ORIGINAL PAPER

Numerical simulation of methane plumes based on effectivemedium theory

Jiachun You1& Canping Li2 & Lifang Cheng1 & Xuewei Liu1

& Muhammad irfan Ehsan1

Received: 16 September 2014 /Accepted: 7 April 2015 /Published online: 22 April 2015# Saudi Society for Geosciences 2015

Abstract Because they offer direct evidence of seafloor seepsand may indicate the presence of gas hydrates, methaneplumes have attracted increasing research attention. Here,we attempt to understand the seismic response of methaneplumes through simulation and analysing the characteristicsof the seismic scattering wave field caused by methaneplumes. Through forward modelling, stochastic medium the-ory was used to set the random distribution of bubbles, andeffective medium theory is applied to create a bubble velocitymodel. We then used the finite-difference method to calculatethe common shot gather. To achieve true amplitude migrationof methane plumes, reverse-time migration method is intro-duced to perform it. To study the differences in seismic re-sponse to variable methane gas content and to establish therelationship between various attribute parameters and gas con-tent, we create five models with gradually increasing gas con-tents. After imaging these five models, amplitude class attri-butes, frequency class attributes and phase class attributes arecomputed from the migration section, and a theoretical modelbetween attributes and gas content is built. Through quantita-tive analysis of the change of attributes as a function of gascontent, we find that amplitude class attributes vary more lin-early with methane gas content than do the other two attributeclasses. Therefore, we conclude that amplitude class attributeshave most potential application for inversion of gas content infurther exploration of bubble plumes.

Keywords Methane plume . Effectivemedium theory .

Reverse-timemigration . Attribute analysis

Introduction

Gas hydrates are water-gas clathrates that are formed mainlyin low-temperature, high-pressure environments (Sloan2007). With increasing exploitation of conventional oil andgas resources, mankind is facing a mounting energy crisisand the deterioration of the environment; on the other hand,natural gas hydrates have a wide distribution and rich reservesaround the world and produce almost no residue after com-bustion, unlike oil and coal (Kvenvolden, 1993a, b). By cal-culation, 1 m3of gas hydrate can be transformed into 164 m3

of natural gas and 0.8 m3 of water. Therefore, gas hydrateshave been widely studied by scientists and known as a futureenergy resource (Kalland, 1994;Collett, 2002).

Gas hydrates play an important role in the future energyresource, and scientists have conducted much research onthem. However, there are few studies of methane plumes,which have close relationships with gas hydrate exploration(Paull et al., 1995). In recent years, the phenomenon ofoverflowing methane plumes has been detected by seismicmethods (e.g. side scan sonar, multi-beam survey etc.) ingas-hydrate-bearing zones (Tryon et al., 2002; Luan et al.,2010; Klaucke et al., 2010). Luan et al. (2010) detectedflare-type reflections in seismic sections using side scan sonarin the Okhotsk Sea; they also found a similar phenomenon in asingle-channel seismic profile on the continental slope area ofthe East China Sea bearing gas hydrates (Luan et al. 2009).Greinert et al. (2006) discovered 1300-m-high rising methaneplumes discharging from a mud volcano in the Black Sea(Fig. 1). Many articles have noted that where methane plumesare found, gas hydrates are likely to be probed. Figure 2 is

* Jiachun Youyoujiachun2009@163.com

1 School of Geophysics and Information Technology, ChinaUniversity of Geosciences, Beijing 100083, China

2 Laboratory of Ocean Remote Sensing and Information Technology,Guangdong Ocean University, Zhanjiang 524088, China

Arab J Geosci (2015) 8:9089–9100DOI 10.1007/s12517-015-1916-2

Fig. 1 Themethane plume in the Black Sea

Fig. 2 The seismic migration section of Shenhu area in the South China Sea

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seismic migration section of Shenhu area in the South ChinaSea. Seismic interpretations of this area show that there arespecial vent structures (a fault passes through the stratum andreaches the seafloor) as well as a typical bottom simulatingreflector (BSR) and a blanking zone. Figure 3 shows the con-ventional seismic migration section of seawater containingbubble plumes in the same area as Fig. 2. Integrating theanalyses of Figs. 2 and 3 leads us to believe that the gaschimney and fault provide a channel to let methane spill intothe sea and that the decomposition of gas hydrates is thesource of methane plumes. Therefore, the occurrence of meth-ane plumes plays an indicative role in gas hydrate explorationtarget areas (Katja, 2003).

Methane plumes are a natural phenomenon where methanegas occurring in the seabed migrates from the earth interiorand leaks into the sea through a seabed fault or fracture. Whenthe methane gas penetrates into the sea, due to the largeimpedance contrast between gas and water, the methane gaswill produce a strong scattering effect on seismic waves. Thisis the theoretical basis for the study of methane plumes byseismic methods. Currently, plume detection is based onsonar technology; its dominating frequency is oftenthousands of hertz so that it is easy to detect very smallbubbles. The study of the seismic response of methaneplumes using conventional seismic methods is still relativelyuncommon. Generally, the main frequency of conventionalseismic methods is at most hundreds of hertz, which limitsits resolution. However, Fig. 3 suggests that conventionalseismic exploration methods have the potential to surveybubble plumes. In addition to its wide exploration area andrich data, seismic exploration technology is a powerful tool tostudy the internal structure of the earth. Due to the strongground penetration ability of seismic waves, seismicexploration technology can be used to study the submarinestratigraphic structures and investigate the causes of plume

formation. Li et al. (2013) used stochastic medium theory tobuild a plume model in which the diameter and content ofmethane plumes are randomly distributed. They achievedgood results using the finite-difference method for numericalsimulation of the plumes. Their result has too strongly layeredphenomena (Fig. 4), which contrasts with the actual seismicmigration section of bubble plumes. Applying effective medi-um theory to this question, the methane and its surroundingwater makes up a two-phase medium model. Based on this,the finite-difference method is employed to implement theforward modelling of the methane plume and the reverse-time migration technique, the best migration method, is usedto process the shot common records. It is significant for pro-viding the evaluation of gas hydrate reservoirs, our under-standing of the carbon cycle and deep-sea environmental re-search to study the basic characteristics of methane plumesand their distribution using conventional seismic explorationmethods (Blunier 2000;Leifer and MacDonald 2003).

Fig. 3 The seismic migration section with bubble plumes from the samearea as Fig. 1 Fig. 4 The pre-stack time migration section of Li et al. (2013)

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The methane plume model

Crustal dynamic processes can cause gas from inside theearth’s crust to pass through pores, cracks, fractures orfault channels and leak into the sea, forming a methaneplume. When the gas enters the sea, a small amount dis-solves, but most exists in bubbles. Studies have found thateven a small amount of gas in the water can cause a largechange in velocity (Li et al., 2010). When gas exits theseafloor, it will rise slowly because of its buoyancy. In therising process, changes in water pressure and temperatureand other physical conditions will cause the radius ofbubble to grow. When its radius reaches a certain extent,the bubble will burst into several smaller bubbles, some ofwhich dissolve into the sea, causing the gas content todecrease gradually. The bubble will keep rising until allgas dissolves. If the gas does not completely dissolve, itwill flow out of the water and form a Bwater boiling^phenomenon. According to previous studies, in thebubble-rising process, the methane content initially in-creases to a maximum and then decreases as the distancefrom the seafloor increases.

Based on the above research results, we use effective me-dium theory to establish a velocity model of methane plumesin numerical simulations. In actual sonar imaging pictures, thelocation of bubbles in methane plumes are a random distribu-tion, with their location based on a random function (Korn,1993) given as follows:

φ x; zð Þ ¼ exp

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

−x2

a2þ z2

b2

� �

s

!

: ð1Þ

Here, a and b are autocorrelation lengths in the x and zdirections, respectively.

When methane gas exists in the form of bubbles in water,microscopically, bubble and the surrounding water constitutea typical gas-liquid two-phase medium; therefore, we can useeffective medium theory to calculate the velocity of methaneplume area. Reuss average effective theory (Mavko et al.,2003) is introduced below.

1

Kfl¼ Sg

Kgþ 1−Sg

Kw

ρ ¼ Sgρg þ 1−Sg� �

ρw

v ¼ffiffiffiffiffiffiffi

Kfl

ρ

s

8

>

>

>

>

>

<

>

>

>

>

>

:

ð2Þ

Here, Kg and Kw are the bulk moduli of gas and water,respectively; Sg is methane gas content; ρg and ρw are thedensities of gas and water, respectively; and Kfl, ρ and v arethe effective bulk modulus, density and velocity of gas andwater, respectively.

Much previous work indicates that changes in bubble radi-us produce a very small effect on the velocity of methaneplumes (Li et al. 2010, 2013), so this paper does not considerthe effect of bubble radius on velocity. Gas content varies withdepth, but within a certain depth range (e.g. 10 m), variationsin gas content are modest. Therefore, we divide the methaneplume into multiple 10-m-thick vertical layers. Each layer hasa background gas content value; the methane gas contentwithin the layer is defined through random perturbationsaround the background value. The background gas contentversus depth is described by the above law of bubble rising.The formula for the methane content in each layer is

S x; zð Þ ¼ S0 þ δS x; zð Þ ¼ S0 1þ σ x; zð Þð Þ ð3Þwhere S(x,z) is methane content, S0 is the backgroundmethanegas content, δS(x,z) is the random fluctuation in methane gascontent and σ(x,z) is a second-order, steady spatial randomprocess with zero mean and variance; this random fluctuationvalue is calculated by the random function of Eq. (1).

To simulate the Bflame^ shape of plumes observed in sonarprofiles, an elliptic function is used to depict the appearance ofmethane plumes.

Higher-order finite-difference methodand reverse-time migration

We compute the seismic response of the methane plumesbased on the acoustic wave equation:

∂u∂t

¼ −ρv2∂vx∂x

þ ∂vz∂z

� �

∂vx∂t

¼ −1

ρ∂u∂x

∂vz∂t

¼ −1

ρ∂u∂z

8

>

>

>

>

>

>

<

>

>

>

>

>

>

:

ð4Þ

where vx and vz are velocities in the x and z directions, respec-tively, u is displacement, ρ is density and v is velocity of themedium.

The finite-difference (FD) method is implemented usinghigh-order staggered-grid operators for spatial differentiationand second-order derivative operators for time differentiation.The following high-order FD discretization in the x direction,as an example, is usually used:

∂ f∂x

¼ 1

Δx

X

N

n¼1

C Nð Þn f xþ Δx

22n−1ð Þ

� �

− f x−Δx

22n−1ð Þ

� �

ð5Þwhere f represents either a velocity component or displace-ment and Δx is the step length in the x direction. The notationsf xþ Δx

2 2n−1ð Þ� �

and f x−Δx2 2n−1ð Þ� �

are used to indicate

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that the field derivatives are calculated at staggered node po-sitions. The dimensionless coefficients Cn

(N) can be found ei-ther from Taylor approximations or through an optimizationprocedure (Holberg, 1987). To achieve high accuracy and ef-ficiency and suppress dispersion effects as much as possible,18th-order spatial differential coefficients and second-ordertemporal differential coefficients were used to solve the waveequation.

By using the finite-difference scheme to model the propa-gation of seismic waves, boundary reflections were generatedwithout an absorbing boundary. The perfect match layer tech-nique is applied to absorb boundary reflection (Zeng et al.,2001).

Thanks to improving computer hardware, especially GPU/CPU technology that is often applied in seismic migration,reverse-time migration (RTM) for high-resolution imagingof complex structures (Baysal et al., 1983; Liu et al. 2010)has rapidly developed.

RTM is based on a two-way wave equation to performthe wave field extrapolation, which overcomes the diplimitation of traditional one-way wave migration methods.In theory, it can image any type of waves, including ro-tating waves, prism waves and multiple reflection waves;it also estimates more accurate amplitude information andcan realize the true amplitude migration (Zhang et al.,2007; Deng and McMechan 2008).

The reverse-time migration algorithm is performed using astaggered-grid finite-difference scheme with second-order ac-curacy in time and 18th-order accuracy in space, which is thesame accuracy achieved in the forward modelling. Reverse-time migration is applied on each shot gather; we then stackthe migration results.

The migration imaging condition is given by cross correla-tion imaging theory:

image x; zð Þ ¼X

t

S x; z; tð ÞR x; z; tð Þ ð6Þ

where S(x, z, t) and R(x, z, t) are the source wave field pro-duced by forward modelling and the receiver wave field pro-duced by reverse-time extrapolation, respectively; S(x, z,t)*R(x, z, t) at a certain time is interpreted as the coherenceof the forward modelling wave field and the reverse-timewave field.

Using the cross correlation imaging condition in RTM,a low-frequency, high-amplitude illusion appears in theprofile, which we interpret as a low-frequency noise prob-lem, especially in shallow, high-speed interfaces. Aftercomparing the result in many previous studies involvinglow-frequency de-noising algorithms, we applied theLaplace transformation method (Zhang and Sun, 2009)to solve it.

Numerical simulation

To simulate the seismic response of methane plumes, we es-tablish a two-layer model. The first layer is seawater; methaneplumes appear in a random distribution with their backgroundmethane gas contents changing with depth: first increasingand then decreasing. The secondary layer is submarine gas-bearing sediment. In the bubble-rising process, methane bub-bles with large radii are constantly broken into smaller meth-ane bubbles. We establish a piecewise linear relationship be-tween the background methane content and seawater depth;more specifically, the background methane content increasesto a maximum and then decreases to a minimum linearly withdistance above the seafloor.

To study the difference in seismic response as a function ofbackground methane gas content, five background methanegas content models are created; they are 1∼5∼1, 5∼10∼5,10∼15∼10, 15∼20∼15 and 20∼25∼20 %. The methaneplumes are divided into several small layers every 10 m. Ineach small layer, we use stochastic medium theory to set themethane content based on the background methane contentvalue where the bubble exists. An example velocity modelof these methane plumes is shown in Fig. 5; in this example,the background methane gas content is 1∼5∼1 %.

The acquisition parameters are as follows: the survey line is1000 m in the horizontal direction and at zero depth, the gridsubdivision is 1 m×1 m and the dominant frequency of aseismic wavelet is 140 Hz. The observation system is as fol-lows: seismic waves are received at all arrays, the receiverarray is fixed and the shot point moves left to right, its intervalis 10 m and there are 101 shots in total, the seismic source is atzero depth, the trace interval is 1 m and there are a total of1000 traces, the least offset is zero, the record length is 1.4 sand the sampling rate is 0.2 ms.

Compared to the bubble plumes profile (Fig. 2) scannedfrom sonar, the migration section (Fig. 4) imaged by Li et al.(2013), and the actual seismic migration section of a seawaterbody (Fig. 3), our proposed method (the migration section

Fig. 5 The velocity model of the 1∼5∼1 % background methane plume

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processed by reverse-time migration, Fig. 6) agrees with theactual situation very well and attains better imaging accuracythan Li’s. It also maintains the characteristic appearance ofsonar methods.

From Fig. 6, we can see the outline of the methane plumevery clearly, which demonstrates that our proposed methodcan correctly reflect the basic features of methane plumes.This provides a theoretical basis to study the relationship be-tween the seismic response and the gas content of methaneplume. Qualitative analysis of the migration section showsthat the outer shell of the methane plumes provides a clearerimage than the inner side; the higher the background methanecontent is, the more imaging difference there is between theouter and inner shells. This is because when the seismic wave

propagates across the methane plumes zone, the bubble can betreated as a scattered point, which will cause the energy toattenuate so much that it hardly records the wave field infor-mation from the internal. It is also interesting that the shadowdepth of the methane plumes is more distinct than the bottomover the horizontal length. Wide-azimuth seismic explorationand three-dimensional seismic surveying are powerful toolsfor imaging deep-sea methane plumes.

From Fig. 6, we observe that the event just under the bub-ble plumes is very weak and almost invisible. This is becausethe reflecting wave from the interface (just below the bubbleplumes) is scattered highly by the bubble when it propagatesforward and downward, so that it is nearly impossible to re-cord a wave field from this interface. Therefore, we propose a

Fig. 6 a The reverse-time migration section of 1∼5∼1 % backgroundmethane content. b The reverse-time migration section of 5∼10∼5 %background methane content. c The reverse-time migration section of

10∼15∼10% background methane content. d The reverse-time migrationsection of 15∼20∼15 % background methane content. e The reverse-timemigration section of 20∼25∼20 % background methane content

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new application of seismic section to identify bubble plumesin actual seismic exploration. The reflection amplitude of theseafloor is weaker at where bubble plumes exist than wherethere are not bubble plumes. Hence, we can pick the maximalamplitude value along the seafloor from the migration sectionto identify the location of the amplitude minimum; this posi-tion is where bubble plumes may exist.

Attribute analysis

After migrating the shot gathers, it is necessary to furtheranalyse the relationship between the seismic response andthe methane gas content. The target of this attribute analysisis to build such a relationship so that the methane gas contentcan be determined from actual seismic data.

Seismic attribute analysis technology has been widely usedin stratigraphic and lithological interpretation, reservoir eval-uation, reservoir characterization and reservoir fluid dynamicdetection. It plays an increasingly important role in oil and gasexploration and development. There are almost 200 seismicattributes that have been used in seismic exploration. Brown(1996), Taner et al. (1979) and Chen and Sidney (1997) havestudied these classifications in detail. According to their clas-sification, we use amplitude class attributes, frequency classattributes and phase class attributes in our analysis of the char-acteristics of methane plumes.

Generally, the seismic wave is regarded as an analyticalsignal (Taner et al. 1979). It can be defined as

x tð Þ ¼ f tð Þ þ ih tð Þ ð7Þwhere f(t) represents a seismic trace as a function of time t andh(t) is the Hilbert transform of the seismic trace f(t). The con-cept of the analytical signal is a foundation of attribute calcu-lation. The seismic attribute data from three different depthranges, 120∼130, 200∼210 and 290∼300 m, are extracted tostudy whether the variation between attribute parameters andmethane gas content is consistent at various depths. Seismicattributes are imperative properties in the study of seismicwave dynamics. These attributes can be employed to quanti-tatively analyse how the seismic response varies with methanegas content.

Amplitude class attributes analysis

In this section, various attributes involving the reflection am-plitude are listed to quantitatively analyse the seismic responseas a function of methane gas content. The absolute amplitudeattribute, reflection strength attribute, root mean square ampli-tude attribute and power attribute are the major factors thatallow zones of large acoustic impedance changes to becomemore visible and so are effective tools for identifying bright

and dim spots. The arc length attribute is defined as the seis-mic waveform length; it mainly manifests the changes in am-plitude and frequency, which may mirror other facies orseismic wave attenuation characteristics. The perigram at-tribute is the result after the low-frequency component ofthe reflection eliminated. This attribute therefore high-lights the locations of energy maxima in the seismic pro-file. The perigram multiplied by the cosine of the phaseyields another useful complex trace, the perigram multiplyby cosine of phase. When the value of the perigram isgreater than zero, this attribute is equal to the perigrammultiplied by the cosine of phase, or the value of thisattribute is zero. This attribute is helpful because it em-phasizes high-amplitude, continuous events. The differen-tiation and integration attributes are opposing attributes.Simply speaking, the differentiation attribute is the resultof a difference operation applied to the seismic data; itseffect is to magnify the high-frequency component of theseismic profile and to reflect detailed information aboutthe structure. The antithesis of the differentiation attributeis the integration attribute, which runs a sum operation onthe seismic data. Its effect is to present a high-frequencyestimation of acoustic impedance.

The quadrature trace attribute is based on a Hilbert trans-form of the seismic trace. It is given by

h tð Þ ¼ 1

πt* f tð Þ ð8Þ

The actual seismic trace indicates the kinetic energy of theparticle, while the quadrature trace indicates the potential en-ergy of the particle. Because the quadrature trace is 90° out ofphase from the seismic trace data, it provides a new viewpointfrom which to observe the seismic data, rather thanuncovering new information; however, this difference in per-spective can highlight certain features that are hidden in theseismic trace. The relationship between these amplitude classattributes and the methane gas content are shown in Fig. 7.

The curves relating the amplitude class attributes to themethane gas content in Fig. 7 show that the values of theamplitude class attributes all increase with increasingmethane gas content at the three depth ranges; in otherwords, those attributes are mostly directly proportionalto methane gas content. Furthermore, the red line inFig. 7 has the largest value, the blue line has the secondlargest value and the black line has the smallest value.Those three lines correspond to three different gas con-tents at three different depth ranges, which suggest thatthe attribute values increase more when the contentchanges in the longitudinal direction. This phenomenoncan be explained by scattering wave theory. Where thebubble exits in the seawater, the impedance differencebetween gas and seawater occurs, which scatters the wave

Arab J Geosci (2015) 8:9089–9100 9095

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generated on the bubble. The scattering wave strengthincreases with increasing methane content. Figure 7 sug-gests that a positive linear relationship between each at-tribute and methane gas content exists, which demon-strates that amplitude information is a clear, distinct anddirect response to methane gas content.

We now discuss the application of the relationship betweenthese various attributes and methane gas content. The aim ofestablishing such relation is to inverse gas content in actualseismic migration section of bubble plumes in the future.Because inversing gas content through just one attributewould produce a potentially large error, we propose a multipleattribute technique. This could become a comprehensive anal-ysis tool for inversing gas content and could reduce uncer-tainties of methane concentrations in solution and thus gener-ate more reliable data products.

Frequency class attributes analysis

Frequency class attributes are usually related to the attenuationof a seismic wave field. Attenuation attributes are indispens-able attributes of seismic propagation; they can reveal infor-mation that is covered in amplitude class attributes and usuallyused as a powerful tool to detect gas or oil. Therefore, it isnecessary to study the relation between this type of attributeand gas content. Six frequency attributes are discussed in thissection. The most common attribute is the instantaneous fre-quency attribute, which is a good indicator of a chaotic reflec-tion zone such as a gas-bearing zone. It is often also used toestimate attenuation values such as the quality factor. Theinstantaneous bandwidth attribute was introduced by Barnes(1992) and is defined as the absolute value of the time rate ofchange of the natural logarithm of the instantaneous ampli-tude, divided by 2π. The instantaneous bandwidth attribute isused in quantifying amplitudes by their sharpness rather thantheir magnitude. Sharper amplitude changes give rise to great-er bandwidth, which causes greater attenuation. The dominantfrequency attribute is defined as the square root of the sum-mation of the squares of the instantaneous frequencies and theinstantaneous bandwidths. This attribute is sensitive to ab-sorption properties of the stratum and is used to indicatewhether the stratum contains hydrocarbons. The instantaneousquality factor attribute is directly applied to study the attenu-ation change and is a very important parameter to study theviscoelastic medium. The concept of response frequency, firstproposed by Bodine (1984), forms the signal analysis and is

applied in geophysical waveform analysis. This attribute isdefined as the instantaneous frequency value at the peak ofthe amplitude envelope. It has a similar function as the instan-taneous frequency and may be beneficial to study the frequen-cy absorption phenomenon. The energy half-time attribute isdescribed as the average time of the trace power relative to thecentre of the window. It is applied to quantitatively measurethe energy distribution in a given analytical window and mea-sures the average amplitude change within the window. Thelateral variation of energy half-time can be expressed by anamplitude anomaly caused by a change of lithology, fluidcontent etc. The relationship between these frequency classattributes and methane gas content is shown in Fig. 8.

In Fig. 8a, d, the frequency class attributes tend to decreasewith increasing methane gas content. This is because thescattered effect produced by the bubble increases with meth-ane gas content. This causes the high-frequency energy toattenuate considerably, which causes the instantaneous fre-quency and instantaneous quality factor to decrease substan-tially. For the same reason, the value of the instantaneousbandwidth and dominant frequency increase with methanegas content in Fig. 8b, c. The response frequency (Fig. 8e)and energy half-time (Fig. 8f) do not show a good correlationwith methane gas content. A puzzling observation is that thered line in Fig. 8 is between the blue line and the black line;therefore, it appears that the variation of frequency class attri-butes as a function of methane gas content is less clear in thedepth domain.

Comparison of Figs. 7 and 8 shows that the frequency classattributes apparently do not correlate to gas content as well asthe amplitude class attributes do. Some frequency attributesdo not even show any clear relationship with gas content.Based on the complexity of the relationship between changesin frequency class attributes and gas content, we suggest thatsome frequency attributes, such as the instantaneous band-width attribute and the instantaneous quality factor attribute,can be used as optional tools to inverse gas content. A bubblein water does not resemble the porous medium in rock; thereare obvious hardness differences between rock particles andporous fluids that would affect energy attenuation as the wavepropagates through the porous medium. Supposedly, that canbe the reason why the attenuation phenomenon of bubbleplumes is not apparently.

Phase class attributes analysis

Phase class attributes as one of three types of attributeanalysis tools. We investigate whether there is a relationbetween these attributes and gas content. Here, we listthree phase class attributes as typical examples. The in-stantaneous phase attribute is independent of the ampli-tude and shows continuity or discontinuity of events. Theresponse of this phase attribute has a similar definition as

�Fig. 7 The relationship curves between amplitude class attributes andmethane gas content. a Absolute amplitude attribute. b Reflectionstrength attribute. c RMS amplitude attribute. d Arc length attribute. ePerigram attribute. f Perigram cosine of phase attribute. g Differentiationattribute. h Integration attribute. i Power attribute. j Quadrature traceattribute

Arab J Geosci (2015) 8:9089–9100 9097

that of response frequency. It is the instantaneous phaseattribute value at the peak of an amplitude envelope and isthe function that detects phase changes associated withlateral fluid content or lithological changes. The cosineof phase attribute is smoother than the instantaneousphase (which has discontinuities) and is primarily usefulfor seismic stratigraphic sequences and character recogni-tion. The relationship between phase class attributes andmethane gas content is shown in Fig. 9.

Figure 9 shows that the relationship between phaseclass attributes and methane gas content is various andsometimes shows chaotic behaviour. This suggests thatthe phase class attributes do not directly relate to meth-ane gas content. Considering the role that phase classattributes play in seismic exploration, which is to showwhether the event is continuous, we believe that phaseclass attributes are not useful in inversing methane gascontent. In this case, a methane bubble exists in

Fig. 8 The relationship between frequency class attributes and methane gas content. a Instantaneous frequency attribute. b Instantaneous bandwidthattribute. c Dominant frequency attribute. d Instantaneous quality factor attribute. e Response frequency attribute. f Energy half-time attribute

9098 Arab J Geosci (2015) 8:9089–9100

seawater as a pot, but phase class attributes analysis isbest suited to a continuous stratigraphic horizon.Therefore, phase class attributes analysis is unfit touse here. For the same reason, phase class attributesof seismic sections are not well adapted to identify theposition of bubbles.

Conclusions

Based on the analysis of the physical mechanism andmicroscopic structure of methane plume, effective medi-um theory is used to construct a methane plume model.This method is more suitable for simulating methaneplumes than previous research based on stochastic medi-um theory. To obtain true amplitude migration informa-tion about methane plumes, reverse-time migration wasused to process the seismic data. We applied five methanegas content models to study the different seismic responseto various gas concentrations. The migration result obtain-ed is very satisfactory. Quantitative analyses of amplitude,

frequency and phase class attributes point out that theamplitude class attributes are linearly proportional tomethane gas content; this relationship can be used to in-verse methane gas content. In future research, we willcollect seismic data that image the bubble plumes anduse the relationships between amplitude class attributesand methane gas content to estimate the methane gas con-tent. Multiple attribute inversion will be included to im-prove accuracy. Our work also reveals that some frequen-cy class attributes, such as the instantaneous frequencyand the instantaneous quality factor attributes, can be usedto study attenuation near bubble plumes. Although thefrequency class attributes do not always exhibit a directrelationship with gas content, some of them can potential-ly be exploited to inverse gas content. Therefore, we pro-pose that amplitude attribute should be the first optionused to inverse gas content and some frequency attributesare an alternative. Because of the physical meaning of thephase attributes, the relationships between phase class at-tributes and methane gas content is confusion; the appli-cation of phase class attributes is not well suited to

Fig. 9 The relationship between phase class attributes and methane gas content. a Instantaneous phase attribute. bResponse phase attribute. cCosine ofphase attribute

Arab J Geosci (2015) 8:9089–9100 9099

inverse methane gas content and is also inappropriate toidentify the position of bubble plumes.

Acknowledgments The authors thank Professor XueWei Liu of ChinaUniversity of Geosciences, Beijing, for providing the seismic migrationsection and the bubble plumes migration section of the Shenhu area in theSouth China Sea. This work is financially supported by the NationalNatural Science Fund (grant no. 41306050 and no. 41104073) and theNational High-Technology Research and Development Program (863Program.2012AA09A404). The authors would like to thank the anony-mous reviewers for their helpful comments which have improved thequality of the paper.

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