A limitation of well velocity surveys in highly deviated wells drilled parallel to bedding

Geophysics ◽  
1996 ◽  
Vol 61 (3) ◽  
pp. 627-630
Author(s):  
Jesper M. Smidt
Keyword(s):  
Simple Formula ◽  
Seismic Energy ◽  
Depth Interval ◽  
Average Interval ◽  
Interval Velocity ◽  
Layer Interface ◽  
The Difference ◽  
Interval Velocities ◽  
Deviated Wells

Well velocity surveys (or check‐shot surveys) in vertical or moderately deviated wells provide average velocities and formation interval velocities by assuming a horizontally layered subsurface. The interval velocity, [Formula: see text], is calculated using the simple formula, [Formula: see text]where DZ is the vertical depth interval between two consecutive well geophone locations, [Formula: see text] and [Formula: see text], as shown in Figure 1a, and DT, the difference in the seismic traveltime from a source S at the wellhead to these two locations (Telford et al., 1976, 347). This quantity is the average interval velocity of Al‐Chalabi (1974) (see also Sheriff, 1991, 317). Vertical incidence of the seismic energy at the geophone is assumed, i.e., the source is located vertically above the geophone location. This assumption is made throughout this note; it would only serve to confuse the issue to correct for the usually small horizontal offset between source and receiver locations. I also assume throughout this note that no refraction takes place at any layer interface. Since only two‐layer cases are dealt with, this assumption is hardly a serious limitation.

A technique for stabilizing interval velocities from the Dix equation

Geophysics ◽  
1988 ◽  
Vol 53 (9) ◽  
pp. 1241-1243 ◽  
Author(s):  
John B. Dubose
Keyword(s):  
Root Mean Square ◽  
Mean Square ◽  
Average Interval ◽  
Interval Velocity ◽  
The Earth ◽  
Interval Velocities

Interval velocities, the velocities at which sounds travel in the earth, can be computed from stacking or root‐mean‐square (rms) velocities by applying the Dix equation (Dix, 1955): [Formula: see text] where [Formula: see text] are the stacking velocity picks, [Formula: see text] are the associated times, and [Formula: see text] is the average interval velocity between [Formula: see text] and [Formula: see text].

A method for direct estimation of interval velocities

Geophysics ◽  
1982 ◽  
Vol 47 (12) ◽  
pp. 1657-1671 ◽  
Author(s):  
Philip S. Schultz
Keyword(s):  
Estimation Procedure ◽  
Estimation Accuracy ◽  
Substantial Contribution ◽  
Interval Velocity ◽  
Direct Estimation ◽  
Enhanced Resolution ◽  
Prior Estimate ◽  
Sensitive Function ◽  
Interval Velocities ◽  
Ray Parameter

The most commonly used method for obtaining interval velocities from seismic data requires a prior estimate of the root‐mean‐square (rms) velocity function. A reduction to interval velocity uses the Dix equation, where the interval velocity in a layer emerges as a sensitive function of the rms velocity picks above and below the layer. Approximations implicit in this method are quite appropriate for deep data, and they do not contribute significantly to errors in the interval velocity estimate. However, when the data are from a shallow depth (vertical two‐way traveltime being less than direct arrival to the farthest geophone), the assumption within the rms approximation that propagation angles are small requires that much of the reflection energy be muted, along with, of course, all the refraction energy. By means of a simple data transformation to the ray parameter domain via the slanted plane‐wave stack, three types of arrivals from any given interface (subcritical and supercritical reflections and critical refractions) become organized into a single elliptical trajectory. Such a trajectory replaces the composite hyperbolic and linear moveouts in the offset domain (for reflections and critical refractions, respectively). In a layered medium, the trajectory of all but the first event becomes distorted from a true ellipse into a pseudo‐ellipse. However, by a computationally simple layer stripping operation involving p‐dependent time shifts, the interval velocity in each layer can be estimated in turn and its distorting effect removed from underlying layers, permitting a direct estimation of interval velocities for all layers. Enhanced resolution and estimation accuracy are achieved because previously neglected wide‐angle arrivals, which do not conform to the rms approximation, make a substantial contribution in the estimation procedure.

Velocity computation from checkshot surveys in deviated wells

Geophysics ◽  
1995 ◽  
Vol 60 (6) ◽  
pp. 1930-1932 ◽  
Author(s):  
Ilkka T. Noponen
Keyword(s):  
The Other ◽  
Velocity Measurements ◽  
Horizontal Movement ◽  
Wave Source ◽  
Interval Velocity ◽  
Drilling Rig ◽  
The Common ◽  
Deviated Wells

When checkshot surveys are done in deviated wells, two source‐receiver geometries are used. In one, the wave source is moved on the earth’s surface in unison with the horizontal movement of the receiver in the well so that the raypath from the source to the receiver is always vertical. This is the source‐over‐receiver approach. In the other approach, called source‐at‐rig, the source is fixed, usually staying in the vicinity of the drilling rig. The source‐over‐receiver method is usually preferred because the source‐at‐ rig method does not measure vertical traveltimes. If velocity varies with depth, the seismic rays from a source at the rig will bend, and a correction to vertical using the common straight‐ray assumption will not produce accurate vertical traveltimes or interval velocity measurements.

Derivation of seismic cone interval velocities utilizing forward modeling and the downhill simplex method

2002 ◽  
Vol 39 (5) ◽  
pp. 1181-1192 ◽  
Author(s):  
Erick J Baziw
Keyword(s):  
Elastic Constants ◽  
Simplex Method ◽  
Forward Modeling ◽  
S Wave ◽  
Cone Penetration ◽  
Interval Velocity ◽  
Wave Velocities ◽  
Downhill Simplex Method ◽  
Downhill Simplex ◽  
Interval Velocities

The seismic cone penetration test (SCPT) has proven to be a very valuable geotechnical tool in facilitating the determination of low strain (<10–4%) in situ compression (P) and shear (S) wave velocities. The P- and S-wave velocities are directly related to the soil elastic constants of Poisson's ratio, shear modulus, bulk modulus, and Young's modulus. The accurate determination of P- and S-wave velocities from the recorded seismic cone time series is of paramount importance to the evaluation of reliable elastic constants. Furthermore, since the shear and compression wave velocities are squared in deriving the elastic constants, small variations in the estimated velocities can cause appreciable errors. The standard techniques implemented in deriving SCPT interval velocities rely upon obtaining reference P- and S-wave arrival times as the probe is advanced into the soil profile. By assuming a straight ray travel path from the source to the SCPT seismic receiver and calculating the relative reference arrival time differences, interval SCPT velocities are obtained. The forward modeling – downhill simplex method (FMDSM) outlined in this paper offers distinct advantages over conventional SCPT velocity profile estimation methods. Some of these advantages consist of the allowance of ray path refraction, greater sophistication in interval velocity determination, incorporation of measurement weights, and meaningful interval velocity accuracy estimators.Key words: seismic cone penetration testing (SCPT), downhill simplex method (DSM), forward modeling, Fermat's principle, weighted least squares (l2 norm), cost function.

Comparative study of the operational properties of deviated and straight gas-lift wells and sensitivity analysis of pressure gradient

2020 ◽  
pp. 108-117
Author(s):  
V.J. Abdullaev ◽  
Keyword(s):  
Pressure Gradient ◽  
Gas Flow ◽  
Dynamic Pressure ◽  
Flow Simulation ◽  
Mathematical Expression ◽  
Flow Properties ◽  
The Difference ◽  
Gas Lift ◽  
Working Agent ◽  
Deviated Wells

The article presents a benchmarking analysis of the complex well body structure effect on the hydraulic parameters of the liquid-gas flow pattern in deviated wells. The difference between the consumption of the working agent (gas) required to lift the same amount of liquid from the same depth in vertical and inclined gas-lift wells is shown. Considering the complexity of the hydrodynamic flow properties in deviated wells, the impossibility of analytical flow simulation, the article provides the problem study using statistical methods and gives its practical solution. The article presents a mathematical expression to determine the dynamic pressure gradient using this method, that is, by group calculation of indicators of gas-lift wells with an deviated body, and its numerical value was found.

Forecast of the Pyroclastic Volume by Precursory Seismicity of Merapi Volcano

2019 ◽  
Vol 14 (1) ◽  
pp. 51-60 ◽  
Author(s):  
Masato Iguchi ◽  
Haruhisa Nakamichi ◽  
Kuniaki Miyamoto ◽  
Makoto Shimomura ◽  
I Gusti Made Agung Nandaka ◽  
...  
Keyword(s):  
Seismic Energy ◽  
Volcanic Eruptions ◽  
Pyroclastic Flows ◽  
Energy Calculation ◽  
Cumulative Energy ◽  
Merapi Volcano ◽  
Tectonic Earthquakes ◽  
Order Of Magnitude ◽  
The Difference ◽  
Log Linear

We propose a method to evaluate the potential volume of eruptive material using the seismic energy of volcanic earthquakes prior to eruptions of Merapi volcano. For this analysis, we used well-documented eruptions of Merapi volcano with pyroclastic flows (1994, 1997, 1998, 2001, 2006, and 2010) and the rates and magnitudes of volcano-tectonic A-type, volcano-tectonic B-type, and multiphase earthquakes before each of the eruptions. Using the worldwide database presented by White and McCausland [1], we derived a log-linear formula that describes the upper limit of the potential volume of erupted material estimated from the cumulative seismic energy of distal volcano-tectonic earthquakes. The relationship between the volume of pyroclastic material and the cumulative seismic energy released in 1994, 1997, 1998, 2001, 2006, and 2010 at Merapi volcano is well-approximated by the empirical formula derived from worldwide data within an order of magnitude. It is possible to expand this to other volcanic eruptions with short (< 30 years) inter-eruptive intervals. The difference in the intruded and extruded volumes between intrusions and eruptions, and the selection of the time period for the cumulative energy calculation are problems that still need to be addressed.

THE REFRACTION SEISMOGRAPH IN THE ALBERTA FOOTHILLS

Geophysics ◽  
1956 ◽  
Vol 21 (3) ◽  
pp. 828-838 ◽  
Author(s):  
G. J. Blundun
Keyword(s):  
Operating Conditions ◽  
Radio Communication ◽  
Interval Velocity ◽  
Mississippian Limestone ◽  
Interval Velocities ◽  
Definition Of ◽  
Characteristic Interval ◽  
Consequent Improvement ◽  
Continuous Determination

In the Alberta foothills the most valuable use of the refraction seismograph is for the definition of overthrust faulting in the Mississippian limestone which is overlain by a faulted, overthrust, and overturned Cretaceous section. Normally, two refracted arrivals are recorded with characteristic interval velocities of 14,000 ft/sec and 21,000 ft/sec, the former arising from an unknown Cretaceous marker, and the latter from the Mississippian. In contrast to a shot‐range of 65,000 ft required to record the refracted arrival from the Mississippian at a depth of 10,000 ft as the first event, a range of 20,000 ft permits recording it as the later event, with consequent improvement in the quality and reliability of the data, reduces the amount of surveying required together with smaller dynamite charges, and improves radio communication. A geophone spread of 6,300 ft with single geophones at 300 ft intervals recorded on 22 traces is recommended. Both in‐line and broadside refraction with the Mississippian arrival recorded as the later event have been used successfully with certain advantages to each method. The former permits continuous determination of the interval velocity of the refracted events as well as providing two‐way control; the latter is considerably faster, and often faulting may be observed directly on the seismograms without reduction of the data. Specimen seismograms are included to illustrate the two methods. Field operating conditions pertaining to survey tolerances, shot formation, size of dynamite charges, the weathering shot as a polarity check, filtering, geophone frequency, and costs are discussed.

SEISMIC SIGNATURES OF SEDIMENTATION MODELS

Geophysics ◽  
1972 ◽  
Vol 37 (1) ◽  
pp. 45-58 ◽  
Author(s):  
J. C. Harms ◽  
P. Tackenberg
Keyword(s):  
Cross Sections ◽  
Quality Data ◽  
Interval Velocity ◽  
Reflection Seismic ◽  
Depositional Processes ◽  
Velocity Changes ◽  
Interval Velocities ◽  
Processing Techniques ◽  
Direct Location ◽  
Stratigraphic Sequences

Seismic techniques have been used mainly for structural interpretation, but mounting interest in stratigraphic applications is evident. Estimation of sand‐shale ratios from seismically derived average velocities is a recent example of a stratigraphic application. Except in the case of tall pinnacle reefs, today direct location of stratigraphic traps by reflection methods is restricted, at best, to areas of very high quality data and abundant well control. However, it may be possible to interpret some useful stratigraphic characteristics from seismic reflections, the interpretation being based upon the concept of sedimentation models. Most stratigraphic sequences are not random stacks of various lithologies. Commonly, they are well organized and have units with characteristic contacts, thicknesses, lateral extents, lateral facies changes, and vertical sequence. These orderly characteristics are summarized in sedimentation models, where the control of lithologic distribution by dominant depositional processes is emphasized. Three sedimentation models for sandstone and shale sequences are presented. For each, one example is described and converted to a synthetic reflection seismic cross‐section. These cross‐sections are each distinct in terms of reflection polarities, areal changes in reflection amplitudes, continuity of events, and lateral interval velocity changes. The simplified models, although limited in their scope, suggest that additional stratigraphic information can be gleaned from reflection seismic data. To exploit this promise, record processing techniques that emphasize recognition of reflection polarities, amplitudes, continuity, and interval velocities must be developed or improved. It is also necessary to improve our knowledge of seismic boundaries in a variety of stratigraphic sequences. Though difficult, these valuable goals appear attainable.

Nonlinear distortion of signals radiated by vibroseis sources

Geophysics ◽  
2004 ◽  
Vol 69 (4) ◽  
pp. 968-977 ◽  
Author(s):  
Andrey V. Lebedev ◽  
Igor A. Beresnev
Keyword(s):  
Thin Layer ◽  
Nonlinear Response ◽  
Nonlinear Distortion ◽  
Near Field ◽  
Quantitative Description ◽  
Harmonic Distortion ◽  
Seismic Energy ◽  
Field Observations ◽  
Contact Nonlinearity ◽  
The Difference

A model of nonlinearity of the contact between the vibrator baseplate and the ground is proposed to describe the distortion of vibroseis signals in the near‐field. A thin layer between the baseplate and the soil exhibits a strong nonlinear response because of the difference in its rigidity between the compression and tension phases. The model allows for a quantitative description of the transmission of seismic energy into the ground, including the observed harmonic distortion. However, the contact nonlinearity does not lead to the dependence of wave traveltimes on the amplitude of the force applied to the ground. This fact can be used in field observations to localize the source of the observed harmonic distortion.

INTERVAL VELOCITIES FROM SURFACE MEASUREMENTS IN THE THREE‐DIMENSIONAL PLANE LAYER CASE

Geophysics ◽  
1976 ◽  
Vol 41 (2) ◽  
pp. 233-242 ◽  
Author(s):  
Peter Hubral
Keyword(s):  
Three Dimensional ◽  
Normal Incidence ◽  
Plane Layer ◽  
Three Dimensions ◽  
Seismic Parameters ◽  
Interval Velocity ◽  
Common Depth Point ◽  
Measured Time ◽  
Surface Measurements ◽  
Interval Velocities

The basic requirements to recover plane layers of constant interval velocity, arbitrary dip and strike from common depth point (CDP) recordings are the following four quantities related to the primary event of each reflector at the common midpoint of a CDP profile: a) Two‐way normal time b) Normal moveout velocity within one arbitrary CDP profile c) Time slope of normally reflected rays within the profile d) Time slope of normally reflected rays in some other direction. The solution of the inverse problem is obtained directly. The moveout velocity is expressed in terms of seismic parameters along the normal incidence path in three dimensions and the direction of the profile within the free surface. A formula connecting dip and strike of the emerging normal ray with the measured time gradients is given and discussed. The method includes, as a special case, the Dix formulas for plane parallel layers.

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