As this is an introductory text, we have not attempted to be completely comprehensive in our coverage of the topic. Readers seeking additional information on any of the research methods described should refer to the more advanced texts listed at the end of each chapter.
Introduction
The survey methods
As expected, the salt dome is associated with a negative magnetic anomaly, although the magnetic layer is slightly displaced from the center of the dome. Grand Saline Salt Dome, Texas, USA (contours in gravity units — see Chapter 6). The dotted area represents the subcrop of the dome.
The problem of ambiguity in geophysical interpretation
If a salt dome is encountered, rays reflected from its upper surface will delineate the shape of the hidden body. Much greater penetration can be achieved by using the natural Earth currents (telluric currents) generated by the movements of charged particles in the ionosphere.
The structure of the book
And since rocks vary considerably in the speed with which they propagate seismic waves, it is by no means a simple matter to translate the travel time of a seismic pulse into an accurate depth to the geological interface from which it was reflected. The solution to this particular problem, as discussed in Chapter 4, is to measure the travel times of reflected pulses at various offset distances from a seismic source because the variation of travel time as a function of distance provides information about the velocity distribution with depth.
Introduction
Digitization of geophysical data
Sampling at this rate will keep all frequencies up to 250 Hz in the sampled function. This frequency of half the sampling frequency is known as the Nyquist frequency (fN), and the Nyquist interval is the frequency range from zero to fN. The relationship between input and output frequency in the case of a sampling frequency of 500 Hz is shown in fig.
Spectral analysis
Digitalization of the waveform in the time domain (section 2.2) provides a way to deal with the continuous spectra of transient waveforms. This digital expression of a continuous spectrum in terms of a finite number of discrete frequency components provides an approximate representation in the frequency domain of a transient waveform in the time domain.
Waveform processing
Convolution
2.11(d)) is now the superposition of the two impulse response functions offset in time by the separation of the. 2.11(f )) can be thought of as the sum of a set of impulse responses associated with a sequence of spikes simulating the overall shape of the input waveform.
Deconvolution
Correlation
Side lobes in the autocorrelation function (Fig. 2.15) are indicative of the existence of periodicities in the original waveform, and the distance between the side lobes defines the recurrence period. This property is especially useful in the detection and suppression of multiple reflections in seismic data (see Chapter 4). The autocorrelation function contains all the amplitude information of the original waveform, but none of the phase information, replacing the original phase relationships with a zero phase spectrum.
Digital filtering
Frequency filters
The desired output characteristics of the ideal LP filter are represented by the amplitude spectrum shown in Fig. The inverse Fourier transform of the transfer function in the time domain gives the impulse response of the ideal LP filter (see Fig.
Inverse (deconvolution) filters
HP, BP and BR time domain filters can be designed in a similar way by specifying a specific transfer function in the frequency domain and using it to design a finite-length impulse response function in the time domain. As with analog filtering, digital frequency filtering usually changes the phase spectrum of the waveform and this effect can be undesirable. However, zero-phase filters can be designed that facilitate digital filtering without changing the phase spectrum of the filtered signal.
Imaging and modelling
The most obvious examples of this are in the seismic reflection (Chapter 4) and ground-penetrating radar (Chapter 9) sections, where the waveform of the change of reflected energy with time is used to derive an image related to the geological occurrence. limits in depth. In modeling, the geophysicist selects a particular type of subsurface structural model and uses this to predict the shape of the actual recorded waveforms.
Introduction
Stress and strain
Up to a certain limiting value of stress, known as the yield strength of a material, the strain is directly proportional to the applied stress (Hooke's Law). Note that the extension of such a rod will be accompanied by a decrease in its diameter; that is, the bar will undergo lateral and longitudinal strain. The ratio of lateral to longitudinal strain is known as Poisson's ratio.
Seismic waves
Body waves
Although knowledge of P-wave velocity is useful, it is a function of three separate properties of the rock and is only a very ambiguous indicator of rock lithology. One application of shear-wave seismology is the investigation of engineering sites, where the separate measurement of vpand versus near-surface layers allows a direct calculation of the Poisson's ratio and an estimate of the elas-.
Surface waves
If the surface is layered and the shear wave speed of the surface layer is lower than that of the underlying layer, a second set of surface waves is generated. Love waves are polarized shear waves with particle motion parallel to the free surface and perpendicular to the direction of the surface. wave propagation (Fig. The speed of love waves is between the speed of the surface layer shear wave and that of deeper layers, and love waves are inherently dispersed.
Waves and rays
The same methodology, applied to surface waves generated by a sledgehammer, can be used to examine the strength of near-surface materials for civil engineering investigations. The observed pattern of Love wave scattering can be used in a similar way to Rayleigh wave scattering to study subsurface structure.
Seismic wave velocities of rocks
It is important to note that laboratory measurements at low confining pressures are of questionable validity. The intrinsic velocity of a rock is not normally achieved in the laboratory below a confining pressure of about 100 MPa (megapascals), or 1 kbar. at which pressure the original solid contact between the grains, characteristic of the pristine rock, is restored. Typical compression wave velocity values and ranges for a wide variety of earth materials are given in Table 3.1.
Attenuation of seismic energy along ray paths
Wave amplitude, which is proportional to the square root of the wave energy, therefore decreases as r-1. In general, the effect of absorption is to produce a progressive lengthening of the seismic pulse (Fig. 3.7).
Ray paths in layered media
- Reflection and transmission of normally incident seismic rays
- Reflection and refraction of obliquely incident rays
- Critical refraction
- Diffraction
Relating this simple measure to the physical properties of materials at the interface is a complex problem. The transmission coefficient is the ratio of the amplitude A2 of the transmitted beam to the amplitude A0 of the incident beam.
Reflection and refraction surveying
At the critical distance, the travel times of reflected rays and refracted rays coincide because they actually follow the same path. The above characteristics of the travel time curves determine the methodology of refraction and reflection research.
Seismic data acquisition systems
Seismic sources and the seismic/acoustic spectrum
The vibrator unit needs a solid base to work on, such as an asphalt road, and will not perform well on soft ground. The maximum force of a vibrator is only about 105N. An alternative is to fire a blank cartridge into a hole using a suitable device, commonly called a buffalo gun (Fig 3.16). The blank shotgun cartridge provides an impulse source that delivers far more energy than a sledgehammer, with some of them. explosives safety issues.
Seismic transducers
Above the resonant frequency, the output of a moving coil geophone is proportional to the speed of the coil. Moving coil geophones are only sensitive to the component of ground motion along the axis of the coil.
Seismic recording systems
The individual detector outputs can be powered via a multi-core cable. The weight and complexity of multi-conductor cables become prohibitive as the number of cables increases. The number of data channels runs into the hundreds. What is the attenuation in amplitude of the pulse caused by energy partitioning at all interfaces that occur in its path.
Introduction
Geometry of reflected ray paths
- Single horizontal reflector
- Sequence of horizontal reflectors
- Dipping reflector
- Ray paths of multiple reflections
This is the intersection point on the time axis of the time-distance curve (see Fig. 4.4). This form of the travel-time equation (4.4) represents the simplest way to determine the velocity V. The root-mean-square velocity of the section of ground up to the nth interface is given by.
The reflection seismogram
The seismic trace
The basic reflection seismic trace can then be considered as a convolution of the reflection function with a time-varying seismic pulse. The trace will be further complicated by the superposition of different types of noise, such as multiple reflections, direct and refracted body waves, surface waves (ground waves), air waves, and coherent and incoherent noise unrelated to the seismic source. In seismic reflection measurement, seismic traces are recorded, and the purpose of seismic processing can be understood as an attempt to reconstruct the different columns in Figure 1.
The shot gather
In these seismic records, the identification of reflection events and their correlation between traces is greatly aided if one half of the normal "flicker trace" waveform is blocked. Shortly after the instant of lightning, the first arrival of seismic energy reaches the innermost geophones (central traces) and this energy flows out symmetrically through both arms of the split width. The first arrivals are followed by a series of rebound events revealing their hyperbolic motion.
The CMP gather
In shot collections, the seismic traces are plotted side by side in the correct relative positions and the records are usually displayed with their time axes arranged vertically in a draped manner. In two-dimensional CMP surveying, known as CMP profiling, the reflection points are all assumed to lie within the vertical section containing the survey line.
Multichannel reflection survey design The basic requirement of a multichannel reflection sur-
- Vertical and horizontal resolution
- Design of detector arrays
- Common mid-point (CMP) surveying If the shot–detector spread in a multichannel reflection
- Display of seismic reflection data
Energy returned to a detector within half a wavelength of the initial reflected arrival interferes with. The effective displacement of an array is assumed to be the distance from the shot to the center of the array.
Time corrections applied to seismic traces Two main types of correction need to be applied to re-
Common mid-point (CMP) profiling, which has become the standard method for two-dimensional multi-channel seismic surveys, involves ensuring that a series of traces recorded at different offsets contain reflections from a common mid-point (CDP). on the reflector (Fig. 4.14). The fold of the stack refers to the number of traces in the CMP collection and can conventionally or, exceptionally, be more than 1000. The fold is alternatively expressed as a percentage: single = 100% coverage, sextuple = 600% coverage and so on. The fold of a CMP profile is determined by the amount N/2n, where Nis is the number of geophone arrays along a spread and nis is the number of geophone array distances by which the spread is moved forward between shots (the move-up rate).
Static correction
Static elevation corrections that correct the elevation of the image and geophone above standard elevation (usually sea level). Calculating the static weathering correction requires knowledge of the variable velocity and thickness of the weathered layer.
Velocity analysis
The static correction is commonly limited to a conversion of travel times to mean sea level datum without removing the overall effect of the water layer. Prior to this velocity analysis, static corrections must be applied to the individual tracks to remove the effect of the low velocity surface layer and to reduce travel times to a common elevation datum. The method is exemplified with reference to fig.
Filtering of seismic data
Frequency filtering
Any coherent or incoherent noise event whose dominant frequency differs from that of reflected arrivals can be suppressed by frequency filtering (see Chapter 2). The filtering can be performed by a computer in the time domain or the frequency domain (see Chapter 2).
Inverse filtering (deconvolution)
The resultant seismic trace xk will be given by the convolution of the reflection function rk with the composite input waveform wk as schematically shown in the figure. It follows from assumption (1) that the autocorrelation function of the seismic trace represents the autocorrelation function of the composite waveform wk.
Velocity filtering
Therefore, a plot of frequency f versus apparent wavenumber ka for the pulse will give a straight curve with a gradient va (Fig. 4.24). It is clear that different types of seismic events fall within different areas of the f-kplot and this fact provides a filtering tool to suppress unwanted events based on their apparent velocity. Normal means.
Migration of reflection data
The general goal of three-dimensional surveys is to achieve a higher degree of resolution of the subsurface geology than is achievable with two-dimensional surveys. Three-dimensional survey therefore samples a volume of the subsurface rather than an area located in a vertical plane as in two-dimensional survey.
Three component (3C) seismic reflection surveys
Once an oil field is in production, the oil and/or gas is extracted and its place in the pores of the reservoir rock is taken up by inflowing groundwater. As the pore fluids change, the seismic response of the formations also changes.
Vertical seismic profiling
It can be argued that there are more hydrocarbon resources to be recovered from careful monitoring of known fields than from searching for new fields. Comparison of this accumulated trace with a conventional seismic section from the vicinity of the pit (Fig. 4.46) enables the reliable identification of the geological content of the latter.
Interpretation of seismic reflection data Differing procedures are adopted for the interpretation
- Structural analysis
- Stratigraphical analysis (seismic stratigraphy)
- Seismic modelling
- Seismic attribute analysis
Structural interpretation of three-dimensional data can benefit from the surface coverage of reflection. Variations in amplitude along a reflector should therefore indicate changes in the properties of the formations.
Single-channel marine reflection profiling
Shallow marine seismic sources
Consequently, by choosing a suitable source, single-channel profiling can be applied to a wide range of offshore surveys from high-resolution surveys of near-surface sedimentary layers to surveys of deep geological structure. Pingers are low-energy (typically around 5 J), tunable sources that can be operated within the frequency range.
Sidescan sonar systems
This distortion can be automatically corrected before displaying so that the sonograph provides an isometric top view of seafloor features. Sidescan sonar is also useful for locating artefacts on the seabed such as wrecks, cables or pipes.
Applications of seismic reflection surveying
Three-dimensional seismic may need to be used when critical structural details are unresolved when interpreting the two-dimensional survey data. Crustal reflection profiling results from several different continental areas reveal that the upper part of.
Introduction
Geometry of refracted ray paths
- Two-layer case with horizontal interface Figure 5.1 illustrates progressive positions of the wave-
- Three-layer case with horizontal interface
- Multilayer case with horizontal interfaces
- Dipping-layer case with planar interfaces
- Faulted planar interfaces
In general, the travel time tn of a critically refracted ray along the top surface of the ninth layer is given by. The general form of the equation for the travel time tn of a critically refracted ray in the nth dipping refractor (Fig. 5.6; Johnson 1976) is given by.
Profile geometries for studying planar layer problems
In the case considered, v2d is derived from the single-ended travel-time curves, so v2u can be calculated from the difference in travel time of refracted rays from adjacent shots recorded at the same offset distance x.
Geometry of refracted ray paths
Delay time
This is the same result as derived earlier in equation (5.1), indicating that the concept of delay is implicit even in simple horizontal-lateral methods of interpretation. Hagedoorn's (1959) plus–minus method provides a way of solving equation (5.18) to derive individual time delay values for calculating local depths of an irregular refractor.
The plus–minus interpretation method Figure 5.12(a) illustrates a two-layer ground model with
The plus-minus method is only applicable in the case of shallow refractor dives, and is generally considered valid for dips of less than 10°. Furthermore, there is an inherent smoothing of the interpreted refractor geometry in the plus-minus method.
The generalized reciprocal method
For the valid range of detectors defined by the minus-time graph, the delay times can now be calculated. When calculating the plus term for each detector, the refractor is assumed to be planar between the refractor exit points of the forward and reverse beams, for example between A and B in Fig.
Construction of wavefronts and ray-tracing Given the travel-time plots in the forward and reverse
The hidden and blind layer problems
A blind layer presents a more subtle problem, resulting from a low-velocity layer, as illustrated in Fig. In the presence of a low-velocity layer, the interpretation of traveltime curves leads to an overestimation of the depth at the base. interfaces.
Refraction in layers of continuous velocity change
Methodology of refraction profiling
- Field survey arrangements
- Recording scheme
- Weathering and elevation corrections The type of observational scheme illustrated in Fig. 5.18
- Display of refraction seismograms
The velocity and thickness of the weathered layer varies greatly laterally and the travel times of the rays from the lower refractors must vary. The weathering correction is applied by effectively replacing the weathered layer at velocity vw with material at velocity v1 equal to the velocity of the underlying layer.
Other methods of refraction surveying Although the vast bulk of refraction surveying is carried
The time expression method uses a form of the travel time equation that contains delay times (Eq. (5.18)) and is subject to the same basic assumptions as other interpretation methods that use delay times. In fact, with a time-term approach to refraction measurements, it is usually arranged that m well exceeds (n+1) and that multiple shot and detector positions need to be interchanged. The resulting overdetermined set of equations is solved by deriving values for the individual delay times and refractor speed that minimize the sum of squared errors eij.
Seismic tomography
Common methods of solving the resulting equations are the algebraic reconstruction technique (ART) and the simultaneous reconstruction technique (SIRT). Particular examples would be the S-wave travel times and the attenuation of the seismic wave.
Applications of seismic refraction surveying
- Engineering and environmental surveys
- Hydrological surveys
- Crustal seismology
- Two-ship seismic surveying: combined refraction and reflection surveying
Typically seismic and resistivity studies can be used together to attempt to 'characterize' the nature of landfill materials. Refraction and wide-angle surveys have been widely used for the regional investigation of the internal structure and thickness of the Earth's crust. Information derived from such studies is complementary to direct seismic imaging of crustal structure derived from large-scale reflection. surveys of the type discussed in section 4.16.
Introduction
Basic theory
Units of gravity
Measurement of gravity
In such a case, the overall effect of the horizontal accelerations is to produce a systematic error in the beam position. The most successful axially symmetric instrument to date is the Bell gravimeter (Bell & Watts 1986). The sensing element of the meter is the accelerometer shown in Fig.
Gravity anomalies
In the zero position, the weight of the mass is balanced by the forces exerted by the permanent magnets. Consequently, the measured perturbations in gravity effectively correspond to the vertical drag component of the causative body.
Gravity anomalies of simple-shaped bodies Consider the gravitational attraction of a point mass m at
In general, the gravity anomaly of a body of any shape can be determined by summing the attractions of all the mass elements that make up the body. The whole-body anomaly Dgis was then found by summing all such elements that make up the body.
Gravity surveying
As shown before, the attraction of bodies with regular geometry can be determined by integrating equation (6.10) analytically. The anomalies of irregularly shaped bodies are calculated by numerical integration using equations in the form of equation (6.9).
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Gravity reduction
- Drift correction
- Latitude correction
- Elevation corrections
- Tidal correction
- Eötvös correction
- Free-air and Bouguer anomalies
On land, the Bouguer correction must be subtracted, as the gravitational attraction of the rock between observation point and datum must be removed from the observed gravity value. The regions designated A form part of the Bouguer correction plate although they do not consist of rock.
Rock densities
The terrain data are reduced with a set of different densities for Bouguer and terrain corrections (Figure 6.15). The density value that yields the Bouguer anomaly with the smallest correlation (positive or negative) with topography is taken as the density representation of importance. Gravity reductions were made using densities ranging from 1.8 to 2.8 Mg m-3 for both Bouguer and terrain corrections. The profile corresponding to a value of 2.3 Mg m-3 shows the least correlation with topography, so this density is considered as the feature density.
Interpretation of gravity anomalies
- The inverse problem
- Regional fields and residual anomalies Bouguer anomaly fields are often characterized by a
- Direct interpretation
- Indirect interpretation
This method requires the calculation of the maximum amplitude of the anomaly (Amax) and the maximum horizontal gravity gradient (A¢max) (Fig. 6.21, which extends to infinity inside and outside the picture plane. the gravity anomaly of this plate Dgis given by.
Elementary potential theory and potential field manipulation
Equation (6.25) makes it possible to state the general form of the equation for any value of z. 6.27). Selective enhancement of the low or high wavenumber components of the potential field can be achieved in a different but similar way by.
Applications of gravity surveying
Comment on the accuracy of the value obtained and compare it with the answer to (b). In the eastern part of the map, horizontally bedded Mesozoic sediments unconformably overlie the shales.
Introduction
Basic concepts
The magnetic fields of the dipoles are self-cancelling, so there is no external magnetic effect. The size of J determines the amplitude of the magnetic anomaly and the orientation of Jin influences its shape.
Rock magnetism
When stronger fields are applied, the domain walls break down irreversibly across small imperfections in the grain, so that those fields magnetized in the direction of the field are permanently enlarged. Remanent magnetization can slowly develop in a rock standing in an ambient magnetic field as the primary magnetizations relax in the direction of the field (viscous remanent magnetization, VRM).
The geomagnetic field
The effects of each fictitious dipole contribute to a function known as a harmonic, and the technique of successive approximations of the observed field is known as spherical harmonic analysis—the equivalent of Fourier analysis in spherical polar coordinates. The required magnetic dipole moments are much larger than considered realistic, and the prevailing high temperatures far exceed the Curie temperature of any known magnetic material. The cause of the geomagnetic field is attributed to the dynamic action caused by the circular .
Magnetic anomalies
A magnetic anomaly is now superimposed on the Earth's field, causing a change DB in the strength of the total field vector B. Substitution equation (7.8) and angular descriptions of geomagnetic element ratios give this. 7.9) where I is the slope of the geomagnetic field.
Magnetic surveying instruments
- Introduction
- Fluxgate magnetometer
- Proton magnetometer
- Optically pumped magnetometer
- Magnetic gradiometers
7.10(e)), the magnitude of which can be shown to be proportional to the amplitude of the external field component. The energy difference between levels 1 and 2 is proportional to the strength of the external magnetic field.
Ground magnetic surveys
In these alkali atoms there exist valence electrons which are divided into two energy levels 1 and 2. The wavelength of the energizing light is chosen to excite electrons from level 2 to the higher level 3, a process called polarization. Depolarization then occurs through the application of radio frequency power. The wavelength corresponding to the energy difference between levels 1 and 2 depolarizes the cell and is a measure of the magnetic field strength.
Aeromagnetic and marine surveys
Many modern proton magnetometers use the Overhauser effect. A liquid containing several free electrons in "unpaired" orbits is added to the sensor liquid. Magnetic gradiometers are differential magnetometers in which the spacing between the sensors is fixed and small relative to the distance of the causative body whose magnetic field gradient is to be measured.
Reduction of magnetic observations
- Diurnal variation correction
- Geomagnetic correction
- Elevation and terrain corrections
The magnetic equivalent of the latitude correction in gravity measurement is the geomagnetic correction, which removes the effect of a geomagnetic reference field from the survey data. After applying diurnal and geomagnetic corrections, any remaining magnetic field variations should be caused solely by spatial variations in the subsurface magnetic properties and are referred to as magnetic anomalies.
Interpretation of magnetic anomalies
- Introduction
- Direct interpretation
- Indirect interpretation
For the above reasons, magnetic anomalies are often much less closely related to the shape of the causative body than gravitational anomalies. In the magnetic case, the horizontal DH, vertical DZ, and DB anomalies of the total field (nT) of the plates are shown in Fig. 1b.
Potential field transformations
Due to the dipolar nature of magnetic anomalies, trial and error methods of indirect interpretation are difficult to perform manually, as the anomaly shape is not closely related to the geometry of the causative body. An additional processing operation that can be applied to magnetic anomalies is known as reduction to the pole and involves the conversion of the anomalies to their equivalent form at the north magnetic pole (Baranov & Naudy 1964).
Applications of magnetic surveying
Consequently, oceanic crust can be dated based on the pattern of magnetic polarity transitions preserved in it. What is the effect on the profile if the dipole strikes 25°E of the magnetic meridian.
Introduction
Resistivity method
- Introduction
- Resistivities of rocks and minerals
- Current flow in the ground
- Electrode spreads
- Resistivity surveying equipment
- Interpretation of resistivity data
In CST surveys with the Schlumberger configuration, various lateral movements of the potential electrodes can be accommodated without the need to move the current electrodes. In VES recordings, the potential electrodes remain fixed and the current electrodes are symmetrically extended around the center of the distribution.
