimensional geologic model and the reservoir three-dimensional geologic model through a variation function to obtain a compressible reservoir model. By combining microseismic monitoring, acoustic logging and a pressure sensor, generation and extension of the crack and reservoir pressure change can be tracked in real time, it is ensured that the crack is effectively extended according to a design path, and a real-time feedback system provides accurate data support in the crack extension process.

The invention relates to the technical field of shale reservoir logging evaluation, in particular to a lamellar fracture development section identification method and device, equipment and a medium, and the method comprises the steps: obtaining dipole transverse wave train data corresponding to each receiver obtained by acoustic logging in a research area, and calculating an amplitude time window; determining transverse wave amplitudes corresponding to all receivers according to the dipole transverse wave train in the amplitude calculation time window; determining a shear wave amplitude attenuation index corresponding to each receiver by taking a compact sandstone section on the shear wave amplitude as a baseline; assigning a corresponding non-shale section in the shear wave amplitude attenuation index as 0; and establishing a lamellar fracture classification standard, performing category division on the shear wave amplitude attenuation index according to the classification standard, and identifying a lamellar fracture development section of the shale section according to a category division result. And quantitative evaluation of the lamellar fracture development condition provides technical support for reservoir geological dessert optimization.

The utility model discloses a sounding pipe structure with a protection structure, which relates to the technical field of sounding pipes, and comprises a pipe body, a protection end cover is sleeved on the pipe body, a second clamp is clamped outside the protection end cover, a second clamp is sleeved outside the pipe body, and the second clamp is clamped outside the protection end cover. And an elastic buffer piece is arranged between the second clamp and the first clamp. According to the sounding pipe structure with the protection structure, the elastic buffering piece is arranged between the second clamp and the first clamp on the sounding pipe, buffering can be conducted through the elastic buffering piece when the sounding pipe is impacted, and then the sounding pipe can be protected.

The invention discloses a complex stratum exploration method and device based on geological radar and drilling data fusion, and relates to the technical field of geological exploration, and the method comprises the steps: collecting geological radar waveform data and acoustic logging data, obtaining the prior geological information of a work area, carrying out the uncertainty quantification processing, and generating posterior probability distribution; performing Bayesian inversion on the posterior probability distribution and the prior geological information to generate posterior statistics, and generating an interpretation confidence cloud picture based on the posterior statistics; and constructing a spatial uncertainty weighting matrix by using the interpretation confidence cloud atlas, fusing the anisotropy parameters at the drill hole and the anisotropy characteristics of the geological radar data, establishing anisotropy constraint terms of the geological radar data, and generating an anisotropy full-waveform inversion target function. According to the method, fusion of different types of data and quantification of space-time uncertainty are realized, and the underground structure prediction precision and the model reliability are improved.

This invention discloses an integrated logging-while-drilling (LOD) and measurement drill string assembly, relating to the field of oil and gas drilling engineering technology. It provides a series connection scheme for core protective drill string components, offering two switchable configurations: one with a mud motor and one without. Both configurations consist of an azimuth density neutron logging sub, a bidirectional communication power supply sub, an acoustic logging sub, a resistivity logging sub, an upper connecting sub, a flexible sub, a lower connecting sub, an azimuth gamma logging sub, and a steering actuator connected in series according to a fixed logic. The configuration with a mud motor only requires adding a mud motor at a designated location to complete the structural switch, without changing the series connection of the remaining subs. This assembly scheme is applicable to various drilling scenarios such as offshore exploration and development, deepwater drilling, complex directional wells, highly deviated wells, and horizontal wells. It enables integrated operations of geological steering, formation evaluation, and wellbore stability analysis during drilling, effectively improving drilling efficiency and reducing operational risks.

This utility model proposes a sealing joint for connecting sonic logging pipes, relating to the field of sonic logging pipe sealing test technology. It includes a sonic logging pipe body and a water pressure resistance testing device, as well as an upper mounting block, a lower mounting block, a wedge block, a column, a through hole, a flow hole, an internal pressure connection assembly, a mounting cylinder, a wedge groove, and an adjustable sealing assembly. This application can not only seal both ends of the sonic logging pipe body, but also apply internal pressure along the axial direction of the sonic logging pipe to further improve the sealing effect. Furthermore, the adjustable sealing assembly allows for sealing of sonic logging pipes of different specifications after installation, meeting and adapting to the sealing test requirements of diverse specifications of sonic logging pipes in different projects. Therefore, the sonic logging pipe sealing joint has a better performance.

The invention discloses an interlayer multiple identification and model construction method and device, a medium and equipment. The method comprises the steps that logging data and a seismic migration profile of a working area are obtained, the logging data comprise at least one of an acoustic logging curve and logging stratified data, and a longitudinal wave speed two-dimensional numerical model and a density two-dimensional numerical model are constructed in the main measuring line direction or the connection measuring line direction based on the logging data. The constructed longitudinal wave velocity two-dimensional numerical model and density two-dimensional numerical model provide accurate data for the establishment of subsequent models. And based on the longitudinal wave velocity two-dimensional numerical model and the density two-dimensional numerical model, generating zero well spacing VSP simulation data by using a seismic exploration numerical simulation method, and constructing an inter-layer multiple model based on the zero well spacing VSP simulation data. The interlayer multiple wave model constructed by the method is closer to the multiple waves actually generated in the working area, and the interlayer multiple waves in the working area can be accurately identified by identifying the interlayer multiple waves through the wave field features of the interlayer multiple wave model.

The present application relates to the technical field of acoustic logging, and particularly relates to a high-stability wide-frequency distributed optical fiber acoustic wave sensing logging method and system. The method comprises the following steps: acquiring logging requirements and downhole geological structure characteristic data, simultaneously collecting corresponding acoustic wave signals, temperature field distribution signals and wellbore structure stress signals, and performing preliminary denoising and synchronization processing and wide-frequency expansion and distortion compensation processing, to generate downhole wide-frequency enhanced acoustic wave signals; based on the downhole wide-frequency enhanced acoustic wave signals, performing downhole propagation stability evaluation and stable adaptive optimization adjustment, to generate corresponding high-stability wide-frequency acoustic wave sensing signals; based on the high-stability wide-frequency acoustic wave sensing signals, performing distributed optical fiber acoustic wave sensing logging analysis, to generate corresponding geological structure and reservoir characteristic logging information. The present application can solve the problems of bandwidth limitation, signal distortion and poor stability of traditional optical fiber acoustic logging in a complex downhole environment, so as to realize high-precision detection of oil and gas reservoirs.

The invention relates to the field of oil-gas exploration, and provides a method and a system for predicting a heterogeneous deepwater ultra-shallow gas layer and an associated thin hydrate layer. The method comprises the following steps: performing lithofacies division on a stratum through logging data to obtain a lithofacies identification result; performing time-depth conversion on the lithofacies identification result by using the acoustic logging data to obtain time domain lithofacies data; performing horizon interpretation on the seismic data, and constructing a stratigraphic framework model; performing lithofacies proportion statistics on the time domain lithofacies data in the stratigraphic framework model to obtain a lithofacies stratigraphic model; taking the lithofacies stratigraphic model as a constraint condition, and introducing the lithofacies stratigraphic model into a statistical inversion algorithm for inversion processing to obtain a longitudinal wave impedance data volume and a lithofacies data volume; and interpreting and analyzing the stratum by combining the longitudinal wave impedance data body and the lithofacies data body to obtain a spatial distribution prediction result of the heterogeneity deepwater ultra-shallow gas layer and the thin hydrate layer. According to the method, the interpretation rationality of the ultra-shallow gas layer with high heterogeneity in spatial distribution is improved.

The application discloses a design method and device of a low-frequency transducer, and the method comprises the following steps: obtaining specification size information and detection characteristics of a sonic logging instrument; the specification size information comprises geometric size parameters and environmental tolerance parameters; the detection characteristics comprise measured sound wave types and detection depths; determining the size of a single piezoelectric ceramic sheet in the low-frequency transducer of the sonic logging instrument according to the specification size information; determining the working frequency band of the low-frequency transducer according to the detection characteristics; determining the number of piezoelectric ceramic sheets in the low-frequency transducer according to the working frequency band; and obtaining the design scheme of the low-frequency transducer of the sonic logging instrument according to the size, the number and a preset piezoelectric ceramic sheet physical connection mode. The application can meet the excitation demand of low-frequency sound waves.

The present disclosure relates to borehole sonic logging and, more particularly to, improved reflection imaging of formation structures away from the wellbore. A method for borehole sonic reflection imaging may comprise: disposing a borehole sonic logging tool in a wellbore, wherein the borehole sonic logging tool comprises one or more transmitters and one or more receivers; emitting sound waves from the one or more transmitters; receiving sound waves at the one or more receivers to obtain borehole sonic data; separating up-going arrivals in the borehole sonic data from down-going arrivals in the borehole sonic data; generating a first reflection image based at least on the borehole sonic data; estimating a relative dip angle of a formation bed from the first reflection image; generating an updated velocity model based at least on the relative dip angle; and generating an updated reflection image based at least on the updated velocity model.

Aspects provide for methods that successfully evaluates multiple compressional and shear arrival events received by a sonic logging tool to evaluate the presence of structures, such as shoulder beds, in downhole environments. In particular, the methods described herein enable automated determination of properties of laminated reservoir formations by, for example, enabling the automated determination of arrival times and slownesses of multiple compressional and shear arrival events received by a sonic logging tool.

This invention provides a low-frequency monopole acoustic logging transducer, acoustic logging instrument, and system, belonging to the field of geological exploration technology. The low-frequency monopole acoustic logging transducer includes: a circumferential frame and an even number of dipole triplet plates, which are vertically mounted on the circumferential frame in a circumferential array. Each dipole triplet plate includes: a metal substrate, a first piezoelectric material element, and a second piezoelectric material element. The first piezoelectric material element is disposed on the upper surface of the metal substrate, and the second piezoelectric material element is disposed on the lower surface of the metal substrate relative to the upper surface. The even number of dipole triplet plates arranged in a circumferential array allows the overall circumferential monopole logging transducer to expand and contract radially to generate a symmetrical sound field. By using dipole triplet plates to reduce the fundamental frequency of vibration through axial space, a low-frequency acoustic signal is obtained, thereby more accurately acquiring Stoneley wave information from the formation and increasing the detection depth.

This invention proposes a logging-while-drilling (LWD) acoustic receiver, its manufacturing method, and its usage method, comprising: a drill collar skeleton, the drill collar skeleton being a hollow cylindrical structure with a water inlet in its center; an arc-shaped frame support, the arc-shaped frame support being evenly arranged circumferentially on the sidewalls of the drill collar skeleton, and receiving transducers being disposed on the arc-shaped frame support, the receiving transducers being evenly arranged circumferentially on the drill collar skeleton; wherein, a watertight insulating prestressed layer is provided on the outer surface of the arc-shaped frame support, which seals and fixes the receiving transducers.

The invention relates to the technical field of acoustic logging, in particular to acoustic logging equipment and an acoustic logging method.The acoustic logging equipment comprises a water injection hole packer, a hole packer guide rod, a pushing guide rod, an acoustic probe and an exhaust pipe, and a communicated hollow channel is formed in the water injection hole packer and the hole packer guide rod; the push guide rod slidably penetrates through the push guide rod, a third hollow channel is formed in the push guide rod, the sonic probe is fixed to the front end of the push guide rod, one end of the exhaust pipe is fixed to the top of the sonic probe, and the other end of the exhaust pipe is communicated with the inner channel of the push guide rod. An efficient and reliable directional exhaust path is constructed through an exhaust pipe and an internal channel of a pushing guide rod, and the problem that gas is retained at the top of an upward drilling hole is thoroughly solved; the visual phenomenon that water flows out of the tail end of the push guide rod is used as a full water indication signal, a clear and reliable judgment basis is provided for operators, and the accuracy of test data and the reliability of engineering application are remarkably improved.

This invention provides an acoustic logging azimuth receiver assembly and an acoustic logging instrument, belonging to the technical field of logging devices. It includes: a mandrel with multiple transverse sound-insulating grooves spaced along its length; multiple receiving transducer assemblies spaced along the mandrel's length; each receiving transducer assembly includes: a base fitted onto the mandrel; at least one receiving transducer mounted on the base via a mounting mechanism; and a locking mechanism mounted on the base for fixing the mounting mechanism to the base. This invention features a simple structure, small size, applicability to various logging instruments, wide applicability, high receiving sensitivity, and compatibility with both azimuth receiving transducers and conventional receiving transducers.

This invention discloses a method for inverting the velocity of the cemented medium behind the casing based on ultrasonic Lamb waves, relating to the field of geophysical logging. This invention utilizes a back-casing scanning imaging logging instrument to perform ultrasonic Lamb wave logging and ultrasonic pulse reflection logging at various depth points, acquiring waveform records at each depth point. The casing thickness and acoustic impedance of the cemented medium behind the casing at specified azimuths are inverted and calculated. Based on the ultrasonic Lamb wave logging waveform records, Fourier transforms are performed on the near-curved and far-curved Lamb wave full-wave waveforms at each specified azimuth of each depth point, calculating the phase difference between near and far-curved Lamb waves and performing group delay processing. Combining this with the operating frequency band of the back-casing scanning imaging logging instrument, the frequency values ​​corresponding to the minimum values ​​of the group delay at each azimuth of each depth point are obtained. After obtaining the frequency set, the wave velocity and medium type of the cemented medium behind the casing are determined based on the frequency values, the number of minimum frequencies, and the acoustic impedance values ​​at each azimuth of the frequency set.

The invention relates to the technical field of geothermal well sand production identification, and discloses an intelligent identification method and system for a geothermal well sand production position. The method comprises the steps that acoustic logging, resistivity and gamma ray data of a geothermal well are collected, and an original data set is formed; multi-dimensional feature extraction is carried out on the Gamma ray abnormal features, and a feature parameter set composed of the interval transit time, the resistivity gradient and the Gamma ray abnormal features is obtained; a dynamic stratum model is constructed based on the set, and the stratum characteristics of different underground depth intervals are represented; comparing the model with a preset standard stratum characteristic library, and identifying a target depth interval with significant difference; in combination with historical sand production records, the stratum parameter change trend is analyzed to determine a potential sand production layer; calculating a stratum stability index to generate a sand production risk grade, and correcting the risk grade in combination with underground real-time monitoring data; and finally, an identification report containing the stratum characteristic description and the sand production risk distribution of the target depth interval is generated, and targeted sand production prevention and treatment suggestions are output.

The application provides a sandstone type uranium ore prediction method based on pseudo-three-dimensional seismic data. The method comprises the following steps: a. obtaining two-dimensional seismic SGY profile data of a working area; b. performing trace head analysis on the SGY profile data; c. obtaining point coordinate data; d. processing the point coordinate data; e. processing the SGY profile data; f. collecting gamma and acoustic logging curves of the working area; g. processing the logging curve data; h. performing multi-parameter lithology inversion according to the processed SGY data and the logging curve data; and i. predicting a favorable sandstone type uranium ore forming area. The application fully utilizes two-dimensional seismic data, acoustic logging data and gamma logging data sensitive to sandstone type uranium ore to accurately and effectively predict the favorable sandstone type uranium ore forming area, reduces the uranium resource key exploration range in the working area, provides geophysical prospecting basis for subsequent drilling construction, greatly reduces the exploration cost and improves the exploration efficiency.

A method for acoustic logging a wellbore includes making a plurality of directional sonic logging measurements while rotating an acoustic logging tool in a wellbore. A plurality of orthogonal pairs of measurements are identified among the measurements. Each of the orthogonal pairs includes a first measurement having a measured angle of a transmitter firing direction that is perpendicular with a measured angle of a transmitter firing direction of a second measurement within a predetermined tolerance. A set of 4C component waveforms is compiled for each of the identified orthogonal pairs and mathematically rotated to align with predefined axes. Selected ones of the rotated waveforms are transformed to a frequency domain and stacked in the frequency domain to compute a median or average slowness at each of a plurality of frequencies.