The Seismic Exploration Survey Information Technology Essay
Seismic surveys aims at measuring the earth’s geological properties employing various physics principles of electric, gravitational, thermal and elastic theories. It was first employed successfully in Texas and Mexico by a company named Seismos in 1924. Since then, many oil companies have used the services of seismology to forecast the presence of hydrocarbon. Major oil companies have actively researched in the seismic technology and this has also found applications in various other researches by scientists around the world.
Seismic exploration surveys are method employed in exploration geophysics that uses principles of reflection seismology to estimate the subsurface properties. The method requires a controlled source of energy that can generate seismic waves and highly sensitive receivers that can sense the reflected seismic waves. The time delay in sending and receiving signals can optimally be used to calculate the depth of the formation.
Since different formation layers have different densities, they reflect back seismic waves at different velocities. This aspect can be used to estimate the depth of the target formation, usually shale or other rock formations that can form a cap rock or contain oil. Seismic surveys form a part of the preliminary exploration surveys and form the basis for further study of the area under consideration.
Seismic waves are a form of elastic waves. When these waves travel through the medium, it creates impedance. The impedance generated between two layers will be different due to density contrast and thus at boundaries, some waves are reflected while other travel through the formation. For this reason, seismic exploration surveys require optimum energy waves which can penetrate through kilometers deep inside the earth to gather data. Hundreds of channels of data are recorded using multiple transmitters and reflectors spread over thousands of meters. Each seismic survey uses a specific type of wave and its arrival pattern in multichannel record.
Seismic waves are categorized as :
For seismic survey, S-wave or the shear wave is the main concern.
Seismic waves can be generated by Vibroseis. It employs the use of heavy damping of weight on the surface that generate seismic waves in the subsurface. Alternatively explosives can also be used that can be dug inside the surface to a few meters. The explosion can generate seismic waves. In marine acquisition, streamers are used to gather data. Coil shooting is employed by streamers to gather data.
Seismic acquisition has evolved over time and with better technologies in place, the reliability of seismic surveys has been increasing. The 4-D seismic technology being the newest addition to the seismic technology is based upon time varying solutions to the data gathered. The better the acquisition, better are the correspondence analysis.
The various seismic acquisition techniques apply to where the survey is being carried out. Surveys have effectively been carried out on land, seas or transition zones. The various techniques applied are :
2-D Seismic Survey – they employ the use of seismic maps based on time and depth. Various group of seismic lines are acquired at significant gaps between adjacent lines.
3-D Seismic Survey – a cubical arrangement of different slices that is arranged using computer algorithms and can be viewed on software. For a 3-D survey, different surveys are carried out at closely spaced line locations over the area which can be combined to form a cube.
4-D Seismic Survey – a relatively new technology, which is an alteration to the 3-D survey. It takes into account the changes happening in the subsurface strata over the production years. Thus it takes into account time as the fourth dimension. This can be very beneficial while determining the well locations in field development.
Processing of seismic data is the most important aspect since it undermines the potential of the interpretation process. Processing has mainly been done through various analysis that are majorly mathematical functions fed into computers. A major part of processing is done simultaneously along with acquisition. The data collected can be demultiplexed, convoluted or deconvoluted. This has been dealt with further in the project.
Seismic data processing uses the concepts of geometrical analysis and powerful techniques of fourier analysis. The digital filtering theory and practical applications of digital techniques to enhance the images of subsurface geology can virtually be applied to any information sampled in time. The basis aspects of processing is to recognize and remove noise from the signal, correct the Normal Move Out (NMO), and stacking of data to form a chart of seismic image that can be used for further study.
Interpretation follows exploration and processing of data. The structural interpretation of seismic images determines all decisions in hydrocarbon exploration and production. Since drilling a well for exploration proves costly, maximum information is derived from the seismic data to establish an opinion about the probability of finding petroleum in the structures. However, drilling is required to verify whether the structures are petroleum rich or not. Thus the main challenge is to establish a model which includes geologically reasonable solutions.
Computer-aided seismic interpretation has been of much interest in the later years. The use of unique and highly complicated software has been recommended by various petroleum organizations, which can serve high reliability. However, automating the whole seismic process is an impossible job due to high heterogeneity and varying contrasts between data sources in different parts of the world. Horizon tracking and autopicking is gaining interest among various researchers and developers. This has successfully not been sought as yet.
This project is aimed to study the various problems faced in horizon tracking while trying to execute an automated seismic interpretation process. Horizon tracking is basically carried out through autotrackers which are either feature based or correlation based. Feature based looks for similar configuration while the correlation method is more robust and less sensitive to noise. However, tracking across discontinuities is a difficult job. Thus the project is aimed at finding a way to track horizon across fault lines.
CHAPTER 2 LITERATURE REVIEW
SEISMIC EXPLORATION SURVEY
Seismic exploration surveys in the field of oil and gas are an application of reflection seismology. It is a method to estimate the properties of the earth’s surface from reflected seismic waves. When a seismic wave travels through the rock surface it creates impedance. A wave travels through materials under the influence of pressure. Because molecules of the rock material is bound elastically to one another, the excess pressure results in a wave propagating through the solid.
A seismic survey can reveal pockets of lower density material and their location. Although this cannot be guaranteed that oil can be found in these pockets, since the presence of water is also possible.
Acoustic impedance is given by :-
Z = pV
,where p – density of the material and V – acoustic velocity of wave
Acoustic impedance is important in :-
the determination of acoustic transmission and reflection at the boundary of two materials having different acoustic impedances.
the design of ultrasonic transducers.
assessing absorption of sound in a medium.
Thus the acoustic impedance of each rock formation in the subsurface will be different due to different densities. This density contrast is helpful in tracking the waves in the subsurface and an acoustic impedance chart is obtained which is known as a seismic chart. However, the impedances recorded by the instruments on the surface is not correct due to noise and other factors that change the impedance factor of the wave.
When a seimic wave is reflected off a boundary between two materials with different impedances, some energy is reflected while some continues through the boundary. The amplitude of this wave can be predicted by multiplying the amplitude of the incoming wave by the Seismic Reflection Coefficient, R.
,where Z1 and Z0 are impedances of the two rock formations.
Similarly the amplitude of wave travelling through the formation can be determined using the Transmission Coefficient, T.
,where Z1 and Z0 are impedances of the two rock formations.
By noting the changes in strength of the wave, we can infer the change in acoustic impedances and thus conclude the change in density and elastic modulus. This change can be used to notify the structural changes in the subsurface and thus predict the formation based upon impedances.
It might also happen that when the seismic wave hits the boundary between two surfaces it will be reflected or bent. This is given by Snell’s Law.
The reflection and transmission coefficients are found by applying the appropriate boundary conditions and using Zoeppritz equations. These are a set of equations which determine the partitioning of energy in a wavefield at a boundary across which the properties of rock or the fluid changes. They relate the amplitudes of P-waves and S-waves at each side of the surface.
Zoeppritz equations have been useful in deriving workable approximations in Amplitude versus Offset (AVO). These studies attempt with some success to predict the fuid content in the rock formations.
The parameters to be used for each seismic survey depends on various variables, including whether the survey is being carried out on land or a marine environment. Other geophysical issues such as sea depth, terrain also play a big role. Safety issues are also important.
A Seismic Exploration Survey is broadly divided into three steps :-
Seismic Data Acquisition
Seismic Data Processing
Seismic Data Interpretation
Each step in the survey needs high reliability and complicated equipments that can deliver the best results. More often, based on these results, the drilling of exploration wells is based. Since drilling can prove costly, thus capital investment is one of the major concern of every company.
The Seismic Exploration Survey can be shown as :-
SEISMIC DATA ACQUISITION
Seismic data acquisition refers to collection of seismic data. The acquired data is further sent to a computer network where processing of data takes place.
With better technologies, the prospect of better acquisition surveys have come into place. A generation and recording of seismic data requires :-
Receiver configurations – includes geophones of hydrophones in the case of marine acquisition.
Transmitter configurations – includes laying of transmitter as according to the survey configuration predecided.
Orientation of streamers in case of marine surveys.
Proper computer network to carry the information from receivers to the programming network.
When a survey is conducted, seismic waves generated by dynamite or vibrators travel through the subsurface strata, which are in turn reflected or refracted. These reflected waves and their time to complete one interval is noted by the receivers. The receiver configuration has to be well determined so that maximum data can be collected over an area.
ACQUISITION ON LAND
In a typical land seismic acquisition process, the survey is planned in an attempt to minimize the terrain constraints. It basically includes the sensor layout scheme and the source development scheme.
The source development scheme is used to configure the number of transmitters being used to send the signal down the surface. One or more transmitters can be used based on the programme employed. Similarily one or many receivers can be employed to collect the reflected waves data.
The receiver configuration is an important aspect. The configuration can be in such a way that the closest receiver gathers only the high amplitude wave on the first line of receivers or it can be different based on the signal strength and seismic line survey.
The data collected through receiver or geophones is converted to binary data that can is further handed over to the computer network for processing.
Marine acquisition involves processes such as :-
Wide-Azimuth Marine Acquisition – Azimuth surveys provide a step-change improvement in imaging of seismic data. These surveys provide illumination in complex geology and natural attenuation of some multiples. Azimuth shooting illustrates the acquisition of data in all directions. This acquisition technique can help in generating 3-D models.
Coil Shooting – this technique acquires marine seismic data while following a circular path by improving upon multi and wide azimuth techniques. This includes vessel steering, streamers and sources in a fashion which delivers greater range of azimuths. Sometime single-sensor recording while steering the vessel in different directions has proved to be more beneficial in case of noise attenuation and signal fidelity.
Different seismic surveys can be classified as :-
TWO DIMENSIONAL SURVEYS
In such a survey seismic data is acquired simultaneously along a group of seismic lines which are differentiated with some gaps, usually 1 km or more. A 2-D survey contains many lines acquired orthogonally to the strike of the geological structures with a minimum number of lines acquired parallel to geological structures to allow line-to-line tying of the seismic data and interpretation and mapping of structures.
This technique generates a 2-D cross-section of the deep seabed and is used primarily when initially reconnoitering for the presence of oil and gas reservoirs.
THREE DIMENSIONAL SURVEYS
Multiple streamers shoot on closely spaced lines. The seismic data gathered on close spacing, the 3-D seismic cube can be formed. This innovation requires use of high performance computers and advanced data processing techniques.
The computer generated model can be analyzed in greater detail by viewing the model in vertical and horizontal time slices, or even an inclined section can be viewed.
In a standard 3-D seismic survey, the streamers are placed at about 50-150 meters apart, each streamer being 6-8 kilometers long. Airguns are fired every10-20 seconds. However, many other objectives and economical constraints determine the specific acquisition parameters.
FOUR DIMENSIONAL SURVEYS
The 4-D survey is also called the time-lapse survey. It involves processing of repeated seismic surveys over an area of reservoir under production. The changes occurring in the reservoir due to production and injection can be determined overtime which further helps in field development of the reservoir.
One important aspect of a 4-D survey is that there should be minimum difference in the position of the seismic lines when a repeated survey is done after sometime. Significant cost savings can be done by the use of 4-D surveys due to better planning and understanding of reservoir characteristics.
DIFFERENT SHOT METHODS
The common shot gather uses one transmitter source (vibroseis or explosives) and many receivers (geophones) places at some distance from the source. They geophones are placed at equal spacings from each other.
Commom midpoint gather is the most widely used survey technique. It uses one transmitter placed at the midpoint exactly above the formation area to be surveyed. Receivers are set in all the directions surrounding the transmitter.
Common offset gather uses multiple shot and receiving technique.
Common receiver position gather, as the name states, has only on receiver. While the many shots are employed, the various seismic waves reflecting back to the receiver have different amplitudes and frequencies, thus can be varied and collected differently.
COMMON MIDPOINT METHOD
It was discovered that relection seismic sections can be improvised by repeated sampling of the subsurface formations using different travel paths of the seismic waves. This can easily be achieved by using commom midpoint method which states that increasing the spacing between source and receiver about a commom midpoint and generating duplicated data of the subsurface coverage.
The processing of a common midpoint gather system requires sorting of data from the Commom Shot Gather into a Commom Midpoint Gather. The data collected is usually in the form :
In this method, the inclination of the data occurs since the wavefronts reaching out to the receivers are at an inclined angle, this results in much larger raypath than the corresponding receiver placed close to the shot point. In order to use the recordings to a common depth point, one needs to correct the data for all the time travel distances. This is known as Normal Moveout Correction (NMO).
After NMO, the summation of various wavepaths gives us a horizontal section at time travel equal to zero. This is known as time stacking procedure.
After NMO correction the data is shown as :-
SEISMIC DATA PROCESSING
A reference seismic processing sequence is applied to input raw gathers to obtain reference seismic output data. A series of test seismic processing sequences are applied to the input raw gathers to obtain test seismic output data. The RMS value of the test seismic output data is normalized to that of the reference seismic output data on a trace by trace basis. The normalized difference between the test and the reference seismic output data is calculated on a sample by sample basis in the time domain and are displayed on color coded plots in the time scale format over the CDP range. Linear regression is performed for each CMP gather to obtain the stack and the zero offset calculated for each time index and the difference is recorded. The normalized differences between the error for the test and the reference sequences are calculated and displayed on color coded plots. The order of sensitivity for each processing step in the reference processing sequence is determined. If necessary, any processing step is rejected and the reference processing sequence is revised. 2
Integrating well data throughout the seismic workflow for superior imaging and inversionÂ
Well-Driven Seismic (WDS) is the integration of borehole information throughout the surface-seismic workflow to provide better seismic images, more reliable stratigraphic interpretation, and greater confidence in global reservoir characterization.
Wireline logs (compressional, shear, and density), VSPs, and surface-seismic data represent the elastic response of the earth at various resolution scales. A principle of the Well-Driven Seismic concept is that these data should be processed with respect to their mutual consistency, i.e., that the seismic data must tie with logs and VSPs in time and depth. The aim of the Well-Driven Seismic method is to involve all the available borehole information to optimize the entire seismic workflow to deliver seismic images of superior resolution (in time or depth) and calibrated prestack seismic amplitudes that are suitable for inversion and detailed seismic reservoir description.Â
Earth properties from logs, VSPs, and surface-seismic dataÂ
The Well-Driven Seismic workflow invokes new proprietary software and analysis techniques from WesternGeco and Schlumberger to derive an earth property model from the integrated analysis of wireline logs, VSPs, and surface-seismic data. The property model includes compressional and shear velocities, attenuation (Q) factors, VTI anisotropy parameters, and interbed multiple mechanisms, and is derived at the well location (or locations) and extended across the survey area in 3D. The 3D model is applied in the seismic processing sequence for true amplitude and phase recovery, deconvolution, multiple attenuation, anisotropic prestack time and depth imaging (including of converted-wave data), AVO analysis, and 4D processing.Â
WELL DATA FOR HIGH RESOLUTION SEISMIC IMAGING
Well information can improve many key stages of the conventional seismic processing sequence. VSP data provide excellent discrimination of primary and multiple events, and are used to guide surface-seismic multiple attenuation processes. Furthermore, interbed multiple mechanisms identified in separated VSP wavefields are used as input to data-driven multiple attenuation processes, such as the WesternGeco Interbed Multiple Prediction (IMP). Inverse-Q operators derived from VSP data (and new methods for walkaway VSP data) can significantly improve seismic resolution. WesternGeco employs a proprietary deconvolution process that is constrained by the signal-to-noise level in the seismic data and by the well reflectivity to enhance further the seismic resolution. The calibrated anisotropic velocity model is vital for prestack time and depth migration (including of converted waves) to improve steep-dip imaging, lateral positioning of reflectors, signal-to-noise ratios, and seismic resolution.Â
OPTIMIZED WELL TIES
The Well-Driven Seismic method optimizes the processing sequence and the processing parameters within that sequence to tie the seismic data to the wells. Attributes based on the well tie and on the quality of the extracted wavelets are used for deterministic seismic processing decisions. Space-adaptive wavelet processing corrects 3D seismic data to true zero phase between well locations, and stabilizes residual spatial wavelet variations.Â
BOREHOLE CALIBREATED SEIMIC INVERSION
The Well-Driven Seismic approach provides greater sensitivity to seismically derived reservoir attributes through calibrated AVO or acoustic impedance inversion. The well data are particularly important for successful processing of seismic data for inversion. Compensation for the offset-dependent effects of Q, geometric spreading, transmission losses, and anisotropy are essential for processing data over very long offsets (where the strongest AVO expression of the reservoir may be visible). The method calibrates the AVO signatures in the prestack seismic data with the offset-dependent amplitude response synthesized from well logs and/or the response expressed in the walkaway VSP to provide assurance of the seismic processing sequence.Â
With the seismic processing sequence optimized for resolution and consistency with the well data, Well-Driven Seismic processing is a vital prerequisite for acoustic impedance or AVO inversion and subsequent reservoir characterization.
AVO AND INVERSION
Amplitude variation with offset (AVO) has been used extensively in hydrocarbon exploration over the past two decades. Traditional AVO analysis involves computation of the AVO intercept, gradient, and higher-order AVO term from a fit of P-wave reflection amplitude to the sine square of the angle of incidence. This fit is based on the approximate P-wave reflection coefficient formulation in intercept-gradient form, given by Bortfeld (1961) and Shuey (1985) among others. Under the assumption of a background PS velocity ratio, the AVO intercept and gradient values can also be combined to obtain additional AVO attributes such as pseudo-S-wave data, Poisson’s ratio contrast, and others. AVO intercept and pseudo-S-wave data are also used in conjunction with prestack waveform inversion (PSWI) in a hybrid inversion scheme. Hybrid inversion is a combination of prestack and poststack inversion methodologies. Such a combination allows efficient inversion of large data volumes in the absence of well information.
Amplitude Variation with Offset (AVO) inversion is a prestack technique that is readily applied to seismic gathers but which is still largely under-utilised in the exploration community despite its ability to effectively discriminate between fluid and lithology effects.
AVO inversion is equally applicable to both 2D and 3D seismic data in time or depth providing that sufficient care has been taken to preserve amplitudes during processing. A reliable velocity model is also a critical component of the AVO process as accurate angle information is a prerequisite for AVO inversion. The more accurate the angles, the better the partitioning of amplitudes to P-wave and S-wave reflectivities. In addition, both angle and ray path information can be incorporated in a variety of model based amplitude corrections that are preferable and often more accurate than scalars derived from empirical equations.
The inversion process is then performed, completing in about the same time as a conventional stack. The resulting outputs are a series of AVO reflectivity sections or volumes that are determined by the Zoeppritz approximation used.
Fluid Factor is one of the most useful attributes derived from AVO inversion due its ability to make such distinctions and directly identify hydrocarbons.
Multi-Measurement Reservoir Definition workflows include the following components:
Reservoir Synthetic Modeling
Forward modeling to generate pre-stack synthetics from geological models
Anivec (prestack elastic modeling)
Prestack Waveform Inversion (PSWI)
Full waveform prestack inversion is a non-linear inversion process that estimates elastic model (Vp, Vs, and density) from prestack seismic data using a genetic algorithm.
AVO Modeling and analysis
Conditions angle band stacks prior to performing AVO analysis
Elastic impedance modeling and inversion from angle band cubes
Space adaptive wavelet processing and inversion to relative seismic impedance
Elastic Impedance Inversion
Combining low frequency trends with seismic relative inverted impedance cubes to generate absolute impedance
Integrated Rock Physics Modeling
Fluid and rock property analysis, modeling and substitution
Rock Property Calibration
Generating rock properties from seismic using transforms derived from petrophysical analysis of well data.
The outputs are high-resolution absolute acoustic and shear impedance and density volumes consistent with the seismic data and the well-log data. The inverted elastic parameter volumes are used for detailed interpretation of lithofacies and pore-fluid content in the subsurface. Combined with rock physics modeling and rock property mapping through lithology classification and joint porosity-saturation inversion, the method provides a powerful tool for quantitative reservoir description and characterization. The results are the most-probable litho-class, porosity, and saturation with uncertainties of prediction at every sample point in the 3-D volume.
Some elements of the seismic data processing sequence are virtually universal – regardless of whether the intention is to performÂ timeÂ imaging,Â depthÂ imaging,Â multicomponentÂ imaging, orÂ reservoirÂ studies. Data conditioning and signal processing form the foundation of the seismic processing workflow.
Signal processing encompasses a wide variety of technologies designed to address numerous challenges in the processing sequence: from data calibration and regularization through to noise attenuation, demultiple, and signal enhancement techniques.
Data caliberation and regularization
Prestack time migration (PSTM) may not be the most sophisticated imaging method available, but it remains the most commonly used migration algorithm in use today. Kirchhoff PSTM combines improved structural imaging with amplitude preservation of prestack data in readiness for AVO, inversion, and subsequent reservoir characterization.
Advances in this field also mean that time imaging, more than ever before, is an ideal first step in aÂ Depth ImagingÂ workflow, reducing the number of velocity model building iterations and decreasing overall turnaround time.
Imaging: Regularization, migration and datuming techniquesÂ
Velocities and moveout
Enhanced Migration Amplitude Normalization
Depth Imaging is the preferred seismic imaging tool for today’s most challenging exploration and reservoir-delineation projects. In areas of structural or seismic velocity model complexity, many of the assumptions underpinning traditional time-domain processing are invalid and can produce misleading results. Typical situations might be heavily faulted sequences or salt intrusions. In these cases, only the careful application of 3D prestack depth imaging can be relied on to accurately delineate geological structure, aiding risk assessment and helping operators to improve drilling success rates.
From a technology perspective, high quality depth imaging has two main aspects: the ability to build detailed and accurate velocity models, coupled with a superior imaging algorithm.
VELOCITY MODEL BUILDING
Velocity Model Building is a key critical element in imaging the Earth. Tomography provides the best high resolution calibrated velocity and anisotropic Earth Models, powerful refraction tomographies detect shallow velocity anomalies. All those algorithms work with any acquisition configuration and can be applied to any geological setting. Also, these computer intensive algorithms are integrated with an interactive graphics environment for rapid and accurate quality control of the interim and final results.
Conventional seismic recording uses a single scalar measurement of pressure or vertical displacement throughout the 2D or 3D survey to derive images and models of the subsurface. Subsequent processing and inversion steps can be linked to the relative shear-wave contrasts in the subsurface using rock property relationships. However, sometimes it is impossible to meet a survey’s seismic imaging or reservoir definition objectives using compressional (P) waves alone.
SEISMIC DATA INTERPRETATION
Computer aided interpretation is the mainstay of 3D seismic interpretation as the amount of data used is voluminous.
The important services are:Â
IIWS (Intergrated Intelligence Workstation) based interpretation of 2D, 3D dataÂ
Â Structural mappingÂ
Â Integrating seismic attributes with wireline, core and reservoir data for reservoir characterisationÂ
Â Seismic modeling
Â 3D visualisation and animationÂ
Â Palinspastic restorationÂ
Structural restoration is an established method by which to validate seismic interpretations. In addition, palinspastic reconstruction can help identify potential reservoir depocentres, enable the measurement of catchment areas at the time of hydrocarbon migration and lead to an improved understanding of complex hydrocarbon systems such as those in the deepwater. Restoration is achieved by the sequential backstripping of the present day depth model. Upon removal of each successive layer, the remaining surfaces within the model are adjusted to account for faulting, decompaction and isostatic adjustment.
Â AVO analysis
Â Formulation of geological models for exploration and developmentÂ
Â Reservoir characterization
CHAPTER 3 THEORITICAL DEVELOPMENT
Computer-aided seismic interpretation involves the use of horizon tracking. Horizon tracking is based upon algorithms that require manually selection of a start point for autotracking operation. A similar value or feature is searched in the adjacent trace and if found within the specified limits, the tracker moves on to the next trace.
Autotrackers are based upon two functions – feature based or correlation based. While the feature based look for similar trace values, the correlation based technique is more robust and less sensitive to noise.
The main problem faced in autotracking is their incapability to track horizons along discontinuities. Since a similar value or feature in the adjacent trace is not found, it automatically stops there. On the other hand, manually tracking horizons along the fault line is very time consuming and is highly subjective.
In the following points, we shall first deal with horizon tracking and then recommend solutions for tracking horizons over discontinuities.
Horizons are strong reflections event which indicate boundaries between rock formations. Tracking across faults is a time consuming task and has not been automated satisfactorily. Faults are discrete fracture along which measurable displacement of rock layering has taken place. Partially disturbed or noise signals cause a major problem in horizon tracking.
Horizon tracking includes structural analysis of a three dimensional dataset. The seismologist should combine knowledge of stratigraphic and structural relationships within the seismic reflection to determine the events that can be grouped as same horizon.
CROSS CORRELATION TECHNIQUE
It is a measure of two waveforms as a function of time lag applied to one of them. This is also known as a sliding dot product or inner-product. Cross-correlation finds it application in pattern recognition, single particle analysis, electron tomographic averaging and cryptanalysis.
For continuous functions,Â fÂ andÂ g, the cross-correlation is defined as:
whereÂ fÂ * denotes theÂ complex conjugateÂ ofÂ f.
Similarly, for discrete functions, the cross-correlation is defined as:
By considering the two functions f and g that differ by a shift, once can estimate the through cross-correlation technique as to how much g should be shifted to make it identical to f. When the two functions shall match the product f*g should attain a maximum value.
This can be explained by the reason that, in two adjacent wavelets, when they are indentical or shall be combined they attain a maximum value along the same axis by contributing to make the intergral larger. The same applies to if both the functions have a negative value factor, since the product of two negative values shall give us a positive value only.
HORIZON TRACKING METHODOLOGY
A programming code is written which shall deal with the trace amplitude values. The amplitude values can easily be known by viewing the SEG-Y file of the seismic data. The SEG-Y file contains all the information about the the seismic acquisition process and the values computed after the processing of data.
The SEG-Y has been adopted as a standard for trace sequential data. It contains different headers namely –
EBCDIC format header – this contains all the information about the area, seismic line name, shotpoint range, recording parameters and processing history.
Binary header – this contains information about the number of samples, sample rate and format code.
Trace header – for each trace in the data, there is a unique trace header that contains information related to shotpoint number, CDP, and survey locations.
Data samples – this is also repeated for each trace in the file. It contains the number of bytes per sample which is dependent upin the format of the data sample.
A program written to execute cross-correlation technique is made to perform a sequential array. The programming steps are given as –
It first takes up values of time interval and only the first trace to find the highest amplitude value among them. The values of time interval can be requested by the user or a random time interval range can be used.
It then takes up the next trace and forms an array using the values of amplitude. The highest value of the previous step to be the centre value and equal number of values above and below it so as to attain a time window.
Then a calculation is done and with the help of cross-correlation technique it finds the highest coffecient and the correspoding amplitude of the reflection.
The next step follows as step 2 and the program proceeds futher by sliding the window(array of numbers) and further until the end of number of traces.
The time interval in which such calculations need to be made or where a particular horizon needs to be dealt with is given at the beginning of the program. The values of how large the array maybe can be given among 3 or 5 (window size) when asked by the program.
The smaller the time interval the better the resolution of the horizon.
The SEG-Y file and output overlain over one another after execution of this program is given as :
The difference between traced and actual horizon due to the presence of a fault.
The actual horizon to be traced
It can clearly be seen that, once a discontinuity is encountered, the program tracks down the wrong horizon and the results and haphazard.
To improve upon this we shall make use of a different approach for horizon tracking. In the following part we shall discuss a model based approach to correlate several horizons simultaneously across discontinuities to find a realistic solution.
The solution to the problem can be divided into two parts:-
First of all, we shall deal with horizon pairs. The horizon pairs shall be found using the similarity if reflector sequences. Checking the consistent polarity of the signal and to find the relationship between the fault length and maximum vertical displacement.
Secondly, the two horizon pairs interpolated using the first technique have to be combined to finally form a single horizon.
This approach, if correctly implemented, can help in correct horizon tracking across a fault.
In the first part, the different constraints can be described as follows :-
In simple horizon tracking we dealt with the local attributes of the horizons namely amplitude, polarity and wavelength which pose a problem of being distinct to be correlatable on its own. Thus we shall deal with reflector sequences. Reflector sequences can be compared by calculating their cross-correlation coefficients. Also that we shall compare the polarity over a certain array along the fault line.
CROSS CORRELATION COEFFICIENT
We calculate the cross-correlation coefficient of each horizon pair by using amplitude of corresponding horizons in the neighborhood by performing this technique over an array. The number of values taken in the array is set to a particularly large value since the strata of different sides of a fault maybe unequally compressed.
Since the sequence of horizons remains same even across the fault line, the sign of amplitude must be equal for corresponding horizon segments. We use this feature to determine the same horizon pattern by correlating the positive and negative amplitudes representing the strata.
MAXIMUM FAULT THROW
Upon study of various faults, independent of material and scale, the best relationship between fault length, L and maximum vertical displacement of horizons, D is given as :-
D = 0.03 L1.06
This relationship can be used in this model to constrain horizon segment matches to those, whose displacement values do not exceed D.
The second part of the programming includes the combining horizon pairs :-
To combine the horizon pair not only require correlation and similarity between different values but also consider the geometrical and geological constraints.
The geometrical constraint can be explained by simple procedure that the horizons tracked must not cross.
The geological constraint takes into consideration the sign of the fault throw. This can be calculated by knowing the fault type. Fault are categorized on the basis of the footwall and hanging wall. The throw of a normal fault is vertical and dips towards the downthrown side of the fault while it is opposite in the reverse fault i.e. towards the upthrown side.
The study of forces that influence the area can be used to determine the throw of the fault. We shall need the sign of the throw of fault for programming purpose since that shall determine as to where the horizon pair must be located in the seismic file.
To examine the data two methods were used :-
Exahaustive search algorithm – this model takes into account that the model is correct and thus it follows the algorithm to a certain value where it terminates, then it continues with the other node in the algorithm again to a value where it terminates and so on. Since upon tracking many horizons, this model can be very time consuming and impractical, thus to track over a particular horizon the next model was chosen.
Stochastic method – this method induces randomization in the model. Thus this can serve to solve the algorithm by introducing some random variables that can serve to solve the algorithm to result in a particular solution.
The horizon to be tracked should have a strong reflection. Since the program is used to converge the horizon segments across the fault line, thus the fault line needs to be highlighted, this can be done manually along the region of interest or the region of discontinuity. The fault line is interpolated by defining the presumed fault pixels in the data sheet.
Horizon segments are then assigned to the two discontinued classes – left or right. This approach is used to calculate the fault throw. Then the user can select as to which horizon is to be used for correlation.
Since no seed points are required in the initial step for horizon tracking, this proves to be a terminal advantage in the process.
EXHAUSTIVE SEARCH ALGORITHM
This algorithm estimates the similarity of all possible horizon pairs, then upon application of geological constraints it can find an best possible solution.
This takes place as follows :-
The single similarity of all horizon pairs is selected.
The total similarity for each combination is calculated from the similarity values of horizon pairs. Global similarities in the total data structure are then searched.
After obtaining different pairs, the constraints of polarity, maximum fault throw, sign of fault throw and that the horizons must not cross are implemented over the solution and the best possible pairs are assigned.
All such horizon pairs are found in the solution tree. Many such pairs are invalidated in the solution tree due to geological constraints. The similarity of all pairs is checked, the the pairs with lower similarities are restricted, this is due to the fact that they may lead to an incorrect geological solution.
CONSISTENCY CHECK CYCLE
This method then follows a tree structure that proceeds in a stepwise fashion. If all the constraints are provel right, it moves forward and solves the algorithm for the next step for consistency. If the similarities continue with each step ahead, the cycle repeats itself to track down the correct horizon, in the other case it takes into account the next pair. The cycle terminates when a horizon pair of maximum total similarity is found that fulfills all the constraints.
This can also be termed the generic algorithm for correlating horizons. This approach is more straightforward and precisely defines the evaluation criteria, therefore it can prove to be a more appropriate strategy.
Here a horizon is termed as a string and the string is assigned an integer value. The index of the string has two defined values l and r(l)m which represents the left horizon and the right horizon number. If a combination is not found for the left horizon, it is assigned a value -1.
At the start of the program, many horizon pairs are created randomly. This can although lead to a large number of pairs, thus constraints are set to reduce the number of horizon pairs. This can be done by defining a fixed space around an string to which it can connect to. Then the horizon pairs which do not follow geological constraints of polarity, fault throw, sign of fault throw, are neglected. Then the horizon pairs which cross are neglected. This gives us a result of all possible horizon pairs.
A roulette wheel procedure is applied where in the pairs are selected on the basis of their compatibility with the initial value. The values which remain unchanged in the following string are termed compatible and are selected to be operated upon by the algorithm.
Now to crossover to the next step, the validated strings are checked with all possible solutions constraining them with the geometrical factors. The fitness of each solution is checked.
CHAPTER 4 RESULTS AND CONCLUSION
Extensive research across discontinuities and application of geological constraints can help in successful horizon tracking across fault lines.
Upon application of both the models, the results have been shown in the figure above.
Although the methods were operated upon a relatively simple dataset, more complex datasets would require more consistency checks and more acquaintance with the geological structure in order to infer the correct solutions.
Generic solution was found to be more consistent with results.
The exahaustive search strategy produce good results with horizon tracking across faults but it can only consider a limited number of horizon segments across the fault. This does not prove too practically correct to be used in case of highly dense datasets.
Generic algorithm proves to be the correct procedure for the problem above, although generic solution needs to be examined to improvise the reliability of generic algorithm.
Further developments can be made upon this research. Investigation and search of more geological constraints and well as geometrical constraints can help improve this program to be tested over more complex datasets.Order Now