Seismic Methods Geoph 465/565 ERB 5104 Lecture 5 – Sept 9, 2015 Lee M. Liberty Research Professor Boise State University

PSWIGB - PostScript WIGgle-trace plot of f(x1,x2) via Bitmap Best for many traces. Use PSWIGP (Polygon version) for few traces. pswigb n1= [optional parameters] <binaryfile >postscriptfile Required Parameters: n1 number of samples in 1st (fast) dimension Optional Parameters: d1=1.0 sampling interval in 1st dimension f1=0.0 first sample in 1st dimension n2=all number of samples in 2nd (slow) dimension d2=1.0 sampling interval in 2nd dimension f2=0.0 first sample in 2nd dimension x2=f2,f2+d2,... array of sampled values in 2nd dimension bias=0.0 data value corresponding to location along axis 2 perc=100.0 percentile for determining clip clip=(perc percentile) data values < bias+clip and > bias-clip are clipped xcur=1.0 wiggle excursion in traces corresponding to clip wt=1 =0 for no wiggle-trace; =1 for wiggle-trace va=1 =0 for no variable-area; =1 for variable-area fill =2 for variable area, solid/grey fill SHADING: 2<= va <=5 va=2 lightgrey, va=5 black nbpi=72 number of bits per inch at which to rasterize verbose=1 =1 for info printed on stderr (0 for no info) xbox=1.5 offset in inches of left side of axes box ybox=1.5 offset in inches of bottom side of axes box wbox=6.0 width in inches of axes box hbox=8.0 height in inches of axes box x1beg=x1min value at which axis 1 begins x1end=x1max value at which axis 1 ends d1num=0.0 numbered tic interval on axis 1 (0.0 for automatic) f1num=x1min first numbered tic on axis 1 (used if d1num not 0.0) n1tic=1 number of tics per numbered tic on axis 1 Seismic Methods Lab 1

SUMUTE - MUTE above (or below) a user-defined polygonal curve with the distance along the curve specified by key header word sumute <stdin >stdout xmute= tmute= [optional parameters] Required parameters: xmute= array of position values as specified by the `key' parameter tmute= array of corresponding time values (sec), in case of air wave muting, correspond to air blast duration ... or input via files: nmute= number of x,t values defining mute xfile= file containing position values as specified by the `key' parameter tfile= file containing corresponding time values (sec) ... or via header: hmute= key header word specifying mute time Optional parameters: key=offset Key header word specifying trace offset =tracl use trace number instead ntaper=0 number of points to taper before hard mute (sine squared taper) mode=0 mute ABOVE the polygonal curve =1 to zero BELOW the polygonal curve =2 to mute below AND above a straight line. In this case xmute,tmute describe the total time length of the muted zone as a function of xmute the slope of the line is given by the velocity linvel= =3 to mute below AND above a constant velocity hyperbola as in mode=2 xmute,tmute describe the total time length of the mute zone as a function of xmute, the velocity is given by the value of linvel= =4 to mute below AND above a user defined polygonal line given by xmute, tmute pairs. The widths in time of the muted zone are given by the twindow vector linvel=330 constant velocity for linear or hyperbolic mute

Mid-term presentations: topics in seismology Oct 19-23 – 2 or 3 per day 15-minute oral presentation Include: history of topic, theory, approach to addressing/solving topic, relevance to industry/society Topic? Andrew: seismic monitoring of volcanoes Tate: glacial monitoring using seismology Aiada: seismoelectric Travis: fat ray path/WET inversions Marlon: nuclear seismology Will: ETS Dmitri

Friday quiz Know these concepts – definitions and use Nyquist frequency fmax=1/(2dt) Convolution (deconvolution) Correlation (cross correlation, autocorrelation) Bandwidth - frequency range contained in a source wavelet or seismic trace Resolution – vertical (Rayleigh criterion) and horizontal (Fresnel zone) Dynamic range: amplitude (A) or power (P) ratio (in dB):

Convolution and Correlation Correlation is a measure of similarity between two signals (t) = ∫ f(t) g(t-t)dt Convolution is a measure of effect of one signal on the other (output response on input signal). h(t) = ∫ f(t) g(t-t)dt In practice, correlation is done the same way as convolution in the time domain, except that the wavelet is not reversed before the multiplication process. If the filter is symmetric, then convolution and correlation produce the same result

Filtering in the time domain - convolution h(t) = f(t) * g(t) = ∫ f(t) g(t-t)dt Given two arrays: 1. Reverse moving array 2. Multiply and add 3. Shift 4. repeat step 2 2 time * = -1

Convolution Source wavelet: 2, 4, 3 Reflectivity sequence: 0, 0, 1, 0, 0, 0, 0 0 0 1 0 0 0 0 3 4 2 0 3 4 2 0 3 4 2 2 3 4 2 4 3 4 2 3 3 4 2 0 3 4 2 0 3 4 2 0

Vibroseis Vibroseis sources use cross-correlation to synthesize a short, zero- phase wavelet from a long source sweep.

Autocorrelation Correlation between a function and itself is called an autocorrelation. The autocorrelation of a function gives the zero-phase wavelet, scaled to the total energy in the trace. Autocorrelation is used to retrieve the zero- phase wavelet from a seismic trace.

Fresnel zone a reflection coming back to the surface from a point in the subsurface is actually being reflected from an area with the dimension of the First Fresnel Zone. The dimensions of the Fresnel Zone can be calculated for a plane reflector in the constant velocity case, allowing for two-way travel time.

Lateral Resolution What is the minimum horizontal distance between two subsurface features such that we can tell them apart seismically? Neidell & Poggiaglioimi, 1977 AAPG©1977 reprinted with permission of the AAPG whose permission is required for further use.

Resolution Wavelength (l), velocity (v) and frequency (f) l = v/f f = v/l fresnel zone  Depth  d=(v*t)/2 where t=two-way travel time Fresnel zone~ For example: v=1,500 m/s, f=100 Hz(dominant) l = v/f = 15 m; vertical resolution =3.75 m Fresnel zone lateral resolution ~47 m @100 ms (75 m depth) Fresnel zone lateral resolution ~15 m @10 ms (7.5 m depth)

Direct/Reflection/Refraction arrivals and travel times

Direct Wave The travel time to each geophone for the direct wave in the first layer is:

Shot record showing relation between refraction/reflecti on Reflections are asymptotic to refracted/direct arrivals Refracted wave Direct wave Shot record showing relation between refraction/reflecti on reflections Surface waves

The Reflected Ray v1 v2 is never a first arrival Plots as a (hyperbolic) curved path on t-x diagram Asymptotic with direct ray Time (t) Distance (x) Receiver Shot Point v1 Layer 1 v2 Layer 2

The Refracted Ray “Critical Distance” No Refracted Rays  v1 v2 The Refracted Ray Arrival Time: Plots as a linear path on t-x diagram (assuming v2>v1) Part travels in upper layer (constant) Part travels in lower layer (function of x) Only arrives after critical distance Is first arrival only after cross over distance Travels long enough in the faster layer Time (t) Distance (x) critical distance cross over distance “Critical Distance” No Refracted Rays  ic ic ic ic v1 Layer 1 Layer 2 v2

Refracted wave The ray path and the travel time for the refracted wave for a 2-layer model can be derived as B C trefract=x/v2+ti

Refraction seismology A refraction refers to the wave energy that travels below the upper interface at the velocity of the lower layer. The refraction travels horizontally along the lower interface, then travel back toward the earth’s surface. The refracted wave can only be received after the critical distance xcrit beyond the critical angle icrit .

Snell’s Law & Critical Refraction Seismic sources radiate waves in all directions Some rays hit an interface at exactly the critical angle, ic This critically oriented ray will then travel along the interface between the two layers If more oblique than critical, all wave energy is reflected

The Time-Distance (t-x) Diagram Intercept time - tint Critical distance - xcrit Cross over distance - xcross

Minimum distance where refractions are generated

Cross over distance At the crossover distance xcross the travel times to the point are the same for the direct wave and the refracted wave, so we have

Intercept time Y-intercept of refracted arrival

Single layer calculation

Summary: Direct/Reflection/Refraction Travel times Travel times for the direct, reflected, and refracted waves for a 2-layer model

3 layer refraction problem

3-layer problem

Dipping Planar Interfaces When a refractor dips, the slope of the traveltime curve does not represent the "true" layer velocity: shooting updip, i.e. geophones are on updip side of shot, apparent refractor velocity is higher shooting downdip apparent velocity is lower To determine both the layer velocity and the interface dip, forward and reverse refraction profiles must be acquired.

Dipping Layer V1 h1  Letting j = 2h1 we can alternatively write  Here, j is distance from the shotpoint to an image point h1  Letting j = 2h1 we can alternatively write 

Complex velocity models Time-distance plots are used to provide a best fit between observed and modeled results

Undulating Interfaces Undulating interfaces produce non-linear t-x diagrams There are multiple approaches to address this delay times & plus minus method

Reciprocal method Used to map an undulating interface that separates two materials of contrasting seismic velocity beneath an undulating surface;

Detecting Offsets Offsets are detected as discontinuities in the t-x diagram Offset because the interface is deeper and D’E’ receives no refracted rays.

Diving waves

Refraction Tomography

Caveats of Refraction Only works if each successive layer has increasing velocity Cannot detect a low velocity layer May not detect thin layers Requires multiple (survey) lines Make certain interfaces are horizontal Determine actual dip direction not just apparent dip

The Low Velocity Layer If a layer has a lower velocity than the one above… There can be no critical refraction The refracted rays are bent towards the normal There will be no refracted segment on the t-x diagram The t-x diagram to the right will be interpreted as Two layers Depth to layer 3 and Thickness of layer1 will be exaggerated

The Hidden Layer Recall that the refracted ray eventually overtakes the direct ray (cross over distance). The second refracted ray may overtake the direct ray first if: The second layer is thin The third layer has a much faster velocity

Geophone Spacing / Resolution Often near surface layers have very low velocities E.g. soil, subsoil, weathered top layers of rock These layers are likely of little interest But due to low velocities, time spent in them may be significant To correctly interpret data these layers must be detected Decrease geophone spacing near source

Fan Shooting Discontinuous targets can be mapped using radial transects: called “Fan Shooting” A form of seismic tomography

Refraction Tomography Complex solution to complex geologic problems