High-Resolution Seismics Methods Applied to Till Covered Hard Rock Environments

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(146) v. List of Papers. This thesis is based on the following papers, which are referred to in the text by their Roman numerals: I. Björn Bergman, Christopher Juhlin and Hans Palm. (2002). Highresolution reflection seismic imaging of the upper crust at Laxemar, southeastern Sweden. Tectonophysics, 355:201213.. II. Björn Bergman, Ari Tryggvason and Christopher Juhlin. (2004). High-resolution seismic tomography incorporating static corrections applied to a till covered bedrock environment. Geophysics, 69(4):1082-1090.. III. Björn Bergman, Ari Tryggvason and Christopher Juhlin. Seismic tomography studies of cover thickness and near-surface bedrock velocities. Submitted to Geophysics, in revision.. IV. Björn Bergman, Christopher Juhlin and Ari Tryggvason. Shallow seismic imaging in hard rock environments: An example from the nuclear waste storage study site of Forsmark, Sweden. Manuscript.. Reprints were made with permission from the publishers.. Technical reports related to the material in the thesis but not included: • Reflektionseismiska studier inom Laxemarområdet. Bergman, B., Juhlin, C., and Palm. H. 2001. Swedish Nuclear Fuel and Waste Management Company (In Swedish). • Vertical seismic profiling and integration with reflection seismic studies at Laxemar, 2000. Juhlin, C., Bergman, B., Cosma, C., Keskinen, J., and Enescu, N. 2002. Swedish Nuclear Fuel and Waste Management Company, SKB TR-02-04. • Reflection seismic studies in the Forsmark area - stage 1. Juhlin, C., Bergman, B., and Palm, H. 2002. Swedish Nuclear Fuel and Waste.

(147) vi. Management Company, SKB R-02-43. • Oskarshamn site investigation: Reflection seismic studies on Ävrö,2003. Juhlin, C., Bergman, B., Palm, H., and Tryggvason, Ari. 2004. Swedish Nuclear Fuel and Waste Management Company, SKB P-04-52. • Estimate of bedrock topography using seismic tomography long the reflection seismic profiles in Forsmark. Bergman, B., Palm. H. and Juhlin, C. 2004. Swedish Nuclear Fuel and Waste Management Company, SKB P-04-99..

(148) CONTENTS. vii. Contents. 1 2. Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . High-resolution seismics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 The three-dimensional reality . . . . . . . . . . . . . . . . . . . . . 2.1.2 Locations of regions studied in this thesis . . . . . . . . . . . . 2.1.3 What can be imaged by seismic techniques? . . . . . . . . . . 2.2 Reflection seismics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Field parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Processing steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3 3D Interpretation of 2D data . . . . . . . . . . . . . . . . . . . . . . 2.3 Seismic tomography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Tomography inversions with source static corrections . . . 2.3.2 Source and receiver statics in seismic tomography . . . . . . 3 Summary of papers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Paper I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Paper II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Conlusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Paper III . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Conlusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Paper IV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.2 Conlusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Summary in Swedish . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 1 3 3 3 5 5 5 10 13 19 21 21 24 27 28 28 32 33 33 38 39 39 43 45 45 47 51 55 57 63.

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(150) 1. 1 Preface. This thesis focuses on imaging the crystalline crust from the upper few meters of the subsurface down to a few kilometers depth. The seismic tomography and reflection seismic methods have been applied, and refined, for conditions typically found in Sweden. The thesis is divided into a summary part and a collection of papers. The first part starts with this preface. Next follows chapter 2, with an introduction, section 2.1, containing a general description of the studied environments and the features that can be imaged using high-resolution seismic methods. Then follows two sections with a description of the utilized seismic methods; reflection seismics (section 2.2) and seismic tomography (section 2.3), focusing on the techniques that have been studied within the scope of this thesis. The papers upon which my thesis is built are summarized in chapter 3, and the thesis ends with some concluding remarks in chapther 4. In chapter 5, a brief summary of the thesis is given in Swedish. The second part of the thesis contains my papers, two reprints, one submitted manuscript under revision and one manuscript..

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(152) 3. 2 High-resolution seismics. My research has focused on high-resolution seismic methods and their applications. So what does that imply? Nearly every seismic study nowadays is termed “high-resolution” and every author of research papers (and funding applications) claims their work to be “high-resolution”, “very high-resolution” or even “ultra high-resolution”! There is also an abundance of seismic techniques, which are all more or less widely used. For my research, I have focused on the upper kilometers of crystalline bedrock using reflection seismics and seismic tomography with data recorded with 1) a station spacing of 10 meters, along profiles with a typical length of a few kilometers, and 2) the successful recording of high frequency signals (around 100 to 200 Hz) with as many as 100 active channels. The data have been collected in several reflection seismic surveys on the mainland of Sweden. The focus of these surveys has been two fold; to image geological structures such as fracture zones, and contrasting boundaries between different bedrock types, and to retrieve the velocity structure of the bedrock. This is what is meant by “high-resolution” studies in this thesis. In this chapter I will first describe the general geological structures present in the studied field areas and which features I aim to image. I will then focus on the methods; reflection seismics and seismic tomography.. 2.1 2.1.1. Introduction The three-dimensional reality. Present Swedish topography is the result of past tectonic events as well as events related to glaciation during the most recent ice ages. The three field areas covered in this thesis are all located in the Svecokarelian Domain (SD), which makes up the central part of the Baltic Shield (Figure 2.1). Rocks formed during the Paleoproterozoic Svecokarelian orogeny (1.881.80 Ga; Lindström et al. (2000); Svecofennian rocks) as a result of convergence between island arc complexes and the stable Archaean domain to the north (Gaál and Gorbatschev , 1987). The rocks within the SD are referred to as early orogenic (1.91-1.84 Ga; Lindström et al. (2000)), late orogenic and post-orogenic (overlapping through 1.84-1.77 Ga; Lindström et al. (2000)). The oldest rocks are migmatized metasediments, metavolcanic rocks,.

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(159). . E*UDYEHUJ F)RUVPDUN. Figure 2.1: Crude tectonic map of Sweden and the location of the areas studied in this thesis. a) Oskarshamn, b) Gravberg, and c) Forsmark. Modified from Gee and Zeyen (1996).. metagranodiorites and metatonalitites (Andersson , 1997). Later migmatization of these rocks, which commenced shortly before and continued during the late-orogenic period resulted in wide-spread magmatism characterized mostly by granites and pegmatites (Romer and Smeds , 1994; Andersson , 1997). The western part of the SD, generally referred to as the Transscandinavian Igneous Belt (TIB), consists of a belt of granitoids and porphyries (Gorbatschev and Bogdanova , 1993). The rocks within the SD have been subject to metamorphism, folding, shearing and fracturing to various degrees. Seismic attributes such as reflections and velocities will, as a result, vary greatly due to these complex sub-surface conditions. Most of the unconsolidated material covering the Swedish bedrock originates from the latest ice age. Below the maximum marine limit are sediments which were deposited in the various seas that existed in the late and postglacial stages of the ice age. The deposits often contain clay-rich, marine sediments that formed on the sea bottom. These unconsolidated sediments contain unsaturated and saturated parts where the boundary between the two varies in location over time..

(160) 2.2. REFLECTION SEISMICS. 2.1.2. 5. Locations of regions studied in this thesis. The study regions in this thesis, listed in the order they were studied, are: • The nuclear fuel and waste repository site study area north of Oskarshamn, Southeast Sweden, Paper I (Figure 2.2); • The deep gas drill site Gravberg in the Siljan impact area, central Sweden, Paper II (Figure 2.3); and • The nuclear fuel and waste repository site study area at Forsmark, East Sweden, Paper III and IV (Figure 2.4). Two-dimensional reflection seismic profiles have been acquired at these sites. No part of this thesis considers true three-dimensional acquisition geometries.. 2.1.3. What can be imaged by seismic techniques?. Every seismic technique uses seismic waves. Seismic waves are defined as packs of elastic strain energy which travel through some medium. The velocity of these waves of energy are dependent on the elastic properties of the medium and the medium density only. All environments having a variation of these fundamental properties can be the subject of a study using seismic waves. A variation in velocity in an area reveals a variation of the elastic properties or density of the underlaying medium. By imaging these velocity variations one has a base for interpreting what and where these variations of characteristic properties originate from. Energy can neither be destroyed nor created, just transformed. Solving the continuity equation for an interface between two media with different elastic properties or densities shows that the seismic wave energy is divided into a reflected part and a possible transmitted part, a fact which is utilized in reflection and refraction seismic methods. The remainder of this chapter describes how seismic energy can be recorded, processed and interpreted. The main steps of the data processing will be presented and also how the information is prepared for interpretation in the context of our “three-dimensional reality”. (Figure 2.5).. 2.2. Reflection seismics. The first pioneering, controlled-source seismic studies were conducted by the Irish physicist and geologist Robert Mallet (1810-1881), who during 1849 and 1850 carried out experiments to determine the velocities of seismic waves in sand and solid rock, respectively (Mallet , 1862). The refraction seismic method was developed during the First World War where it was used in positioning enemy artillery. The reflection seismic method was first (really) used in the 1920s and was, at the beginning of the Second World War, established.

(161) CHAPTER 2. HIGH-RESOLUTION SEISMICS. 6. 6369. a. 6367. 6366. 6365. 1547. 1548. 1549. 1550. 1551. 1552. 1553. RT90 (km) Figure 2.2: The nuclear fuel and waste repository site study area north of Oskarshamn. A number of seismic lines have been recorded. Two lines were recorded in the northeaster part of the island Ävrö in 1996 (white). Two lines were recorded in 1999 around L. Laxemar (black-white). This data was used for paper I. In 2003 new lines on Ävrö were recorded, including the area east of the power plants (gray). In addition, 3D seismics were recorded in a small grid during this survey (gray dots). In 2004, an additional 3 seismic lines were recorded west of L. Laxemar (black).. RT90 (km). 6368.

(162) 2.2. REFLECTION SEISMICS. 7. 6800. 6780. RT90 (km). b. 6760. 1420. 1440. 1460. 6740 1480. RT90 (km). Figure 2.3: The Siljan impact area. The studied area Gravberg, is framed in gray. This data was used for paper II. The short seismic line (white), inside the frame were recorded in 2001. The seismic lines in black were recorded during 1984-1986..

(163) CHAPTER 2. HIGH-RESOLUTION SEISMICS. 8. 6703. 6702. 6700. c. 6699. 6698. 6697. 6696. 1628. 1629. 1630. 1631. 1632. 1633. 1634. 1635. 6695 1636. RT90 (km) Figure 2.4: The nuclear fuel and waste repository site study area at Forsmark. A number of seismic lines have been recorded in the area. The five lines (black) covered in the thesis were recorded in 2002, with a total length of 16 km. This data was used for paper III. In 2004, an additional 10 seismic lines were recorded, with a total length of 26 km (gray). The south-easternmost seismic line (thick black) was studied again in paper IV.. RT90 (km). 6701.

(164) 2.2. REFLECTION SEISMICS. 9. Figure 2.5: Illustration of subsurface conditions found in the regions studied in the thesis. Hard, only slightly weathered, bedrock is covered with loose unconsolidated sediments. A high degree of exposed bedrock is usually present in coastal areas. The sediments originate mostly from the last Scandinavian glaciation. The groundwater table delimits unsaturated and saturated sediments. Numerous fracture zones cross-cut the bedrock. Plastic deformation zones, intrusions and encapsulated foreign bodies are present. The fractures, sub-horizontally to vertically oriented have been reactivated at various times..

(165) 10. CHAPTER 2. HIGH-RESOLUTION SEISMICS. as the dominant method in the exploration for hydrocarbons. The advance in computing power during the last few decades have revolutionized the utilization of the seismic reflection method. Even with the advanced instruments available today, and the ever increasing computing power, a great deal of hand tuning of the field parameters is still required. The processing steps must be followed carefully, and in the proper order, to produce high quality images to allow us to make good interpretations of the structures present in the subsurface. In the following subsections, I will not described every possible variety of target, but instead focus on the conditions present during the projects I have participated in during my time as a Ph.D student. Although seemingly limited geographically, the results of this thesis are not limited in application or usability, since the conditions present in my projects, to varying degree, are found in many regions of the world.. 2.2.1. Field parameters. While designing the acquisition geometries, it is of great importance to consider what kind of features are to be imaged. While horizontal reflective structures can be imaged at any depth, providing the energy source is powerful enough, imaging dipping reflective structures requires more planning. The station separation must be correctly chosen in order to reveal the desired details of the targets and to avoid creating artifacts by aliasing. Also, by positioning the stations properly, a huge gain in data quality can be achieved. In particular, by avoiding noisy areas and by placing the sources and receivers in locations where there is a good ground coupling, large gains in data quality may be achieved. These issues will be discussed further in the following subsections. Dimensions of the acquisition geometry. A reflecting plane can be imaged to steep dip angles if the recording geometry and the bedrock velocity field is favorable (Figure 2.6). The maximum depth a reflector can be imaged to, in a homogeneous medium, is determined by the locations for the source and receiver relative the reflector and its dip. Assume a reflector to imaged at a certain depth z, straight below a certain location on the surface, the zero point (0). Further, assume zero-offset reflection are wanted (i.e. source and receiver at the same location). A reflector with a dip φ requires the source and receiver to be placed at a distance x = z tan φ away from the surface zero point, (Figure 2.7). For none homogenous mediums, with no negative velocity gradients, this relationship gives the maximum surface distance for zero-offset reflections on a reflector at the given depth. For zon-zero, finite offset recording geometries will the location of the source or receiver need to be even further away from the surface. On the.

(166) 2.2. REFLECTION SEISMICS. 11. Figure 2.6: Vertical reflectors can be recorded in reflection seismic surveying if the bedrock has a strong velocity gradient.. [¶. . 6XUIDFH. ǐ. [. 5HIOH. FWRU. ]. Figure 2.7: The distance x from the surface location straight above the zerooffset reflection point at depth z for for a reflector with dip φ is given by x = z tan φ . An incoming seismic wave parallel with the surface will be reflected to a point x´ at the surface, given by equation (2.1)..

(167) 12. CHAPTER 2. HIGH-RESOLUTION SEISMICS. other hand, for instance if a position for a source are getting closer to the zero point, will the wave reflected on the dipping interface travel away from the reflector at an increasingly narrower angle to the surface. In the extreme will the reflected wave travel parallel to the surface (see Figure 2.7). Described by using the inverse ray direction with a direction parallel to the surface (i.e.infinite source distance) towards the point at depth z on a dipping interface, directly below the zero point, will the reflected wave reach the surface at a position x´ defined in Equation (2.1). z 1 x´ = (tan φ − ). 2 tan φ. (2.1). This illustrates the need for long profiles when dipping reflector are supposed to be recorded using seismic reflection. Inversly, using too short profiles, no interface with a certain dip will be recorded at some corresponding depth straight below the studied area. Temporal and spatial aliasing. With modern seismic instruments, temporal aliasing is generally not a problem, since they easily accommodate sampling frequencies higher then those the seismic sources produce. Thus the seismic source is the controlling factor for the frequencies present in the data. However, spatial aliasing may constitute a great problem in the subsequent processing of collected reflection seismic data if the field parameters are chosen erroneously. Spatial aliasing occurs when the wavenumber (k = Vf ) of events, where f is the wavelets frequencies and V the events apparent velocity, is higher than the Nyquist wavenumber, 1 kN = 2∆x , where ∆x is the station separation . Positioning of sources and receivers. Seismic energy is lost along the path from the source to the receivers through geometrical spreading, attenuation, scattering and by energy being transmitted or reflected away from the surface. How much of the energy that returns to the surface also depends upon the conditions of the ground where the source and receivers are positioned. For explosive sources, the bedrock provides an environment that is very well suited for generating seismic waves compared with loose unconsolidated sediments. The explosive charges used in the studies included in this thesis were 75 grams for loose unconsolidated sediments and 15 grams for bedrock charges. This difference in charge size is due to lower ratio of energy being transformed into seismic waves for shoots in loose unconsolidated sediments. However, with these different charge sizes is the recorded reflected energy in both cases approximately similar. No such balancing can, unfortunately, be done for.

(168) 2.2. REFLECTION SEISMICS. 13. the receivers. The recorded surface motion simply depends on the coupling between the ground and the geophones. Outcropping bedrock is more common in costal areas in Sweden than inland. In the Oskarshamn study area (Paper I), as much as 50 percent of the surface area consists of exposed bedrock. Recordings can be sorted to only include data from shots in either till or bedrock (Figure 2.8) and likewise from geophones placed in till or in bedrock (Figure 2.9). Inspection of the stacks shows, that an image of recordings, sorted by shotlocation type irrespectively of origin, has a very similar signature. However, comparing images of stacked sections for recordings sorted by geophonelocation type show large differences. The signal-to-noise ratio is much higher for geophones positioned in bedrock, resulting in much clearer reflector images.. 2.2.2. Processing steps. Large amounts of seismic data are recorded in modern surveys. The advances in computing science with computing power to process such data is doubled every 18 months according to “Moore’s law”. Given this power, one would expect some kind of “black box” program to exist that produces “finished” seismic images from raw data. There are, however, several reasons why this is not the case. First, no matter how well an area is covered, and how high the station density is, the recordings are still limited to the surface region. Second, the earth is highly heterogeneous. This forces the geophysicist to make assumptions on the character of the elastic properties and densities of the rocks. There are many advanced techniques developed for the processing of seismic data, which when applied by skilled and experienced geophysicists can reveal much information which would otherwise be hidden in the raw data. In the following section, I will describe the processing techniques of particular importance for the studies reported in this thesis. Static corrections. Static corrections are time shifts applied to individual recorded time series, or traces, to produce coherent images of reflected events. Lack of focusing may occur for several reasons and may cause reflective events in seismic sections to be incoherently imaged or even worse, be mistaken for noise. Variable time shifts are due to waves passing through subsurface materials for which the thickness and velocity are varying between locations for the individual sources and receivers. Also, variation in the elevation of source and receivers, or different elevations for source and receivers, will produce static shifts (Marsden , 1993). Multi-channel, multi-offset reflection seismic data processing relies on the.

(169) 14. CHAPTER 2. HIGH-RESOLUTION SEISMICS. Figure 2.8: Stacked seismic sections from a profile in Laxemar at the Oskarshamn study area sorted to include recordings of; all shots in till (top) and all shots in bedrock (bottom)..

(170) 2.2. REFLECTION SEISMICS. 15. Figure 2.9: Stacked seismic sections from a profile in Laxemar at the Oskarshamn study area sorted to include recordings of; all shots recorded by geophones placed in till (top), and bottom; all shots recorded by geophones placed in bedrock (bottom)..

(171) CHAPTER 2. HIGH-RESOLUTION SEISMICS. 16. assumption that energy from reflectors may be summed constructively while noise will be summed destructively. This way, events which would otherwise be too faint to be imaged with zero-offset reflection seismic data can now be resolved. However, seismic energy not focused in multichannel reflection seismic data will, even after summation only leave a weak signal, or, in the worst case no signal, resulting in no reflectivity at all. The three reflection seismic studies covered in this thesis have all been located in areas where the topography varies considerably, and/or the loose sediments covering the bedrock have strong variation in thickness. One example of this is shown in Figure 2.10, which shows travel times of first arrivals for a profile from the Oskarshamn region. ms. Geophone position along profile (m). 2000. 20. 10 1500 0. 1000 −10. −20 500. −30. 500. 1000. 1500. Source position along profile (m) Figure 2.10: First arrival traveltime data from Laxemar profile 1 at the Oskarshamn study site. The variation in traveltimes by source and receiver locations is shown. The traveltimes have been reduced for offset with a velocity of 5 km/s.. The vertical and horizontal stripes reveal the variations of travel times by.

(172) 2.2. REFLECTION SEISMICS. 17. source and receiver locations. The larger variation of traveltimes associated with the receivers is surface consistent, since the waves have to pass through additional slow velocity materials. In fact, static corrections can be used to estimate the thickness of the loose unconsolidated sediment cover (Paper III). Care must be taken when applying static corrections to seismic data. Changing the traveltimes will have a direct effect on the velocities assumed for a seismic wave along its ray path, and will change the location of the reflecting event (Frei , 1995). By reducing the travel times, a slower seismic velocity must be used in the imaging step in order not to place the event at a too shallow depth. Dip Move-Out. Much of the imaged reflectivity in crystalline bedrock arises from fracture zones. Fracture zones often have steep dips for which Normal Move-Out (NMO) fails to create zero-offset sections when the seismic energy is constructively summed using real bedrock velocities. To perform an NMO correction of a dipping planar event a higher velocity must be used than for horizontal events. The NMO velocity VNMO depends on the bedrock velocity and the cosine of the event’s dip angle φ (2.2). φ is here given as the angle between the reflector and the surface. VNMO =. V cos φ. (2.2). The NMO relationship for a single dipping reflector is given by equation (2.3), where φ is the reflector dip, x is the source-receiver offset and V is the velocity of the medium above the reflector (Levin , 1971). 2 2 x2 x sin φ 2 2 t (x) = t (0) + 2 − (2.3) V V2 The move-out term is divided into two parts, where the first parts is the zero dip part, and the last part is related to the reflector dip. The larger the dip angle, the larger the needed correction (Equation (2.3)). For crossing reflectors with conflicting dips this will become a problem since different velocities would be needed for different reflectors at the same location. However, by applying pre-stack partial migration, commonly known as Dip Move-Out (DMO), the same velocities may be used for all dips. For traces which have had NMO corrections applied, applying DMO corrections will cause seismic energy to move from offset traces to appropriate zero-offset traces, a migration process (Bancroft , 1997). In constant velocity media, the processing sequence with NMO, DMO stacking, and post-stack (zero-offset) migration is equivalent to pre-stack (offset).

(173) 18. CHAPTER 2. HIGH-RESOLUTION SEISMICS. migration. In media with moderately vertically varying velocities DMO is still appropriate, but in media with laterally varying velocities it will fail. In these cases full pre-stack migration has to be used (Bancroft , 1997). It is important to note that for the post-stack migration procedure which is dependent on NMO corrections, there will be significant information lost at shallow levels and large offsets due to NMO stretch muting (Paper IV). Stretching occurs because a waveform with a given period T on a zero-offset trace will have an increased period T + ∆TNMO at an arbitrary offset x after the NMO correction to generate a quasi-zero-offset trace. Stretching produces a shift to lower frequencies ( f → f − ∆ f ) as quantified in equation (2.4) (Yilmaz , 1987). ∆f ∆TNMO = (2.4) f T Because of this frequency distortion, shallow events are severely distorted in CMP stacks if the far offset waveforms are included and, thus, these must be muted (Miller , 1992). The muting reduces the stacking fold for shallow events, which may then go undetected.. Kirchhoff pre-stack migration. The strength of pre-stack migration is its capacity to handle arbitrary offsets between the source and receiver. In common-midpoint (CMP) stacking procedures, the seismic energy is summed along the NMO hyperbola. In the popular straight forward Kirchhoff pre-stack migration method, the seismic energy is summed over all input traces matching the Double-Square Root (DSR) travel-times and output at the image point on the migrated trace (Claerbout , 1985). The DSR traveltime relationship can be written as in equation (2.5), where xs is the offset between the source and the image point, xr is the offset between the receiver and the image point, z is the depth to the image point and t is the two-way traveltime (see Figure 2.11). t=. xs2 + z2 + v. . xr2 + z2. (2.5). Kirchhoff pre-stack migration is very computationally demanding, but can provide very good results when CMP stacking and post-stack migration does not produced clear seismic images (Paper IV). The main difficulties are to find the correct migration velocities in order not to degrade the section with artifacts..

(174) 2.2. REFLECTION SEISMICS. 6. 19. ;V. ;U. 5. = 9 3 Figure 2.11: Travel path for a seismic wave from source S reaching the receiver R by scattering at P. The scatter point (image point) P is horizontally offset from the source by Xs and from the receiver by Xr . The scatter point is located in an otherwise homogenous medium with the velocity V .. 2.2.3. 3D Interpretation of 2D data. A reflecting dipping plane in a stacked section will only migrate to the correct spatial position if the dip line is parallel with the stacking profile (see Figure 2.12). The migration process will always underestimate the dip and the depth of out-of-the-plane reflections. The relation between the dip αmig for a reflector on a depth migrated zero-offset section recorded along a straight profile that deviates from the dip line at an angle θ , and the reflecting plane’s true dip φ , is expressed by Equation (2.6), (Levin , 1971). The angle αmig is measured between the profile and the migrated zero-offset appearance for the reflector. The angle φ is the true dip of the reflecting plane. sin αmig = sin φ cos θ. (2.6). The angle θ can not be determined using data from only one single, straight, seismic line. The dip of a reflecting plane can be found if two stacked seismic sections reveal a reflector at the same time at the crossing point of the profiles, or if the reflector can be tied to a mapped feature at the surface (see Figure 2.12). The reflecting plane may be determined by vectors r1 and r2 using the zerooffset sections coordinates and traveltimes. The cross product of these vectors gives the normal vector of the reflecting plane (2.7). n = r1 × r2. (2.7). The non-migrated dip α (equation (2.8)) measured from the dip line, and the strike δ (2.9) can then be calculated from the components of the normal.

(175) 20. CHAPTER 2. HIGH-RESOLUTION SEISMICS. ] Q]. Q. 6WULNH. Q\. \. H LQ SO. A. 'L. D Q[ [. Q. 6HFWLR Q. U. Q R L FW 6H. . U. Figure 2.12: The relationship between the strike δ and the unmigrated dip α of a reflecting interface. The vectors r1 and r2 are determined from reflectors dip on two crossing unmigrated seismic sections..

(176) 2.3. SEISMIC TOMOGRAPHY. vector n.. 21 . tan α = tan δ =. nx ny. n2x + n2y nz. (2.8) (2.9). The the migration equation tan α = sin φ is then used to calculate the true dip φ .. 2.3. Seismic tomography. Seismic tomography is a schoolbook case nonlinear inversion problem. The velocity model is determined by the traveltimes, which are calculated from the ray paths, which in turn are dependent upon the velocity model, and so forth. Thus, an incorrect velocity in one part of the model can influence the velocity structure in another part of the model. Without constraints, the search for the best fitting velocity model could easily become unstable. The search for the optimum solution is stabilized partly by the numerous travel times usually included in a tomographic inversion. However, it is also common practice to apply a priori constraints while solving for the velocities, in order to get convergence to a realistic model with a minimal residual travel time solution. There for, an incorrect velocity in one part of the model will not affect the entire model in a catastrophic sense. There will, however, remain some degradation in the velocity model which might misguide the interpretation. In the case of a considerable velocity contrast near the source and receivers, great care is needed when creating an initial velocity model for the tomographic inversion. Some aid in this task is presented in this section and in Paper II and Paper III.. 2.3.1. Tomography inversions with source static corrections. Seismic tomography studies of first arrival reflection seismic data can, if they are performed correctly, be used to produce a detailed image of the velocity structure of very shallow depths. Controlled source seismic tomography is different from local earthquake tomography in the sense that the location of both sources and receivers, as well as the travel times, are fully known. This means that the four hypocenter parameters, the source location and earthquake origin times will not be calculated, only the remaining unknowns, the velocities. For controlled source seismic tomography, the non-linear line integral (2.10) describing the travel time t for one source-receiver pair ray, can be expressed in.

(177) 22. CHAPTER 2. HIGH-RESOLUTION SEISMICS. terms of the slowness u(r), the differential length dl , and the ray path l which itself is a function of u(r). t=. . u(r) dl. (2.10). l[u(r)]. Due to the strong non-linearity of the problem there are, however, major disadvantages in having all sources and receivers at the surface. This is due to the ray path geometries, where the fresnel zones of the turning rays increase in size with depth, thereby causing lower resolution. Another drawback of having all sources and receivers at the surface lies in the heterogeneity often present in the shallow subsurface region. In Sweden, this heterogeneity is due to loose unconsolidated sediments and partly fractured bedrock. One approach to account for subsurface heterogeneity can be borrowed from reflection seismic processing by adopting the methodology of static corrections. This is done by adding a static time correction term τ to the (sourcereceiver pair) equation (2.10). This non-linear relationship may then be solved by non-linear inversion techniques or by linearizing the problem and finding the solution by stepwise iterations. By parameterizing equation (2.10) about a starting model with uniformly sized model blocks equation (2.11) is obtained, modified from equation (1) in Benz and Smith (1984). Here ri j is the residual of the measured travel-time and the theoretical time based on the defined model for all I ∂T sources and J receivers. τi j is the static correction to the travel-time. ∂ uinj are the partial derivatives of travel-time with respect to the slowness in block n along the ray path. ∆un is the change of slowness in the model block n which is to be found for all N blocks. N. ri j = τi j + ∑ n. ∂ Ti j ∆un , i = 1..I, j = 1..J ∂ un. (2.11). The linearization is made with the assumption that the raypath distance dn in block n is unaffected by any slowness change in this block (2.12). ∂ Ti j |n ∂ Ti j ≈ = dn ∂ un ∂ un. (2.12). The tomographic inversions presented in this thesis are all made using PStomo_eq (Benz et al., 1996; Tryggvason et al., 2002). In the program, the travel-time fields for the present slowness model are computed with an algorithm based on first-order finite-difference approximations of the eikonal equation (Hole and Zelt , 1995) and the travel-times (2.10) calculated by.

(178) 2.3. SEISMIC TOMOGRAPHY. 23. ray tracing backwards perpendicular to the isochrones of the travel-time field (Hole , 1992). PStomo_eq was developed for local earthquake tomography implying that the static correction is associated with the source. Thus τi j can be reduced to τi . The equations for rays from the source i can then be written as a system of equations (2.13) where γi is the vector of travel-time residuals. Di is the matrix of all travel distances in the model blocks dn for all ray paths from this source. τi + Di ∆u = γi. (2.13). Equation (2.13) can now be arranged into a matrix for all earthquakes (2.14), where M is the total number of travel-times.    .   τ1 γ1 0 D1  .   ..   . ..   =  ..  .      τI  SI DI γM ∆u   1 D11 · · · D1N  . ..  ..  . .  .  , Di =  . J DJ1 · · · DJN . S1. ... .. 0   Sl =  . .    . (2.14).    . Pavlis and Booker (1980) showed that system (2.14) can have the static correction parameters decoupled from the velocity parameters. They also showed that this procedure is equivalent to solving equation (2.14). Equation (2.14) is a mixed determined system, where parts of the model is underdetermined and others are overdetermined. The static correction terms are overdetermined as long as several receivers have recorded the same source. Equation (2.14) can be decomposed into a principal axis system by singular value decomposition i.e. Si = Ui ΛiViT where Ui contains the eigenvectors for Si SiT , Λi is the diagonal matrix containing the eigenvalues of Si , and Vi contains the eigenvectors of SiT Si . In the case with only one station correction parameter, Λi will only contain one non-zero eigenvalue and Ui can therefore be partitioned into [uiU0i ]. Here ui is the eigenvector associated with the single eigenvalue. The eigenvectors for the null-space U0i contain no information of the static correction and relation (2.15) is true. U0Ti Si = 0. (2.15).

(179) 24. CHAPTER 2. HIGH-RESOLUTION SEISMICS. Multiplication of U0Ti into (2.13) will cause the static correction term to vanish (Pavlis and Booker , 1980) and (2.13) will be reduced to (2.16). Di ∆u = γi. (2.16). Solution stability and some degree of artifact suppression is achieved by adopting the constraint of demanding the Laplacian of the slowness perturbation field to be a minimum. The final system of equations to be solved can now be written as in (2.17), where k is a constant scaling the importance of the smoothing constraint and is the Laplacian smoothing operator.

(180). D k.

(181) ∆u =. γ. 0. (2.17). The system of equations (2.17) is solved for the perturbations of the slowness field in PStomo_eq using the conjugate gradient solver LSQR (Paige and Saunders , 1982). The slowness perturbations updates are applied to the velocity filed and the static corrections are applied to the recorded traveltimes. Now a new inversion of the velocity field, simultaneously solving for static corrections can be made. This iteration procedure is continued until the modeler is satisfied with the model convergence. The initial model is critical for the convergence rate and the precision of the final model as the non-linear problem is solved with an iterative application of a linearized approximation (Kissling , 1988; Kissling et al., 1994).. 2.3.2. Source and receiver statics in seismic tomography. Tomographic applications on high resolution reflections seismic data, where both the source and receivers are separated from the bedrock by loose unconsolidated sediments with their characteristic slow seismic velocity, requires special solutions (Paper III, Paper IV). Incorporating a receiver static correction term, τ rj , in (2.13) to accompany the source static correction terms, τis , will yield another J columns to be inserted in (2.14). These columns will have ones at every source-receiver pair where the receiver takes part. Written as matrices, Ri , where the J column data are instead collected for sources i will allow the system to be written as.

(182) 2.3. SEISMIC TOMOGRAPHY. 25. in equation (2.18).  τ1s  .   .   .    s   τ   I     τr  =   1    .   ..     r   τJ  .    . S1. 0. ... . SI. 0. R1 D1 .. . RI. DI.  γ1 ..  .   γM. (2.18). ∆u. For a shooting geometry where all receivers are recording all shots, the matrices will be filled with ones. One can, however, still solve for and do the multiplication of U0Ti to the system and then get the transformed system (2.19). . U0Ti. . R1  .  .  ..   ..   U0TI RJ.   τ1r D1  .   ..   ..     .   r  =   τJ  DI ∆u . .   U0Ti γ1  .  ..   .  .   .  U0TI γM. (2.19). This system is not appropriate to solve directly because there is no complete separation between static corrections (time) and slowness (s/m). To further decouple the remaining receiver static corrections from the slowness perturbations would require performing another SVD decomposition. This is, for any reasonably sized tomography application a task that remains unsolvable in practice since the matrices will be approximately sized to the square of the total amount of travel times used. Even with a computer fulfilling the vast memory requirements, the errors of the smallest eigenvalues and eigenvectors in the null-space might be severe. Instead a simplified method was used in the studies presented here, which approximates the real static correction solution. Synthetic data simulations of tomographic inversion, where source and receivers were positioned both in and on the surface of a slow velocity layer covering the “bedrock”, gave source static corrections that were about twice the size as the true travel-time delays from the slow layer. This suggested an alternative approach for the tomography inversion, where one iteration step is divided into two phases. In the first phase the static correction terms are solved for and then split between the sources and receivers in a surface consistent manner. In the next phase the velocity field of the model is solved for by an inversion where no static.

(183) 26. CHAPTER 2. HIGH-RESOLUTION SEISMICS. correction calculation is performed. This two step iteration procedure is then repeated in the same fashion as in the case where only source static corrections were included in the tomography inversion. In paper III, the computed statics were split equally between the source and receiver at a given location, thus obtaining a crude surface consistency. Any elevation differences between the sources and receivers were taken into account, assuming a constant overburden velocity. These statics were then applied in the next inversion step, when the velocity structure was solved for. This is a very lax way to obtain both source and receiver statics. However, in tests with a synthetic data set, the obtained static corrections were in very much agreement with the depths to bedrock in the true model, suggesting the method has some merit. For paper IV, when converting the obtained statics (in reality estimated depths to bedrock) into statics for use when processing the reflection seismic data, a slightly more sophisticated approach was called for. We made the assumption the calculated static, τi, is in fact J. ∑ τ rj. τi = τis +. j=1. Ji. (2.20). where τis is the contribution from the source static at this position, and the rest is the mean static of all the receiver τ rj recording this shot. Without any method to estimate the individual weights of the different receivers, we just assume they are contributing equally. As we are now trying to estimate I+J unknowns from I data, we need additional information. We used the surface consistency criteria as before, taking the elevation differences ∆ j between the shot and receiver into account. This leads to ∆j = τ rj − τis V. (2.21). where V is the effective overburden velocity, here assumed constant. In fact, ∆j V could be expressed by data commonly recorded in field - the uphole time, compensated for any horizontal shifts in the shot and receiver positions..

(184) 27. 3 Summary of papers. The following sections present the four papers upon which this thesis is based. Each paper is summarized, describing the main objectives, methods used, the main results and, finally, the conclusions. Paper 1 is a high-resolution reflection seismic survey over a nuclear waste storage study site. Small explosive charges were used as sources (15-75 g). After processing, including dip-move out (DMO), several reflections with various dips are imaged. Combined data from the two crossing profiles reveal a complex 3D pattern of fracture zones and larger greenstone lenses down to 3.5 kilometers depths. Paper 2 is a seismic tomography study where we developed a tomography method that calculates receiver statics, tomography inversion with statics (TIS), which produces a velocity image better than images produced from standard tomography. Previously unknown structures could be imaged at the studied site, Gravberg in the Siljan ring impact area which has a glacial till cover of up to 20 meters thickness over the crystalline bedrock. Paper 3 is an extension of the application of seismic tomography to the estimation of the varying thickness of loose unconsolidated sediments overlaying bedrock. Synthetic data were used to study how tomography with TIS best is applied. The findings of these tests were then applied to seismic first break time data from Forsmark, another Swedish nuclear waste repository study site. The results show mostly homogeneous bedrock velocities and a bedrock topography with more variation than the surface topography. Paper 4 is a study where we have used Kirchhoff pre-stack time migration image the uppermost part of the bedrock for depths shallower than the length of the recording spread. This part of the seismic image can’t be well resolved with processing using Norma Move-Out correction. Reflector have been imaged at a depth of just 15 ms, approximately 50 meters depth in this study of the Forsmark area. The reflectivity correlates well a tomographic velocity model, imaging the top 50 meters of the bedrock..

(185) CHAPTER 3. SUMMARY OF PAPERS. 28. 3.1. Paper I. High-resolution reflection seismic imaging of the upper crust at Laxemar, southeastern Sweden.. When I began my Ph.D. studies in november 1999, I joined a research project run in cooperation between the controlled source seismic group at Uppsala University and the Swedish Nuclear Fuel and Waste Management Company (SKB). The project objective was to find the optimal reflection seismic field parameters for imaging depths down to 1-2 kilometers in common Swedish conditions (Juhlin et al., 2001). In the project several individual field studies had been conducted; the Ävrö seismic survey (Juhlin and Palm , 1999), the Ävrö mini source test, 1997, and the Ängeby mini source test, 1998. In December 1999, a reflection seismic survey was conducted in the Laxemar area located in southeastern Sweden. This was the first full scale test using small explosive charges as a source.. 3.1.1. Summary. The three objectives of this study were: • evaluate the usage of small explosive sources and slim shotholes. • map reflectors in three dimensions and correlate the reflections with borehole data. • compare the reflectivity with that of a neighboring area. The Laxemar area has a high percentage of bedrock outcrop. Half of the 417 shots were positioned in bedrock. Previous studies had concluded that a source of 15 grams of plastic explosives could be used in boreholes with a depth of 90 cm and a diameter of 12 mm. This charge size was the strongest that could be deployed without breaking the bedrock severely. In breaking the bedrock not only energy for the seismic signal would be lost but it would also violate the environmental considerations of the study. For shotholes in loose unconsolidated sediments, 150 cm deep, 20 mm diameter boreholes were drilled. The loose sediments consisted of peat and/or glacial till with up to 20 meters thickness, and the bedrock is made of mainly granite or granodiorites. Shotholes were cased with plastic pipes wherever possible, but iron pipes had to be used in a few locations. 75 gram of high detonation velocity dynamite was used for these shotholes. Whenever possible, geophones were placed in holes drilled in the bedrock. Two crossing profiles, 2 and 2.5 kilometers long were shot. The station spacing was 10 meters with shots at almost all stations. The profiles crossed at the location of a 1714-meter deep core-drilled borehole (KLX02). Recorded with a sample rate of 1 millisecond, the data have a high signalto-noise ratio with the exception of a few shots which were degraded by wind.

(186) 3.1. PAPER I. 29. and rain generated noise. The charge sizes and shothole depth used resulted in a minimum of airwave contamination of the data. Groundroll was present only in shots in the loose sediments and could be almost entirely removed by deconvolution and frequency filtering. Accurate static corrections were crucial in processing the data. For this reason all first break picks were inspected manually and only clear picks were kept to maintain high quality. Frequencies of the reflected energy were between 140 and 300 Hz near the surface and between 60 and 180 Hz for the part at 800-2000 milliseconds depth. Due to crossing reflections an iterative velocity analysis with normalmoveout (NMO) and dip-moveout (DMO) corrections was used in order to find the optimal velocity field. We chose not to show any migrated sections in the paper since the dipping reflections come from out of the plane. Migration of such data would yield erroneous positions and result in incorrect interpretations (see section 2.2.3). Instead, we identified intersecting reflectors at the crossing point between the profiles, and by assuming flat plane reflectors we calculated the strikes and dips and the intersection line for the reflector with the surface. Eight reflectors were identified at the location of the borehole and another two which were present on only one stacked section. Four of these reflectors have a significant dip, 35-49◦ , and when projected to the surface they fall within the studied area. (see figure 3.1 and figure 3.2). Two reflectors that were present in only one of the profiles intersect the surface at previously mapped geological features (fracture zones). Assuming the geological feature and reflector are one and the same, the dip of the plane can be determined (see section 2.2.3). The mapped geological feature then define the strike. A large number of measurements have been carried out by SKB in the deep borehole KLX02 (Ekman , 1998) including coring, hydraulic tests and wireline logging (sonic velocities, density and gamma logs). A few main findings can be pointed out from the correlation of the imaged reflectivity and the borehole data. Reflectors A and C (see figure 3.1) intersect the borehole where highly hydraulically conductive zones are found. The reflector package between Ba and Bb corresponds to an interval where greenstones represent 50 percent of the lithology. Based on log data the seismic reflection coefficient of the granite/greenstone contact is as strong as +0.065 which indicates that this is the origin of the reflectivity. Other likely reflections from greenstones or mafic lenses are the high-amplitude diffraction events marked as X and Y. There are two deeper subhorizontal reflections arriving at 1.0-1.1 s dipping about 10◦ to the north. Their strike and dip coincides with reflections seen in a previous study conducted on the nearby island of Ävrö (Juhlin and Palm , 1999) and might represent the same subhorizontal structure..

(187) CHAPTER 3. SUMMARY OF PAPERS. 1 (. 6:. / LQ H . 30. . . 6(1:/LQH. . . . . . 1. . ./; $. . . $ ' *. '. . %D %D *. ;. . % %E. 7LPH V

(188). % . %E (. . (. & . . &. Figure 3.1: Lines 1 and 2 merged at the KLX02 borehole and viewed from the southwest. Reflections A, C, D, E and G are interpreted to originate from dipping fracture zones, while Ba, B and Bb are from greenstones. The horizontal scale refers to CDP number with a CDP spacing of 5 m..

(189) 3.1. PAPER I. 31. NW-SE Line 2 1450. 1400. 1350. 0. I. KLX01. Li ne. 1. 350. SW -N E. 300. H. 250. H. 0.2. 200. N. 150. KLX02. 0. I. C Y. D. 0.2. Ba. Time (s). A. B. 0.4. C. Bb. G. A 0.4. D Ba G. B Bb. 0.6. E. E. 0.6. Figure 3.2: Lines 1 and 2 merged at the KLX02 borehole and viewed from the northeast. Reflections A, C, D, E, G, H and I are interpreted to originate from dipping fracture zones, while Ba, B and Bb are from greenstones. The horizontal scale refers to CDP number with a CDP spacing of 5 m..

(190) CHAPTER 3. SUMMARY OF PAPERS. 32. 3.1.2. Conclusions. The upper 1.5 km of crystalline bedrock was mapped successfully in this full scale test of using small explosive charges in slim shotholes for highresolution seismics. Compared with vehicle-mounted drilling equipment, this technique significantly reduces the costs for acquisition of high-resolution reflection seismic data. This method also has much lower impact on the environment compared with vehicle-mounted drilled shotholes. There is a good correlation between the seismic reflectivity and the geological and geophysical data from the core-drilled deep borehole present at the intersection of the seismic lines. The correlation with the borehole data and surface geology for many of the dipping reflectors shows that they are related to fracture zones. Other reflectivity originates from greenstones which have a significant seismic impedance contrast with the granite forming the host rock..

(191) 3.2. PAPER II. 3.2. 33. Paper II. High-resolution seismic tomography incorporating static corrections applied to a till covered bedrock environment. During my second field project as a Ph.D. student, a short test reflection seismic data set was collected in the Siljan Ring area, central Sweden, close to the 6.7 km deep borehole Gravberg-1. The objective was to investigate if the small charge slim hole method presented in Paper I would work in an area with up to 20 meters of glacial till covering the rock but without bedrock outcrop. During processing of the reflection seismic data, we realized the benefit of having a highly detailed velocity model for the shallowest part of the data. Our short test profile overlapped a relatively long deep reflection seismic profile recorded at the time of drilling of Gravberg-1. This deeper profile allowed us to get detailed velocity information for the upper hundreds of meters of the rock using high-resolution seismic tomography. We had detailed information on the thickness of the glacial till layer covering the bedrock from borehole data from the drilling of shotholes for the deep reflection seismic projects. This was the start of the development of a new approach for seismic tomography in which static correction calculations ended up being included in the velocity inversion.. 3.2.1. Summary. A large near-surface velocity variation from in our case, 20 meters of glacial till covering granite bedrock, is a major obstacle in tomographic inversions. Velocity models can be disturbed considerably by such a low-velocity bedrock cover (see Figure 3.3). This obstacle is not easy to overcome, even using advanced schemes such as defining a fine grid as Böhm et al. (2000) or defining an a priori layering as Osypov (1998). We have developed an approach where we add a receiver correction term in the inversion for the full 3D velocity structure. This is a well known and commonly used technique in reflection seismic processing in order to better focus the seismic energy. Our tomography approach is very similar to the inversion for hypocentral parameters in local earthquake tomography, but we solve only for the time term and not for the three spatial terms since we know the positions of sources and receivers. In the inversion we use reverse ray paths and, thus, solve for the static corrections (the time terms) associated with the receivers. Since almost all (96%) shot points were positioned in the bedrock below the cover, we assume the only significant delays in measured traveltimes will arise when the rays pass through the slow velocity cover. The acquisition geometry is not truly three dimensional, however, the crookedline geometry prevents the use of a two dimensional tomographic approach (see Figure 3.4). 4438 rays were used, produced by a total of 70 shot posi-.

(192) CHAPTER 3. SUMMARY OF PAPERS. 34. tions and 253 recording geophone positions, The offset of the data varies from 180 m to over 4500 m. The size of the explosive charges used was 5 kg to 10 kg. The starting model in controlled-source tomography, with all sources and receivers at the surface, is very important. Our model is a two dimensional model with no variety along the y-axis. The two dimensional model was built to accommodate the varying topography along the profile by using an one dimensional model (see Table 3.1) that was shifted in vertical position to follow the surface . Table 3.1: Velocity-depth pairs for the minimal model and modified minimal model. Depth, (m) Minimal model velocity, (m/s) Modified model velocity, (m/s) 0 25 100 400 800. 1500 3900 4800 5350 5780. 4000 4900 5350 5780. Four suites of inversions were performed: Case A: Standard tomographic approach using the minimum starting model. Case B: Tomography with the traveltimes a priori corrected with receiver refraction statics from the reflection seismic processing of the data and the modified minimum starting model. Case C: Tomography using simultaneous static correction and velocity inversion, and the minimum starting model. Case D: Tomography using simultaneous static correction and velocity inversion, and the modified minimum model. The RMS data fit reveals to which degree the traveltimes could be reproduced in the four different cases. The velocities obtained in case A show the largest variation from the initial values with anomalies tending to follow raypath patterns that indicate that near surface velocity variations are projected deeper into the model (see Figure 3.3). Case D has the smallest RMS values and also the least smearing of velocities into deeper parts. Case B and case C have intermediate RMS values and also fall in between Case A and Case D in the raypath pattern degradation of the images with Case C having slightly more homogenous velocities. Observe that for case B and D, the near-surface velocities do not represent the true velocities. Instead we argue that these velocities represent the underlaying rock velocity. Because it has the best data fit and the most well-behaved velocity model, in addition to being the simplest, we use the velocity model from case D in the interpretation. The model robustness was estimated with checkerboards tests. We added a.

(193) C. D. E. . . . . . . . 35. 7FMPDJUZ NT. &MFWBUJPO N. &MFWBUJPO N. &MFWBUJPO N. &MFWBUJPO N. Figure 3.3: Final velocity fields. Because of the crooked-line geometry, the raypaths are not aligned in a vertical plane and are not below the exact surface location of the line. Instead, the cell with the highest ray coverage in the east-west direction is shown. (a) Case A. (b) Case B. (c) Case C. (d) Case D.. 4PVUI. . . . 4PVUI. . . . /PSUI. . Z N. . /PSUI. 4PVUI. . Z N. . /PSUI. . Z N. 4PVUI. . . . . Z N. . /PSUI. 3.2. PAPER II. B. .

(194) 36. CHAPTER 3. SUMMARY OF PAPERS. perturbation of alternating fast and slow velocities to a single gradient model (4500m/s + 1(m/s)/m) for which theoretical traveltimes were calculated, and to our final model from case D. The velocity perturbations of ±1500m/s were given the shape of vertical stripes with a width of 350 m along the long side of the model and the full model width. The results from the simple gradient model clearly indicated that the model was well resolved to 150-200 m depth. The final model from case D was indicating a slightly deeper well resolved part down to 200-250 m. The final model from case D was compared to the mapped surface geology, the topography, and the aeromagnetic total field map (see Figure 3.4). The flight line spacing was 200 m with a 40-m sampling interval and the data have been gridded to a uniform 40-m grid. The topographic data were sampled on a uniform 50-m grid. We interpreted the maps jointly and could see that in the southern part a low velocity region correlates with a mapped fracture zone. In the middle of the profile there is a correlation between high model velocity, a high in the magnetic map, and a mapped dolerite. A little further north a high-velocity zone in the model and a small high in the magnetic data suggest an unmapped dolerite. In looking at the residual, mean, and standard deviation of the data for case D sorted per receiver we see no indication of larger residuals in regions with a thicker sediment cover. We interpret this as the static correction term solved for in the velocity inversion absorbs the effects on the traveltimes from the loose sediments. Also, the best agreement with sonic-log velocities from the deep-borehole in the middle of the model is the velocity model from case D. This suggests that this is the best approach for finding the bedrock velocities in the present case. Since no sources are located deeper in the model the tomography method has a highly limited depth to which the bedrock is well resolved. In our case, with up to 4.8 km offset, only the upper 250 meters can be imaged with good resolution. Thus, the geometry of the profile and the velocity gradient in the bedrock limit the penetration.Zelt (1999) states that strong near-surface heterogeneity will be smeared out into deeper layers if the parameterization is not detailed enough. We see in our case, that when the near-surface heterogeneity is not accounted for by the use of the static correction term solved for simultaneously with the velocity inversion, we get smearing of low velocities to deeper parts of the models, resulting in a degraded velocity model..

(195) 3.2. PAPER II. 37. 7FMPDJUZ N. . C. . 4PVUI. B. Y N. . 8. . 4PVUI . . . . . Z N . Z N. . . . . . . . /PSUI. /PSUI. . . . . &MFWBUJPO N. & &MFWBUJPO N. D. E. Figure 3.4: Comparison of the velocity field from the best-fitting tomography model (case D). (a) Aeromagnetic map. (b) Topography. (c) Mapped geology (legend in Figure 1, Paper II). (d) Velocity field of the final model..

(196) CHAPTER 3. SUMMARY OF PAPERS. 38. 3.2.2. Conlusions. We have incorporated a receiver static term in a tomography algorithm which is simultaneously solved for with the velocity inversion. This way we can avoid smearing of low near surface velocities to deeper parts of the velocity model. The best results are obtained when the low velocities are replaced with near-surface bedrock velocities. The static correction then absorbs the shortwavelength variations in traveltimes arising from the slow-velocity layer. This is in analogy with the use of static corrections in reflection seismic processing which is used to focus the seismic energy. With the described method we have been able to make a detailed velocity profile of an area with varying topography, low velocity overburden and complex geology, that agrees well with previous geological mapping, but also shows new structures. Given the simplicity of the method and implementation, we believe that the method can be applied successfully to other complex areas..

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