Multiple and Coherent Noise Removal from X-Profile 2D Seismic Data of Southern Iraq Using Normal Move Out - Frequency Wavenumber Technique

Abstract


Introduction
Waves that reflect more than once on their way from the source to the receivers are referred to as multiples.Simpler multiples reflect twice, once more than primaries, but higher order multiples are also feasible and can reflect more times (although they get weaker with each reflection).When using multiples for imaging, especially higher order multiples, it may be necessary to record for longer periods than when using simple primaries since the additional reverberations cause the waves to take longer to reach the receivers.As a result, the survey takes longer to complete and requires more computational resources.This raises the acquisition and processing costs.However, as more long offset surveys are conducted, long recording times are becoming more prevalent, increasing the likelihood that multiples may be recorded (Alan, 2015).The wave fields with a single bouncing point (primaries) (Fig. 1a), must be distinguished from the data with multiples.Two classifications of multiples can be distinguished in Fig. 1.The first is surface-related multiple (Fig. 1b) is one that has secondary reflection points at the surface.
Fig. 1.Schematic representation of the different types of reflection events.1) The primary event, together with some of its associated.2) Surface-related multiples.3) Internal multiples (Verschuur, 2013) These multiples are produced by the air-water or air-Earth (weathering zone) discontinuities and would vanish if the boundary were to become transparent (Verschuur, 2013).They typically have large amplitudes because the Reflection Coefficient (RC) of such an interface is near -1.The second is internal multiples (Fig. 1c), which are those multiples that have points of downward reflection in the subsurface.They are created by the material discontinuities that exist within the Earth.Unless they are produced between two strongly reflecting borders, they typically have low amplitudes (Lopez, 2016).As we can see in Fig. 1, internal multiples have reflection points at the subsurface, but surface-related multiples have all of their reflection points on the surface.The pathways (a, b, and c) all have at least one surfacebased reflection point.There are no surface reflection locations along the pathways (d and e).By transforming the seismic data into different domains, such as Frequency-Wavenumber (FK) domain, the seismic events will be separated according to their frequency and wavelength (Kabir and Marfurt, 1999;Xiao et al., 2003;Al-Rahim and Terky, 2017;Ali et al., 2019).Filtering algorithms are used to pass the desired events (primaries) and reject(multiples) others.After transforming the data back to the timedistance domain, all multiples should be ideally eliminated.The multiple energy is challenging to separate from the main data when the moveout difference is modest between the primaries and multiple events (Iverson, 2020).
Significant seismic characteristics include move-out times.Move-out depends on velocity and gets faster with offsets.This characteristic is used in techniques like stacking (Mayne, 1962), FK Filtering (Ryu, 1982), and Parabolic Radon (Hampson, 1986).Primaries in the common-mid-point (CMP) gathers should undergo a flattening processing named Normal Move Out (NMO) in order to align them inside the vertical zero axis in the FK spectrum.Applying dip filter to pass these aligned signals in the FK domain and transforming the data back to the time distance domain will isolate multiples from the seismic CMP gather and leave the flatten events only that determine the primaries.These flattened primaries are summed (stacked) into a single trace.
Multiples that travel more slowly than coincident primaries have smaller wavenumbers when the CMP collect is transformed into the frequency (cycles per unit time) and wavenumber (cycles per unit distance) domains.According to Ryu (1982), the primary and multiple after Normal Move-out Correction (NMO) and domain transformation to FK present a discernible distinction between them.The multiples may be muted in the FK domain, after which the remaining data may be changed back into the time-offset domain (Mohammed, 2014;Dondurur, 2018).
The aim of the current study is removed multiples from a 2D seismic X-profile data from southern Iraq by applying NMO-FK technique.Examine this profile with velocity analysis for each CMP gather to see if there are multiple included with the 2D seismic data, applying NMO correction to flatten the primaries and later on pass the NMO corrected data to FK filter to remove multiples effects and transfer the data back to the time domain and apply the stack at the end of the process.The method will be tested on a synthetic fake data to validate the method authority.Finally, a comparison is made between the stacked data using only conventional NMO correction with our working method (NMO-FK) to define the enhancement locations in the processed seismic data.All these processing steps are done using an open sources Madagascar reproducible package.

Materials and Methods
The analyzed 2D seismic X-Profile data is consistent of 723 CMP gathered with 45721 traces.The NMO velocity analysis where the primaries appear horizontally is done using auto-pick procedures.Auto-pick (sfpick; automatic picking from semblance-like panels, Fomel, 2009) is one of most important programs that been invented with Madagascar open source package.
Fig. 2, shows a drawn sketch for the steps of this method.Fig. 2a, shows five primaries (blue curves) with three overlapping multiples (red dashed curves).Fig. 2b reveals the effect of applying the NMO on the data, where the primaries line up (flatten) and the multiples are affected by curved upward.In Fig. 2c, the data are transformed to FK domain, the flatten primaries are aligned with the vertical zero axis whilst everything around it will be either noise or multipliers.Dip-filter is applied to the data, which pass the primaries line up in the middle on the vertical zero line and reject (mute) the other data.Fig. 2d shows the primaries after transforming the data back to the time domain.A perfect separation of primaries appeared pure, clean and without multiples, and when removing the effects, the NMO from the primaries and returning them to their normal state, we will notice the isolated multiples as shown in Fig. 2e.These steps of work are applied to a fake event consisting of several primaries with different kinds of surface related and peg-leg multiples.A 10% of random noise is added also to the faked data to see their effect on the analysis procedures.Fig. 3 with its comparable parts with Fig. 2 shows, a) the chosen fake data.b) NMO for primaries.c) FK data domain with dip-filer, where the primaries are passed and anything else are mute or reject.d) Isolation of primaries and e) the remains multiples.

Results
The results of our process for the fully 2D X-Profile data are presented in several figures.Fig. 4 shows the CMP gather of the studied X-Profile 2D seismic data.6a shows the tested CMP gather 450.Fig. 6b, shows NMO velocity analysis with automatic picking where the red circle determines the multiples' locations, whilst Fig. 6c shows the flattened primaries but still contaminated with multiple effects.Fig. 7 is present the FK spectrum for the flatten primaries shown in Fig. 6c, and Fig. 7b shows the application of the dip-filter to the data.In Fig. 7a, the primaries line up with the vertical zero axis line in the middle surrounded by multiples and noise that marked by the yellow circle.Fig. 7b shows the applied dip-filter where most of multiples are rejected.Fig. 7c shows pre-stack multiple clean after applying dip-filter.
Fig. 8, shows a comparison between NMO conventional processes (as in Fig. 6c) and our applied method using FK filter as an additional step to the processing sequence (Fig. 7c).Clear and sharpening primaries in the final pre-stack CMP 450 gather is presented in Fig. 8b and the removed multiples effects in Fig. 8b.We apply the same dimension of the dip-filter to the whole processed auto-picked NMO corrected 2D seismic data using the conventional procedures.Fig. 9 shows the final results where Fig. 9a represents the NMO stacked for the X-Profile before and Fig. 9b after multiple attenuation by using FK, and Fig. 9c shows the difference between them.
There are available multiples in the deep reflectors and fewer multiples in the middle part of the sedimentary secession.Also, the continuity and sharpening of reflectors are more enhanced in our NMO-FK technique which indicates the success of our eliminations of the multiples in the seismic section.

Discussion
It is known that any seismic survey is accompanied by noise and multiples of different proportions, and therefore it is will include a large percentage of errors in the interpreting stage of the surveyed data.So that, all these have to be removed in same how.There are many ways to attenuate and remove multiples, and all of these methods try to reach a common goal, which are clear and pure primaries, free of any multiples, as they can be interpreted and the correct information for the data can be taken through them.The problem is that, the velocity of the multiples is close or similar to the velocity of the primaries especially in deep reflectors which makes it overlap with the primaries and makes it difficult to separate them.Each method of attenuation depends on different principle from the other, and the success rate of each method may be different from the other, but at the end, success lies in reaching the purity of the primaries.

Conclusions
Using an FK filter is a common way to attenuate many multiples and isolate them from the primaries.As we noticed through the NMO velocity analysis on field data from southern Iraq, there are a set of multiples associated with the primaries, and this appeared clearly when the FK filter was applied to the NMO corrected data.So, we add an additional step to the conventional NMO which is FK filter and name the method as NMO-FK technique.The results show a clear image of the primaries and present good evidence for the presence of multiples in the seismic data in southern Iraq that negatively effects on the interpretation.This necessitates the need to remove multiples by attenuation operations, which are considered an essential part of the seismic processing operations.Working on applying the FK filter to the data required many trials as well as time to get the best net results for the primaries.Even thought, programming these steps will fasten the processing time.Madagascar open-source reproducible package provides a lot of programs that help to do that.

Fig. 2 .
Fig. 2. a) A schematic CMP gather involving five primary (P) and three multiple (M) reflections.b) Schematic NMO velocity functions for primary (blue) and multiple (red) reflections.c) A plot of the FK filter where the primaries are aligned vertically in the center line.d) Primaries separation after removing the multiples using mute process (dip-filter).e) Isolated multiples

Fig. 3 .
Fig. 3. a) The fake data.b) NMO for primaries.c) FK data domain with dip-filer (yellow line).d) Isolation of primaries.e) The remains multiples

Fig. 5 .Fig. 7 .
Fig. 5.A selected CMP gather no 450 for velocity analysis plotted in time-offset domain

Fig. 8 .
Fig.8.a) The flatten primaries contaminated with multiples effects (same as fig.6c).b) The flatten primaries after applying dip-filter (same as fig.7c).c) The difference between them is the remaining multiples