Seismic surveys aims at measuring the earth's geological properties using various physics concepts of electric, gravitational, thermal and stretchy theories. It had been first employed successfully in Tx and Mexico with a company called Seismos in 1924. Since that time, many oil companies have used the services of seismology to forecast the existence of hydrocarbon. Major olive oil companies have actively explored in the seismic technology and this in addition has found applications in a variety of other researches by scientists about the world.
Seismic exploration research are method employed in exploration geophysics that uses concepts of reflection seismology to calculate the subsurface properties. The technique requires a managed source of energy that can make seismic waves and highly very sensitive receivers that can sense the reflected seismic waves. The time delay in mailing and receiving alerts can optimally be utilized to assess the depth of the formation.
Since different formation layers have different densities, they reveal back again seismic waves at different velocities. This aspect may be used to estimate the depth of the prospective formation, usually shale or other rock formations that can develop a cap rock and roll or contain essential oil. Seismic research form a part of the preliminary exploration studies and form the foundation for further analysis of the region under consideration.
Seismic waves are a form of elastic waves. When these waves travel through the medium, it creates impedance. The impedance produced between two levels changes due to density contrast and so at restrictions, some waves are mirrored while other travel through the development. For this reason, seismic exploration surveys require optimum energy waves which can permeate through kilometers profound inside the planet earth to gather data. A huge selection of programs of data are documented using multiple transmitters and reflectors distributed over a large number of meters. Each seismic review runs on the specific kind of wave and its arrival structure in multichannel record.
Seismic waves are grouped as :
For seismic survey, S-wave or the shear wave is the main concern.
Seismic waves can be produced by Vibroseis. It employs the utilization of heavy damping of weight on the top that generate seismic waves in the subsurface. Otherwise explosives can also be used that may be dug inside the surface to some meters. The explosion can make seismic waves. In marine acquisition, streamers are being used to gather data. Coil taking pictures is employed by streamers to gather data.
Seismic acquisition has advanced over time and with better solutions in place, the dependability of seismic studies has been increasing. The 4-D seismic technology being the latest addition to the seismic technology is situated upon time differing solutions to the info obtained. The better the acquisition, better are the correspondence evaluation.
The various seismic acquisition techniques apply to where the survey is being carried out. Surveys have effectively been completed on land, seas or transition zones. The many techniques applied are :
2-D Seismic Study - they utilize the utilization of seismic maps based on time and depth. Various group of seismic lines are received at significant gaps between adjacent lines.
3-D Seismic Survey - a cubical layout of different pieces that is organized using computer algorithms and can be looked at on software. To get a 3-D review, different surveys are completed at closely spaced range locations over the region which can be combined to form a cube.
4-D Seismic Study - a relatively new technology, which can be an alteration to the 3-D study. It takes into consideration the changes happening in the subsurface strata in the creation years. Thus it requires into account time as the fourth aspect. This is very beneficial while deciding 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 given into computers. A major part of control is done simultaneously along with acquisition. The info gathered can be demultiplexed, convoluted or deconvoluted. This has been dealt with further in the project.
Seismic data processing uses the ideas of geometrical research and powerful techniques of fourier evaluation. The digital filtering theory and sensible applications of digital techniques to improve the images of subsurface geology can virtually be applied to any information sampled with time. The basis areas of processing is to identify and remove noise from the transmission, correct the Normal RE-LOCATE (NMO), and stacking of data to create a graph of seismic image that can be used for further analysis.
Interpretation comes after exploration and control of data. The structural interpretation of seismic images can determine all decisions in hydrocarbon exploration and development. Since drilling a proper for exploration demonstrates costly, maximum information comes from the seismic data to determine an view about the likelihood of finding petroleum in the set ups. However, drilling must verify if the constructions are petroleum rich or not. Thus the key challenge is to determine a model which include geologically reasonable solutions.
Computer-aided seismic interpretation has been of much fascination with the later years. The usage of unique and highly complicated software has been advised by various petroleum organizations, which can provide high trustworthiness. However, automating the whole seismic process can be an impossible job due to high heterogeneity and varying contrasts between data resources in different parts of the world. Horizon monitoring and autopicking is increasing interest among various experts and developers. It has efficiently not been sought as yet.
This project is aimed to review the many problems confronted in horizon tracking while wanting to execute an automated seismic interpretation process. Horizon tracking is basically carried out through autotrackers which are either feature structured or correlation founded. Feature based looks for similar configuration as the correlation method is better quality and less sensitive to noise. However, checking across discontinuities is a hard job. Thus the project is aimed at finding ways to monitor horizon across problem lines.
CHAPTER 2 Books REVIEW
SEISMIC EXPLORATION SURVEY
Seismic exploration studies in neuro-scientific coal and oil are an application of reflection seismology. It is a method to calculate the properties of the earth's surface from shown seismic waves. When a seismic wave journeys through the rock and roll surface it creates impedance. A influx moves through materials under the influence of pressure. Because substances of the rock and roll material is destined elastically one to the other, the excess pressure results in a influx propagating through the solid.
A seismic review can reveal storage compartments of lower denseness material and their location. Although this cannot be guaranteed that engine oil can be found in these pockets, since the presence of normal 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 perseverance of acoustic transmitting and representation 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 creation in the subsurface will be different anticipated to different densities. This thickness contrast is effective in checking the waves in the subsurface and an acoustic impedance graph is obtained which is actually a seismic chart. However, the impedances recorded by the instruments on the surface is not appropriate due to sound and other factors that change the impedance factor of the wave.
When a seimic influx is reflected off a boundary between two materials with different impedances, some energy is shown while some continues through the boundary. The amplitude of the wave can be predicted by multiplying the amplitude of the inbound influx by the Seismic Representation Coefficient, R.
, where Z1 and Z0 are impedances of both rock formations.
Similarly the amplitude of wave going through the formation can be driven using the Transmitting Coefficient, T.
, where Z1 and Z0 are impedances of the two rock and roll formations.
By noting the changes in power of the wave, we can infer the change in acoustic impedances and so conclude the change in denseness and elastic modulus. This change may be used to inform the structural changes in the subsurface and thus predict the creation based after impedances.
It might also happen that whenever the seismic wave strikes the boundary between two surfaces it will be shown or bent. That is given by Snell's Legislation.
The representation and transmission coefficients are found by applying the correct 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 liquid changes. They associate the amplitudes of P-waves and S-waves at each part of the surface.
Zoeppritz equations have been useful in deriving workable approximations in Amplitude versus Offset (AVO). These studies try out with some success to predict the fuid content in the rock formations.
The variables to be used for every single seismic survey depends upon various parameters, including if the survey is being carried out on land or a marine environment. Other geophysical issues such as sea depth, surfaces also play a large role. Protection issues are also important.
A Seismic Exploration Review is broadly divided into three steps :-
Seismic Data Acquisition
Seismic Data Processing
Seismic Data Interpretation
Each step in the study needs high trustworthiness and complicated equipments that can deliver the best results. More regularly, predicated on these results, the drilling of exploration wells is based. Since drilling can confirm costly, thus capital investment is one of the major concern of each company.
The Seismic Exploration Study can be shown as :-
SEISMIC DATA ACQUISITION
Seismic data acquisition identifies collection of seismic data. The obtained data is further delivered to some type of computer network where control of data takes place.
With better technology, the chance of better acquisition surveys attended into place. A technology and recording of seismic data requires :-
Receiver configurations - includes geophones of hydrophones regarding marine acquisition.
Transmitter configurations - includes laying of transmitter as in line with the survey configuration predecided.
Orientation of streamers in case there is marine studies.
Proper computer network to carry the info from receivers to the programming network.
When a study is conducted, seismic waves made by dynamite or vibrators travel through the subsurface strata, which can be in turn reflected or refracted. These shown waves and their time to complete one period is noted by the receivers. The recipient configuration has to be well identified so that maximum data can be accumulated over a location.
ACQUISITION ON LAND
In a typical land seismic acquisition process, the survey is planned in an attempt to minimize the ground constraints. It basically includes the sensor structure scheme and the foundation development plan.
The source development plan is used to configure the amount of transmitters being used to send the sign down the surface. A number of transmitters can be used predicated on the programme hired. Similarily one or many receivers can be employed to collect the mirrored waves data.
The receiver configuration is an important aspect. The construction can maintain such a way that the closest device gathers only the high amplitude wave on the first line of receivers or it could be different predicated on the signal strength and seismic line survey.
The data collected through recipient or geophones is changed into binary data that can is further paid to the computer network for processing.
Marine acquisition will involve functions such as :-
Wide-Azimuth Marine Acquisition - Azimuth surveys provide a step-change improvement in imaging of seismic data. These surveys provide illumination in intricate geology and natural attenuation of some multiples. Azimuth firing illustrates the acquisition of data everywhere. This acquisition technique can help in producing 3-D models.
Coil Firing - this system acquires marine seismic data while carrying out a circular avenue by improving upon multi and huge azimuth techniques. This consists of vessel steering, streamers and resources in a fashion which gives greater range of azimuths. Sometime single-sensor tracking while steering the vessel in different directions has proved to be more beneficial in case there is noises attenuation and indication fidelity.
Different seismic studies can be categorized as :-
TWO DIMENSIONAL SURVEYS
In such a review seismic data is purchased simultaneously along a group of seismic lines which are differentiated with some spaces, usually 1 km or more. A 2-D review consists of many lines acquired orthogonally to the affect of the geological set ups with a minimum number of lines bought parallel to geological structures to allow line-to-line tying of the seismic data and interpretation and mapping of buildings.
This technique produces a 2-D cross-section of the deep seabed and is utilized primarily when in the beginning reconnoitering for the occurrence of oil and gas reservoirs.
THREE DIMENSIONAL SURVEYS
Multiple streamers photograph on carefully spaced lines. The seismic data compiled on close spacing, the 3-D seismic cube can be made. This advancement requires use of powerful computer systems and advanced data producing techniques.
The computer made model can be examined in more detail by observing the model in vertical and horizontal time pieces, or even an willing section can be viewed.
In a standard 3-D seismic review, the streamers are located at about 50-150 meters aside, each streamer being 6-8 kilometers long. Airguns are terminated every10-20 mere seconds. However, many other objectives and cost-effective constraints determine the specific acquisition parameters.
FOUR DIMENSIONAL SURVEYS
The 4-D review is also called the time-lapse study. It involves control of repeated seismic research over a location of tank under development. The changes occurring in the tank due to development and treatment can be decided overtime which further assists with field development of the reservoir.
One important aspect of the 4-D survey is the fact there should be bare minimum difference in the positioning of the seismic lines whenever a repeated survey is done after sometime. Significant cost savings can be carried out through 4-D surveys scheduled to raised planning and understanding of tank characteristics.
DIFFERENT SHOT METHODS
The common shot get uses one transmitter source (vibroseis or explosives) and many receivers (geophones) places at some distance from the foundation. They geophones are positioned at similar spacings from one another.
Commom midpoint gather is the hottest survey approach. It uses one transmitter put at the midpoint exactly above the creation area to be surveyed. Receivers are occur all the directions encircling the transmitter.
Common offset collect uses multiple shot and receiving technique.
Common recipient position gather, as the name areas, has only on receiver. While the many shots are used, the various seismic waves reflecting back to the recipient have different amplitudes and frequencies, thus can be varied and collected in a different way.
COMMON MIDPOINT METHOD
It was discovered that relection seismic parts can be improvised by repeated sampling of the subsurface formations using different travel pathways of the seismic waves. This can easily be performed by using commom midpoint method which expresses that increasing the spacing between source and device in regards to a commom midpoint and making duplicated data of the subsurface coverage.
The processing of an common midpoint collect system requires sorting of data from the Commom Shot Gather into a Commom Midpoint Collect. The data collected is usually in the proper execution :
In this method, the inclination of the data occurs since the wavefronts reaching out to the receivers are at an inclined viewpoint, this results in much bigger raypath than the matching receiver placed near to the shot point. To be able to use the recordings to a standard depth point, one must correct the info for on a regular basis travel distances. This is known as Normal Moveout Correction (NMO).
After NMO, the summation of various wavepaths offers us a horizontal section at time travel equal to zero. This is known as time stacking treatment.
After NMO correction the info is shown as :-
SEISMIC DATA PROCESSING
A research seismic processing collection is applied to input fresh gathers to acquire reference seismic result data. Some test seismic processing sequences are put on the input organic gathers to acquire test seismic outcome data. The RMS value of the test seismic outcome data is normalized compared to that of the guide seismic result data on a trace by track basis. The normalized difference between the test and the guide seismic productivity data is calculated on an example by sample basis in enough time domains and are exhibited on color coded plots in enough time scale format above the CDP range. Linear regression is performed for every single CMP gather to get the stack and the zero offset calculated for each time index and the difference is noted. The normalized differences between the mistake for the ensure that you the reference point sequences are calculated and exhibited on color coded plots. The order of sensitivity for each digesting part of the reference processing sequence is determined. If necessary, any processing step is rejected and the guide processing collection is modified. 2
Integrating well data throughout the seismic workflow for superior imaging and inversion
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 higher self confidence in global reservoir characterization.
Wireline logs (compressional, shear, and thickness), VSPs, and surface-seismic data represent the stretchy response of the planet earth at various quality scales. A rule of the Well-Driven Seismic principle is these data should be prepared with respect to their mutual reliability, i. e. , that the seismic data must tie up with logs and VSPs with time and depth. The aim of the Well-Driven Seismic method is to entail all the available borehole information to maximize the entire seismic workflow to deliver seismic images of superior quality (in time or depth) and calibrated prestack seismic amplitudes that are suitable for inversion and thorough seismic reservoir explanation.
Earth properties from logs, VSPs, and surface-seismic data
The Well-Driven Seismic workflow invokes new proprietary software and evaluation techniques from WesternGeco and Schlumberger to derive an globe property model from the integrated research of wireline logs, VSPs, and surface-seismic data. The house model includes compressional and shear velocities, attenuation (Q) factors, VTI anisotropy guidelines, and interbed multiple mechanisms, and comes from at the well location (or locations) and expanded across the survey area in 3D. The 3D model is applied in the seismic control sequence for true amplitude and phase recovery, deconvolution, multiple attenuation, anisotropic prestack time and depth imaging (including of converted-wave data), AVO examination, and 4D handling.
WELL DATA FOR HIGH RESOLUTION SEISMIC IMAGING
Well information can improve many key periods of the conventional seismic processing collection. VSP data provide excellent discrimination of principal and multiple happenings, and are being used to guide surface-seismic multiple attenuation operations. Furthermore, interbed multiple mechanisms discovered in separated VSP wavefields are being used as insight to data-driven multiple attenuation techniques, including the WesternGeco Interbed Multiple Prediction (IMP). Inverse-Q providers derived from VSP data (and new options for walkaway VSP data) can significantly improve seismic image resolution. WesternGeco uses a proprietary deconvolution process that is constrained by the signal-to-noise level in the seismic data and by the well reflectivity to improve further the seismic image resolution. The calibrated anisotropic speed model is vital for prestack time and depth migration (including of transformed waves) to improve steep-dip imaging, lateral positioning of reflectors, signal-to-noise ratios, and seismic quality.
OPTIMIZED WELL TIES
The Well-Driven Seismic method optimizes the handling collection and the handling guidelines within that collection to tie the seismic data to the wells. Qualities predicated on the well connect and on the grade of the extracted wavelets are used for deterministic seismic control decisions. Space-adaptive wavelet control corrects 3D seismic data to true zero stage between well locations, and stabilizes residual spatial wavelet modifications.
BOREHOLE CALIBREATED SEIMIC INVERSION
The Well-Driven Seismic methodology provides greater sensitivity to seismically produced reservoir features through calibrated AVO or acoustic impedance inversion. The well data are particularly important for successful control of seismic data for inversion. Reimbursement for the offset-dependent effects of Q, geometric growing, transmission deficits, and anisotropy are essential for control data over very long offsets (where in fact the strongest AVO manifestation 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 portrayed in the walkaway VSP to provide guarantee of the seismic handling sequence.
With the seismic handling 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 following reservoir characterization.
AVO AND INVERSION
Amplitude variation with offset (AVO) has been used extensively in hydrocarbon exploration within the last 2 decades. Traditional AVO analysis involves computation of the AVO intercept, gradient, and higher-order AVO term from a fit of P-wave representation amplitude to the sine square of the perspective 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) amongst others. Under the assumption of an background PS velocity percentage, the AVO intercept and gradient beliefs can be combined to acquire additional AVO features such as pseudo-S-wave data, Poisson's ratio contrast, and more. AVO intercept and pseudo-S-wave data are also found in conjunction with prestack waveform inversion (PSWI) in a cross inversion scheme. Hybrid inversion is a combination of prestack and poststack inversion methodologies. Such a blend allows productive inversion of large data amounts in the lack of well information.
Amplitude Variance with Offset (AVO) inversion is a prestack technique that is conveniently applied to seismic gathers but which continues to be essentially under-utilised in the exploration community despite its potential to effectively discriminate between fluid and lithology results.
AVO inversion is similarly applicable to both 2D and 3D seismic data in time or depth providing that sufficient care has been taken up to protect amplitudes during processing. A reliable speed model is also a critical component of the AVO process as exact position information is a prerequisite for AVO inversion. A lot more accurate the perspectives, the better the partitioning of amplitudes to P-wave and S-wave reflectivities. In addition, both position and ray path information can be contained in a variety of model centered amplitude corrections that are preferable and often more correct than scalars produced from empirical equations.
The inversion process is then performed, completing in about the same time as a conventional stack. The causing outputs are a series of AVO reflectivity portions or amounts that are dependant on the Zoeppritz approximation used.
Fluid Factor is one of the most useful attributes produced from AVO inversion anticipated its capability to make such distinctions and straight identify hydrocarbons.
Multi-Measurement Reservoir Classification workflows include the following components:
Reservoir Synthetic Modeling
Forward modeling to create 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 denseness) from prestack seismic data by using a hereditary algorithm.
AVO Modeling and analysis
Conditions angle band stacks prior to performing AVO analysis
Elastic impedance modeling and inversion from angle strap cubes
Space adaptive wavelet handling and inversion to comparative seismic impedance
Elastic Impedance Inversion
Combining low consistency tendencies with seismic relative inverted impedance cubes to create absolute impedance
Integrated Rock and roll Physics Modeling
Fluid and rock property research, modeling and substitution
Rock Property Calibration
Generating rock properties from seismic using transforms derived from petrophysical research of well data.
The outputs are high-resolution total acoustic and shear impedance and denseness volumes regular with the seismic data and the well-log data. The inverted stretchy parameter volumes are used for in depth interpretation of lithofacies and pore-fluid content in the subsurface. Combined with rock and roll physics modeling and rock and roll 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 test point in the 3-D level.
Some elements of the seismic data processing sequence are practically universal - regardless of whether the goal is to execute time imaging, depth imaging, multicomponent imaging, or tank studies. Data fitness and signal handling form the foundation of the seismic control workflow.
Signal processing encompasses a wide variety of technologies made to address numerous problems in the processing sequence: from data calibration and regularization through to noises attenuation, demultiple, and signal improvement techniques.
Data caliberation and regularization
Prestack time migration (PSTM) might not exactly be the most advanced imaging method available, but it remains the mostly used migration algorithm in use today. Kirchhoff PSTM combines upgraded structural imaging with amplitude preservation of prestack data in readiness for AVO, inversion, and following tank characterization.
Advances in this field also mean that time imaging, more than ever before, is a perfect first step in a Depth Imaging workflow, lowering the number of velocity model building iterations and reducing overall turnaround time.
Imaging: Regularization, migration and datuming techniques
Velocities and moveout
Enhanced Migration Amplitude Normalization
Depth Imaging is the preferred seismic imaging tool for today's most challenging exploration and reservoir-delineation jobs. In areas of structural or seismic velocity model complexity, lots of the assumptions underpinning traditional time-domain processing are invalid and can produce deceptive results. Typical situations might be seriously faulted sequences or sodium intrusions. In these cases, only the careful program of 3D prestack depth imaging can be relied to accurately delineate geological structure, aiding risk evaluation and helping providers to boost drilling success rates.
From a technology point of view, high quality depth imaging has two main aspects: the ability to build specific and accurate velocity models, in conjunction with a superior imaging algorithm.
VELOCITY MODEL BUILDING
Velocity Model Building is a key critical aspect in imaging the Earth. Tomography provides the best high res calibrated velocity and anisotropic Earth Models, powerful refraction tomographies detect shallow velocity anomalies. Those algorithms use any acquisition construction and can be employed to any geological setting up. Also, these computer rigorous algorithms are included with an interactive design environment for fast and exact quality control of the interim and benefits.
Conventional seismic taking uses a sole scalar way of measuring of pressure or vertical displacement throughout the 2D or 3D review to derive images and types of the subsurface. Following processing and inversion steps can be from the comparative shear-wave contrasts in the subsurface using rock property human relationships. However, it is sometimes impossible to meet a survey's seismic imaging or reservoir classification aims using compressional (P) waves by itself.
SEISMIC DATA INTERPRETATION
Computer aided interpretation is the mainstay of 3D seismic interpretation as the quantity of data used is voluminous.
The important services are:
IIWS (Intergrated Brains Workstation) based mostly interpretation of 2D, 3D data
Integrating seismic attributes with wireline, core and reservoir data for reservoir characterisation
3D visualisation and computer animation
Structural restoration is an established way to validate seismic interpretations. Furthermore, palinspastic reconstruction can help identify potential reservoir depocentres, enable the way of measuring of catchment areas at the time of hydrocarbon migration and business lead to an improved understanding of complicated hydrocarbon systems such as those in the deepwater. Recovery is attained by the sequential backstripping of the present day depth model. Upon removal of each successive layer, the remaining areas within the model are tweaked to take into account faulting, decompaction and isostatic modification.
Formulation of geological models for exploration and development
CHAPTER 3 THEORITICAL DEVELOPMENT
Computer-aided seismic interpretation consists of the utilization of horizon monitoring. Horizon tracking is based upon algorithms that require manually selection of a start point for autotracking procedure. A similar value or feature is researched in the adjacent trace of course, if found within the specified boundaries, the tracker moves on to another trace.
Autotrackers are centered upon two functions - feature founded or correlation based mostly. As the feature centered look for similar track values, the correlation based strategy is more robust and less delicate to sound.
The problem experienced in autotracking is their incapability to track horizons along discontinuities. Since an identical value or feature in the adjacent trace is not found, it automatically ceases there. On the other hand, manually monitoring horizons over the fault line is very frustrating and is highly subjective.
In the following points, we shall first package with horizon monitoring and then recommend alternatives for traffic monitoring horizons over discontinuities.
Horizons are strong reflections event which signify boundaries between rock formations. Checking across faults is a period consuming activity and has not been programmed satisfactorily. Faults are discrete fracture along which measurable displacement of rock layering has occurred. Partly disturbed or noise signals result in a major problem in horizon traffic monitoring.
Horizon monitoring includes structural analysis of a 3d dataset. The seismologist should incorporate understanding of stratigraphic and structural romantic relationships within the seismic representation to look for the events that may be grouped as same horizon.
CROSS Relationship TECHNIQUE
It is a way of measuring two waveforms as a function of your time lag applied to one of them. This is also known as a slipping dot product or inner-product. Cross-correlation confirms it application in pattern recognition, solitary particle analysis, electron tomographic averaging and cryptanalysis.
For constant functions, f and g, the cross-correlation is defined as:
where f * denotes the intricate conjugate of f.
Similarly, for discrete functions, the cross-correlation is thought as:
By considering the two functions f and g that differ by a change, 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 merchandise 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 mixed they attain a maximum value across the same axis by contributing to make the intergral greater. The same pertains to if both the functions have a negative value factor, because the product of two negative principles shall give us a positive value only.
HORIZON Monitoring METHODOLOGY
A programming code is written which shall offer with the track amplitude principles. The amplitude prices may easily be known by observing the SEG-Y record of the seismic data. The SEG-Y data file contains all the information about the the seismic acquisition process and the ideals computed following the handling of data.
The SEG-Y has been followed as a standard for trace sequential data. It contains different headers particularly -
EBCDIC format header - this is made up of all the information about the region, seismic line name, shotpoint range, saving parameters and control history.
Binary header - this consists of information about the amount of samples, sample rate and format code.
Trace header - for each trace in the info, there is a unique trace header that contains information related to shotpoint amount, CDP, and study locations.
Data samples - this is also repeated for each trace in the file. It contains the amount of bytes per sample which would depend upin the format of the info sample.
A program written to perform cross-correlation technique was created to execute a sequential array. The development steps are given as -
It first occupies values of your time interval in support of the first trace to find the highest amplitude value among them. The values of your time interval can be wanted by the user or a arbitrary time interval range can be utilized.
It then takes up the next track and forms a wide range using the values of amplitude. The highest value of the prior step to be the centre value and equal number of ideals above and below it in order to attain a time window.
Then a calculation is performed and by using cross-correlation technique it finds the highest coffecient and the correspoding amplitude of the reflection.
The next step follows as step 2 2 and this program proceeds futher by slipping the window(array of numbers) and additional before end of range of traces.
The time interval where such calculations have to be made or where a particular horizon must be dealt with is given at the start of this program. The values of what size the array maybe can be given among 3 or 5 (windowpane size) when asked by this program.
The smaller the time period the better the resolution of the horizon.
The SEG-Y data file and output overlain over one another after execution of this program is given as :
The difference between traced and real horizon due to the presence of an fault.
The genuine horizon to be traced
It can clearly be observed that, once a discontinuity is experienced, the program tracks down the incorrect horizon and the results and haphazard.
To improve upon this we shall make use of a different strategy for horizon monitoring. In the following part we will discuss a model established method of correlate several horizons together across discontinuities to discover a genuine solution.
The means to fix the condition can be divided into two parts:-
First of most, we shall offer with horizon pairs. The horizon pairs will be found using the similarity if reflector sequences. Checking the regular polarity of the signal also to find the relationship between the mistake duration and maximum vertical displacement.
Secondly, the two horizon pairs interpolated using the first strategy need to be mixed to finally form an individual horizon.
This strategy, if correctly put in place, can help in correct horizon tracking across a problem.
In the first part, the different constraints serves as a follows :-
In simple horizon traffic monitoring we dealt with the local traits of the horizons particularly amplitude, polarity and wavelength which present a problem of being different to be correlatable on its own. Thus we will deal with reflector sequences. Reflector sequences can be compared by calculating their cross-correlation coefficients. Also that we shall compare the polarity on the certain array along the fault line.
CROSS Relationship COEFFICIENT
We estimate the cross-correlation coefficient of every horizon match by using amplitude of corresponding horizons in the neighborhood by performing this system over a wide range. The number of values used the array is defined to a particularly large value because the strata of different factors of a fault maybe unequally compressed.
Since the sequence of horizons remains same even across the fault line, the sign of amplitude must be equivalent for equivalent horizon segments. We utilize this feature to look for the same horizon pattern by correlating the positive and negative amplitudes representing the strata.
MAXIMUM FAULT THROW
Upon study of various faults, independent of materials and scale, the best romantic relationship between fault period, L and maximum vertical displacement of horizons, D is given as :-
D = 0. 03 L1. 06
This marriage can be utilized in this model to constrain horizon section matches to the people, whose displacement prices do not go beyond D.
The second area of the programming includes the pairing horizon pairs :-
To combine the horizon match not only require relationship and similarity between different values but also consider the geometrical and geological constraints.
The geometrical constraint can be described by simple method that the horizons tracked must not cross.
The geological constraint requires into consideration the sign of the fault put. This can be calculated by knowing the fault type. Mistake are categorized based on the footwall and suspending wall. The put of a normal mistake is vertical and dips on the downthrown part of the problem although it is contrary in the change fault i. e. into the upthrown aspect.
The analysis of forces that influence the area may be used to determine the throw of the mistake. We shall need the sign of the put of problem for programming purpose since that shall determine as to where the horizon set must be found in the seismic file.
To examine the data two methods were used :-
Exahaustive search algorithm - this model takes into account that the model is accurate and therefore it uses the algorithm to a certain value where it terminates, then it carries on with the other node in the algorithm again to a value where it terminates etc. Since upon checking many horizons, this model can be very time consuming and impractical, thus to observe over a particular horizon another model was chosen.
Stochastic method - this technique induces randomization in the model. Thus this may serve to solve the algorithm by bringing out some random factors that can provide to solve the algorithm to bring about a particular solution.
The horizon to be tracked should have a solid reflection. Because the program is used to converge the horizon segments across the fault series, thus the mistake line must be highlighted, this is done manually along the spot appealing or the spot of discontinuity. The fault series is interpolated by determining the presumed problem pixels in the info sheet.
Horizon segments are then allocated to both discontinued classes - still left or right. This approach can be used to analyze the fault throw. Then the customer can select as to which horizon is usually to be used for relationship.
Since no seed things will be required in the initial step for horizon tracking, this proves to be always a terminal advantage in the process.
EXHAUSTIVE SEARCH ALGORITHM
This algorithm estimates the similarity of most possible horizon pairs, then upon request of geological constraints it can find an best possible solution.
This occurs the following :-
The solo similarity of all horizon pairs is picked.
The total similarity for each and every combination is determined from the similarity prices of horizon pairs. Global similarities in the full total data framework are then searched.
After obtaining different pairs, the constraints of polarity, maximum fault throw, indication of fault toss and that the horizons must not cross are integrated over the perfect solution is and the best possible pairs are allocated.
All such horizon pairs are found in the answer tree. Many such pairs are invalidated in the perfect solution is 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 could lead to the wrong geological solution.
CONSISTENCY CHECK CYCLE
This method then practices a tree composition that proceeds in a stepwise fashion. If all the constraints are provel right, it goes onward and solves the algorithm for the next phase for consistency. When the similarities continue with each step ahead, the circuit repeats itself to track down the correct horizon, in the other case it takes into account the next couple. The cycle terminates when a horizon pair of maximum total similarity is available that fulfills all the constraints.
This can even be termed the general algorithm for correlating horizons. This process is more clear-cut and precisely identifies the evaluation conditions, therefore it can be a far 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 identified values l and r(l)m which signifies the left horizon and the right horizon number. If a mixture is not found for the still left horizon, it is assigned a value -1.
At the start of this program, many horizon pairs are manufactured randomly. This may although business lead to a huge volume of pairs, thus constraints are place to reduce the amount of horizon pairs. This can be done by defining a set space around an string to which it can hook up to. Then the horizon pairs which do not follow geological constraints of polarity, mistake throw, indication of fault chuck, are neglected. Then the horizon pairs which cross are neglected. This gives us a result of all possible horizon pairs.
A roulette wheel technique is applied where in the pairs are preferred based on their compatibility with the initial value. The beliefs which continue to be unchanged in the next string are termed compatible and are chosen to be run after by the algorithm.
Now to crossover to another step, the validated strings are checked with all possible alternatives constraining them with the geometrical factors. The fitness of every solution is inspected.
CHAPTER 4 RESULTS AND CONCLUSION
Extensive research across discontinuities and request of geological constraints can assist in successful horizon monitoring across fault lines.
Upon software of both the models, the results have been proven in the shape above.
Although the methods were operated after a relatively simple dataset, more complex datasets would require more reliability checks and much more acquaintance with the geological framework in order to infer the correct solutions.
Generic solution was found to be more steady with results.
The exahaustive search strategy produce great results with horizon tracking across faults but it can only consider a limited volume of horizon segments across the fault. This will not prove too pretty much correct to be utilized in case there is highly dense datasets.
Generic algorithm proves to be the right procedure for the condition above, although generic solution needs to be analyzed to improvise the stability of generic algorithm.
Further advancements can be produced upon this research. Exploration and search of more geological constraints and well as geometrical constraints can assist in improving the program to be analyzed over more technical datasets.