Frequency Enhancements for Visualizing 3D Seismic Data

Cheng-Kai Chen∗ Carlos Correa†

Department of Computer Science

University of California at Davis

Kwan-Liu Ma‡

ABSTRACT

This application paper introduces a suite of enhancement tech-niques for visualizing seismic data. These techniques provide abetter understanding of the underlying propagation process in thecomplex time-dependent seismic data. Traditional techniques usingthe accumulated displacement as a scalar or vector field for volumerendering fail to capture the dynamic frequency variations, whichis essential for seismic study. We show that using multibandsignalfilters to separate frequency components of the data can highlightdifferent frequency bands explicitly in visualization. The end re-sult is a combination of different displacements, such as drift andshaking along the horizontal and vertical directions whichare per-turbing the accumulated drifts. We have implemented a GPU-basedraycasting renderer to handle unstructured meshes. We alsoemploydeformable textures for effectively composing multiple frequencycomponents. Our analysis and visualization techniques provide anew way for seismic scientists to study their data.

Index Terms: I.3.3 [Computer Graphics]: Picture/ImageGeneration—Viewing algorithms; I.3.7 [Computer Graphics]:Three-Dimensional Graphics and Realism—Color, shading, shad-owing, and texture; I.4.3 [Image Processing and Computer Vision]:Enhancement—Filtering; J.2 [Physical Sciences and Engineering]:Earth and Atmospheric Sciences

1 INTRODUCTION

As the simulation and exploration of seismic data becomes a majorpart of the work for many seismic scientists, visualizationcontin-ues to play an important role in data analysis and interpretation. Inthe past few years, real-time volume rendering has become possi-ble and has been widely utilized in scientific visualizationas theprogrammable graphics process unit (GPU) continues to advance.With the help of an interactive interpretation seismic system, ge-ological study and prediction can be made on the seismic data.More precise predictions of natural disasters such as earthquakescan be obtained by computer-aided visual analysis. Although thereare many interactive volume rendering toolkits available for seismicdata visualization, most of them only support rendering thedata ofall frequencies as a whole. This treatment, however, does not pro-vide insights into the unique aspect of dynamic frequency variationsof 3D seismic data, which is critical for analyzing and understand-ing seismic data. Surprisingly, little work has been done toimprovethis situation.

In our study, the seismic data are available as a continuous func-tion sampled at regular or irregular mesh points. Since the datausually consist of low and high frequencies components includingnoise, obtaining the essential frequency-domain featuresfrom thedata becomes an important aspect of data analysis and visualization.We employ frequency-time (F-T) analysis, a general and effective

∗e-mail: ckchen@ucdavis.edu†e-mail: correac@cs.ucdavis.edu‡e-mail: ma@cs.ucdavis.edu

technique for studying seismic data. F-T analysis includesdelin-eation of sequence interface and determination of seismic sequencecycles. In F-T analysis, spatial-temporal data are first transformedinto the frequency domain. Then, for the frequency componentat each sample point, the corresponding data are separated usingmultiband filters, such as low-pass or high-pass filters. Low-passfilters remove the component above the specific frequency, whilehigh-pass filters keep the component above the specific frequency.After applying F-T analysis, we can obtain the interior structure ofseismic data in a meaningful way by studying the F-T structure.

Once the data are separated into different frequency components,visualizing seismic data turns to be a multivariate data visualiza-tion problem. In this paper, we highlight separate frequency bandsin the visualization so that the scientists can better observe the in-trinsic nature of seismic propagation. Mixing different frequencybands together without visual cluttering and ambiguity is achievedthrough several enhancement techniques including unsharpmask-ing and deformable textures. For example, when each isolated bandis rendered using a different illustrative style, the observers can in-tuitively identify different frequency bands and clearly analyze theirrelationships over time. To our knowledge, we are the first touti-lize frequency-enhanced visualization techniques for effective un-derstanding of the seismic data.

This paper is structured as follows. In the next section, we dis-cuss related work. In Section 3, an overview of the proposed ren-dering process is given. The implementations of frequency analysisand seismic data visualization will also be discussed in details. Sev-eral enhanced techniques will also be explained in this section. InSection 4, the proposed method applied on earthquake seismic datavisualization is demonstrated. The paper concludes in Section 5 bygiving a short overview of the presented concepts.

2 RELATED WORK

In this section, we first review work in the field of seismic datavisualization. Then, we discuss related work dealing with time-varying and frequency data analysis and visualization. Finally, wereview the use of deformation, color, and texture in visualization.

2.1 Seismic Data Visualization

There have been extensive research efforts in the area of seismicdata visualization, and a large collection of major developmentswere captured in several surveys. A pioneer work was presentedby Wolfe et al. [19]. Since the data they studied contain a con-siderable amount of ringing, it is necessary to remove the noise andshape the pulse waveform. The demonstrated interactive 3D visual-ization approach interprets seismic data with a volumetricscheme,and filters out the noisy part by using deconvolution filters.Hence,the users get more clear pictures about the underground structuresin seismic data.

Castanie et al. [1] described a high quality volume renderingalgorithm to visualize 3D seismic data based with pre-integratedtransfer functions. Chourasia et al. [3] proposed an iterative re-finement of the visualization incorporating feedback from scien-tists. Combined with the existing visualization techniques, suchas volumetric and topographic deformations, the proposed systemcreates more meaningful visual results from the data sets. Patel et

al. [10] introduced techniques for visualizing interpreted and unin-terpreted seismic data. The non-photorealistic renderingtechniquewas adopted to render the interpreted data as geological illustra-tions, while the uninterpreted data was rendered in color-coded vol-ume. They also discussed how to combine the two representationstogether so that the users can control the balance between the twovisualization styles accordingly. The concept of focus+context vi-sualization metaphors was presented by Ropinski et al. [11]whereinteractive exploration of volumetric subsurface data is supported.By using specialized 3D interaction metaphors, the user is able toswitch between different lens shapes as well as visual representa-tions, such as emphasizing or removing arbitrary parts of a data set.

To visualize massive data from large-scale earthquake simula-tions, Ma et al. [7] presented a parallel adaptive renderingalgorithmfor visualizing time-varying unstructured volume data. Their goalwas to come up with a scalable, high-fidelity visualization solutionwhich allows scientists to explore in the temporal, spatial, and vi-sualization domain of their data. Yu et al. [21] proposed a parallelvisualization pipeline for studying the terascale earthquake simu-lation. Their solution is based on a parallel adaptive rendering al-gorithm coupled with a new parallel I/O strategy which effectivelyreduces interframe delay by dedicating some processors to I/O andpreprocessing tasks.

2.2 Time-Varying and Frequency Data Visualization

Fang et al. [6] proposed a method to visualize and explore time-varying volumetric medical images based on the temporal charac-teristics of the data. The basic idea is to consider a time-varyingdata set as a 3D array where each voxel contains a time-activitycurve (TAC). Matching TACs based on a given template TAC essen-tially classifies voxels with similar temporal behaviors. Our workis similar to this work in the sense that the F-T analysis operates oneach individual TAC.

In frequency data analysis in visualization, Neumann et al.[9]presented a feature-preserving volume filtering method. The ba-sic idea is to minimize a three components global error functionpenalizing the density and gradient errors and the curvature of theunknown filtered function. The optimization problem leads to alarge linear equation and can be efficiently solved in frequency do-main using the fast Fourier transformation (FFT). Wu et al. [20]introduced the 3D F-T analysis of seismic profile using the wavelettransform, which provides an effective way for the subsequent anal-ysis. Erlebacher et al. [5] also studied a wavelet toolkit for visual-ization and analysis of large earthquake data sets.

2.3 Deformation, Texture, and Color in Visualization

Chen et al. [2] introduced the concept ofspatial transfer functionsas a unified approach to volume modeling and animation. A spatialtransfer function is a function that defines the geometricaltrans-formation of a scalar field in space, and is a generalization andabstraction of a variety of deformation methods. They proposedmethods for modeling and realizing spatial transfer functions, in-cluding simple procedural functions, operational decomposition ofcomplex functions, large-scale domain decomposition and tempo-ral spatial transfer functions.

Effective utilization of color and texture is the main themeofseveral research efforts. Sigfridsson et al. [13] combinedscalarvolume rendering with glyphs. They presented a method for visu-alizing data sets containing tensors in 3D using a hybrid techniquewhich integrates direct volume rendering with glyph-basedrender-ing. Interrante et al. [12, 15] described new strategies foreffec-tive utilization of colors and textures to represent multivariate data.They provided a comprehensive overview of strategies to representmultiple values at a single spatial location, and presenteda newtechnique for automatically interweaving multiple colorsthroughthe structure of an acquired texture pattern. Wang et al. [17] de-

scribed a knowledge-based system that captures established colordesign rules into a comprehensive interactive framework, aiming toaid users in their selections of colors for scene objects by incor-porating individual preferences, importance functions, and overallscene composition.

3 SEISMIC DATA ANALYSIS

In recent years, seismic analysis have been widely applied to thewhole range, from exploration to development and exploitation, ofmany problems, such as reservoir characterization, enhanced oil re-covery strategies, and earthquake investigation. The interpretationof seismic data involves not only the concepts of geology, seismol-ogy, and signal processing, but also various techniques in computergraphics and visualization.

In general, seismic data are a series of data chunks and are avail-able as a continuous function sampled at regular or irregular meshpoints. Such data are acquired directly from simulation results, orindirectly from wave propagation such as earthquake shockwavesthrough the subsurface. The data contain displacements, coher-ent and incoherent noise signals as well. The displacement ofeach node is a multidimensional vector representing the movementcaused by shockwaves under the surface, such as shaking or drift.

F-T analysis is commonly used to separate the data with differentfrequency components, and becomes an important examining tech-nique to interpret the seismic data. F-T analysis is a technique formanipulating signals with frequency components which are varyingin time. It includes delineation of sequence interface and determi-nation of seismic sequence cycles. All the F-T methods map thesequence of data into the frequency domain first, and then performthe analysis.

There exist many F-T methods for seismic interpretation; how-ever, all of them have different properties. In this paper, we usethe fourth order Butterworth filter to separate the different band-pass data. The Butterworth filter [14] is one of the most commonlyused digital filters in motion analysis. It is designed to flatten afrequency response in the passband. Compared to other filters, theButterworth filter rolls off more slowly around the cutoff frequency,but shows no ripples which is desirable for our analysis. A typicalButterworth filter is the low-pass filter, and it can also be modifiedto be used as a high-pass filter.

A low-pass filter passes relatively low frequency components inthe signal and stops the high frequency components. In otherwords,the frequency components higher than the cutoff frequency will bedropped by a low-pass filter. The behavior of a filter can be summa-rized by the so-calledfrequency response function. The followingequation gives the frequency response function of the Butterworthfilter:

|Hc( jω)|2 =1

1+( jω/ jωc)2N , (1)

where j =√−1, ω = frequency (rad/s),ωc = cutoff frequency

(rad/s), andN = the order of the filter.

3.1 Earthquake Dataset

The seismic data used in this work were generated by earth-quake simulation of the Humboldt Bay Middle Channel (HBMC)bridge [23] in the Department of Structural Engineering at the Uni-versity of California, San Diego. The simulation dataset consists ofa finite element (FE) model created with the software frameworkOpenSees (Open System for Earthquake Engineering Simulation)[8]. The simulation dataset consists of a finite element model of theriver channel and banks, represented as a hexahedral mesh. The el-ements discretized an effective-stress, cyclic-plasticity constitutive

model, able to represent layers of soil of different materials and liq-uefaction properties. The simulation then obtains the displacementsat each node by solving the FE system:

MU+

∫Ω

BTσ ′dΩ+Qp− fS = 0 (2)

QT U+Sp+Hp − fp = 0 (3)

whereM is the mass matrix,U is the displacement vector,B thestrain-displacement matrix,σ ′ the effective stress vector (deter-mined by the model),Q the discrete gradient operator,p the porepressure vector,H the permeability matrix,S the compressibilitymatrix andfs andfp the body forces and prescribed boundary con-ditions, respectively. The first equation models the motionof thesystem, while the second represents mass conservation constraints.The HBMC bridge seismic data contains complex incident wavemotions, including drift, or permanent components, and shakingmotions.

In addition, the dataset provides a 3D structure of the HBMCbridge (including the superstructure, piers, and supporting piles).The displacements are obtained using a 2D nonlinear mesh forthebridge piers and linear elastic beam-column elements for the super-structure and piles. The mesh and a cross-section view of thebridgeare shown in Figure 1.

For efficient visualization, we converted the hexahedral elementsin the soil to a tetrahedral mesh. To preserve the interpolation andavoid introducing artifacts due to the splitting operation, we usebarycentric interpolation of the displacement vectors foreach ele-ment.

Eureka Channel(South-East)

Samoa Channel(North-West)

X

Y

Z

Drift motion(Permanent deformation)

Shaking motion(Cyclic component)

Figure 1: A 3D finite element structure, and a cross-section viewalong X-Z direction for HBMC bridge. This simulation structure in-cludes superstructure, piers, and supporting piles. The cross-sectionview also illustrates that there exist different motions, such as driftand shaking, at different frequency bands under the surface.

3.2 Seismic Displacement ComponentsThe earthquake dataset, similar to other seismic data, contains3D displacements that are the product of two different compo-nents. The drift is the permanent deformation component usuallyin low frequency phase, and is the product of slumping and set-tlement/heave of the system. The shaking is the cyclic componentof seismic displacements existing in high frequency band, seen asa back and forth movement. At the beginning of the simulation,P-waves arrive early and correspond to the initial displacements.

Once the cyclic components become apparent, these correspond toS-waves (shear waves). The dynamic shaking motions are super-posed on accumulated drifting values, and therefore it is difficult todistinguish the impact from different motions.

In order to extract these components and provide a better under-standing of the simulation, we use high-pass and low-pass filtersalong the temporal dimension, where the suggested cutoff frequen-cies from scientists are 0.3 and 0.1, for extracting the high-pass andlow-pass filtered data, respectively. To provide an intuitive visual-ization of the simulation, we perform the analysis on the displace-ment magnitude, since most of the permanent components occurin the vertical direction, while the cyclic components occur on thehorizontal directions (parallel to the ground). Later on, we showhow to incorporate direction on the visualization.

4 MULTI-BAND ENHANCED VISUALIZATION

In this paper, we study the enhancement of direct volume renderingfor representing multiple bands of a single scalar or vectorfield. Forthe case of seismic data, we have 3D displacements. Mapping theseto color and opacities is a difficult task. One alternative isto mapthe magnitude of the vector field to color and opacities via one di-mensional transfer functions. An example is shown in Figure2 (a).In this case, “cool” colors represent low magnitude while “warm”colors represent high magnitude displacements. Figure 3 shows thecolormap and data value ranges. Although direction is not encoded,it provides important cues about the distribution of magnitude andchange over time. For seismic data, however, the displacementis the product of two main components, one being the permanentcomponent due to settlement or slumping, and the “shaking” com-ponent, which measures the actual ground movement due to seis-mic activity. In Figure 2 (b) and (c) we show the magnitude of thepermanent and cyclic components for the same two frames. Whencompared to those in Figure 2 (a), it becomes evident that it is notpossible to extract the two components easily. This happensas itbecomes increasingly difficult to distinguish small movements asthe permanent component grows.

Instead, we propose a novel approach that displays the two com-ponents of the displacement as separate entities. Therefore, ourproblem becomes that of visualizing time varying multi-variantthree dimensional data. An example is shown in Figure 2 (d). No-tice how the different components can be easily identified, and nowit is possible to quantify the amount of shaking (high-frequencycomponent), according to the color map. For seismic data, high-frequency components become increasingly small compared to thepermanent components as the shaking dissipates. For this reason,we present a number of methods to enhance a component of inter-est.

We present a number of methods, inspired by both image-processing operators and volume rendering techniques, to enhancedifferent components in a multi-band volume, namely optical oper-ations, temporal unsharp masking and deformation.

4.1 Temporal Unsharp Masking

Unsharp masking is an image processing technique that increasesthe contrast of edges in 2D images. It works by computing an un-sharp mask of a signal, usually by subtracting the signal with a low-pass filtered version of the signal, and then adding a scaled versionof this unsharp masking to the original signal. It has the effect ofenhancing the high-frequency components of the image, which cor-respond to the edges, making it look sharper. In the case of seismicdata, we derive the components as frequencies in the time dimen-sion, therefore we call this techniquetemporal unsharp masking.Let us define a scalar fieldS(x,t) computed as the magnitude of thedisplacement, andSL(x,t) andSH (x,t) the low-pass and high-passfiltered scalar fields, respectively. The newly enhanced field S′(x,t)

(a) Original (b) Permanent (low band) (c) Cyclic (high band) (d) Combined visualization

Figure 2: Volume visualization for the HBMC bridge for time steps t = 380,480. (a) shows the original view of unfiltered seismic data. (b) and(c) show the low-pass permanent deformation and high-pass cyclic components showing with warm and cool colors, respectively. (d) shows thecombined visualization for both low- and high-pass data. Now the different components can be easily identified.

Figure 3: Color map used for the images in this paper and range ofvalues. The high-frequency components are given more granularitythan the permanent component .

can be computed as:

S′(x,t) = S(x,t)+λ (S(x,t)−S(x,t)⋆G(t)) (4)

≈ SL(x,t)+(1+λ )SH (x,t) (5)

whereG(t) is a low pass filter in the time dimension, which is con-volved with the original signal (f ⋆g denotes convolution). The pa-rameterλ indicates the degree of enhancement. Figure 4 shows theresult of applying unsharp masking for three consecutive frames.Note the appearance of regions of higher magnitude due to thead-dition of high frequency magnitude. These appear in the images aspurple-ish regions. Because the enhancement occurs beforeclassi-fication, it may be difficult to extract the actual magnitudesof thelow and high frequency components, and it becomes increasinglydifficult as the permanent component overcomes the cyclic compo-nents. For this reason, we turn to optical operations, as described inthe following section.

4.2 Optical EnhancementThis method combines the different components and performsen-hancement in the optical domain, i.e, after classification of the fil-tered data. In general, classification is a mapping from a scalar field,in our case magnitude, to colorC and opacityα. If we defer en-hancement after classification, for the low and high components weobtain colors and opacitiesCL,αL andCH ,αH , respectively. There-fore, enhancement can be defined as a combination of these. The

combination can be additive (in RGB, HSV or CIELAB space) orcan be obtained with the over operator, used for compositingcolorsin a front-to-back fashion. The latter simulates the effectof hav-ing two scalar fields intertwined together in a single volume. Forexample, our previous enhancement can be performed optically toachievepost-classification temporal unsharp masking. The result-ing color and opacities of a sample are:

C = CL ⊕CH ⊕λCH (6)

α = αL ⊕αH ⊕λαH (7)

where⊕ represents an optical operator. In our examples, we use theover operator used for front-to-back volume rendering. This resem-bles the composition of different samples equally spaces compris-ing each of the components (i.e., low, high and enhancement). Toachieve a comparable per-sample intensity to those images with noenhancement, we make sure that the sample opacity is modulatedto accommodate the extra attenuation per sample. That is, wemod-ulate the sample opacity to simulate the composition of two extrasamples per sample interval.

Figure 5 shows the result of combining the two components inthe optical domain. The superposition of “cool” and “warm” col-ors indicates the overlapping of the two displacement components,i.e., drift and shaking. We can see that, although the drift accu-mulates, the shaking remains fixed within an interval (blue color).Figure 6 shows an example of postclassification unsharp maskingwith λ = 1.2. When compared to the result in Figure 5, we cannow clearly see the distribution of shaking, especially on the firsttimestep. For timestept = 580, the enhancement helps identifymore isosurfaces in the shaking component. Compare for exam-ple the difference with the pre-classification enhancementin Figure4. Similar structures can be found (for example the waving motionin t = 580), but the presence of the two intervals makes it possi-ble to identify and quantify the regions where cyclic componentscontribute to the total displacement.

4.3 Deformable Textures

In the above techniques, we mapped the displacement magnitude tocolor and opacity and used optical operations to combine thehighand low frequency components. However, due to the additive natureof color in the composition process, it becomes increasingly diffi-cult to visualize patterns of interest as both components contributeto occlusion. As an alternative, we propose the use of 3D texturesto modulate the opacity of one of the components. The texturecanbe considered as a scalar fieldT : R3 7→ R, where each sample indi-cates a density value. These can be obtained using texturingmech-anisms such as Perlin noise or procedurally defined primitives, suchas spheres, tubes and thin plates. The advantage of these textures isthat it is now possible to control the degree of occlusion of one ofthe components so that the other component is visible without theadditive operation of colors and opacities. A similar idea has beenexploited in the form of screen-door transparency [16].

There is an issue with simply using texture to modulate opacityand it is that it appears static while the isosurfaces of interest movewithin the textured space. This effect was rather confusingand oflittle help. Instead, we want to move the texture in such a waythatit “follows” the vector field. Therefore, we incorporatedeformabletextures, where the opacity is mapped according to the 3D patternthat would be displayed if the original texture were deformed by thevector field. We can incorporate this directly in the rendering pro-cess by warping the coordinates of the 3D texture with an inversedisplacement. In our case, we use deformable textures to modulatethe opacity of the high frequency components. The opacity ofthehigh frequency component is found using the following expression:

αH (x) = T (x−D(x,t)) (8)

whereT is the scalar field representing the texture andD is thevector field, which varies over time. When combined with a lowfrequency component, the result achieves a better mix of thetwocomponents that minimizes inter-component occlusion but providesa lot of information of the vector field. In our experiments, we triedwith several textures, including semi-transparent spheres and tubu-lar structures. Since most of the high frequency movement occursin the horizontal planes (while vertical movement is associated withthe permanent displacements), a horizontal texture is appropriate.

Figure 8 shows an example of using a texture pattern of a tubealong one of the horizontal directions. Since the shaking often oc-curs on these planes, the deformable texture helps us identify theback and forth motion of the cyclic waves. In addition, the hor-izontal stripes are reminiscent of the horizontal layers inthe soil,facilitating the understanding to geologists.

Depending on the density of the texture, the cyclic componentmay occlude the permanent component of the displacement. InFig-ure 9 we show the result of applying a texture pattern of a sphere,which gives more visibility to the drift component. This textureemulates the rendering of semi-transparent probes in the soil thatmove with the displacement. Since each sphere appears deformed,this method provides insight on the local direction of displacement.To fully appreciate the effect of the deformable textures, please seethe accompanying video.

5 IMPLEMENTATION DETAILS

To test these techniques, we implemented a GPU-based rendererof unstructured meshes. To obtain high-quality rendering,we useraycasting following a similar implementation to that proposed byWeiler et al. [18]. We use 2D textures to encode the mesh ver-tices, the corresponding scalar values and connectivity informationto be able to march through the tetrahedral mesh during rendering.Unlike the original implementation by Weiler et al., we encode in-dexed vertices rather than unrolling the mesh. This is necessary

as we need to store several scalar fields for a single vertice,cor-responding to the different components of the displacementmag-nitude. This method also results in a more compact encoding thatallows us to store more timesteps in GPU memory. In our imple-mentation, the different enhancement techniques are processed dur-ing rendering, which allows us to change their parameter on-the-fly.The addition of the different techniques make the renderingprocessslower than simple volume rendering due to extra texture fetches.In addition, barycentric interpolation within the tetrahedron maybe costly when we require to interpolate additional quantities (e.g.,high-frequency component, displacements). For the case ofde-formable textures, we decided to define it procedurally rather thanadding an extra fetch, since for this case pixel processing power isin general faster than texture fetches. Table 1 summarizes the extra

Technique Extra texture fetchesand interpolations

Total AverageCost(fps)

Unsharp mask-ing

Fetch high-pass 4 + nti 16.66

Post-classificationunsharp masking

Fetch high-pass +classify high-pass

4 + n(ti + t f ) 14.3

Displacement Fetch high-pass +deform coordinate +classify high-pass

4 + n(ti +t f +tb) 5.0

Table 1: Cost of enhancement techniques in terms of extra tex-ture fetches and interpolation operations and overall performance inframes per second (volume rendering without lighting). ti refers tothe time it takes to perform scalar value interpolation, t f is the timeof a texture fetch and tb is the cost of barycentric interpolation for 3Ddisplacements.

texture fetches and interpolations required for the introduction ofenhancement techniques.ti refers to the time it takes to performscalar value interpolation,t f is the time of a texture fetch andtb isthe cost of barycentric interpolation for 3D displacements. Scalarvalue interpolation can be efficiently implemented using linear ap-proximation of the cell gradient. Applying the same technique toapproximate the barycentric interpolation of displacements wouldcost roughly three times as much. As a baseline comparison, therendering algorithm traverses the tetrahedral mesh element by ele-ment. For each tetrahedron, the four scalar values are fetched froma texture and the scalar field is sampled at uniform sample pointswithin the cell (to obtain high quality rendering). Assuming thatthe algorithm traversesn samples in a tetrahedron, the number ofoperations in a traditional unstructured mesh rendererper tetrahe-dron is 4+ n(ti + t f ), where the first 4 refer to the fetching of thescalar values and each sample requires a texture fetch and anin-terpolation. We run our system on an Intel Core 2 Duo with annVidia GeForce 280 card. At high quality resolution, our systemperforms at about 20 and 6.66 fps without and with lighting, re-spectively, in a 512×512 image size. To provide interactive rates,we provide a low-quality mode that runs at much higher speeds. Wenotice that optical operators do not compromise performance con-siderably, while deformation is costlier. Most of the cost is due tothe barycentric interpolation of displacements. The search for moreefficient encoding and interpolation mechanisms are currently be-ing sought.

6 CONCLUSIONS

In this paper, we have presented a number of techniques for en-hancing frequencies of 3D displacement data. Some of these tech-niques operate in the data domain while others operate in theopticaldomain after classification. Although enhancement of frequenciescan be addressed from a signal processing approach using sharp-ening filters, their visualization was not effective at conveying the

(a) t = 380 (b)t = 480 (c)t = 580

Figure 4: Volume visualizations for the HBMC bridge with applying temporal unsharp masking for time steps t = 380,480,580. One of the problemswith this approach is that the unsharp masking exaggerates the magnitude of the original displacement, and it is difficult to extract the actualshaking from the low frequency component.

(a) t = 380 (b)t = 480 (c)t = 580

Figure 5: The HBMC Bridge volume visualization with combinations of low- and high-pass components in optical domain for three consecutivetime steps t = 380,480,580. The superposition of “cool” and “warm” colors indicate the overlapping of the two displacement components, i.e.,drift and shaking. Hence, although the drift accumulates, the shaking remains fixed within an interval (blue color).

(a) t = 380 (b)t = 480 (c)t = 580

Figure 6: Examples of post-classification unsharp masking with λ = 1.2 for three time steps where t = 380,480,580. Compared to Figure 5,we can now clearly see the distribution of shaking, especially on the first timestep. For timestep t = 580, the enhancement helps identify moreisosurfaces in the shaking component.

n samples

1v

v2

v3

v4

SCALAR TEXTURE TRANSFER FUNCTION

Figure 7: Texture Fetches in a tetrahedral mesh renderer. For eachtetrahedron, we must get the four scalar values from the scalar tex-ture and for each sample within a tetrahedron we must fetch the colorand opacity from a transfer function. Enhancement operators onthe entire tetrahedra, such as getting the high-frequency componentdoes not affect much performance. Per-sample enhancement op-erators (post-classification or deformable textures) imply additionalfetches per-sample, which increases the cost.

relationships between the permanent and cyclic components. Webelieve that this is due to a fundamental perceptual and cognitiveproblem that prevents us from understanding the addition ofcol-ors (due to classification) as a metaphor for arithmetic addition. Incontrast, optical combination, which simulates the effectof inter-twining two sets of surfaces, seems to work better, since thecolorranges from the two components can be more easily discerned (e.g.,cool colors for high frequency and warm colors for low frequency).When these intervals overlap there may be problems, and carefuldesign of color maps will prove important. We will address theseissues in our future work. In our experiments, we found that high-lighting optically two components was useful, but highly dependenton the opacity transfer function. When the opacities of bothcom-ponents become high, they may occlude each other in a way thatit is not possible to discover their relationship anymore. The useof deformable textures solves this problem in an elegant manner.The particular choice of texture seems also important for effectivevisualization. In our case, horizontal textures prove effective sincethey are reminiscent of geological layers and thus have a physicalcounterpart. Spheres also emulate a series of deformable probes inthe ground and help see displacement along different directions.

With the ability to extract and enhance the different componentsof seismic data, we are providing unprecedented capabilities to sci-entists to understand the superposition of displacements in com-plex time-varying phenomena. We believe that these ideas can beextended to other domains, such as flow visualization, wherewereplace displacements with velocities. Although our techniques ex-tend to vector field data in general, they need to be adapted ac-cording to the nature of the data to create more meaningful decom-positions and enhancements. For example, textures may needtobe oriented in such a way that they capture the most predominantcomponent of the flow.

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Figure 8: Examples of applying deformable texture enhancement fortime steps t = 380,480,580. The deformable tubes along one of thehorizontal directions represent the corresponding cyclic components.It helps us identify the back and forth motion of the cyclic waves. Toappreciate more the effect of the deforming textures, please refer tothe accompanying video.

Figure 9: The texture is replaced with deformable spheres. Theyprovide more visibility to the drift motions and the shape of sphereshelps us identify the local direction of displacement. To appreciatemore the effect of the deforming textures, please refer to the accom-panying video.