High resolution attributes for seismic data processing and interpretation

Abstract

A visualization method for the computation and display of seismic attributes from time-frequency spectral analysis enables high resolution investigation of 3D seismic data for the exploration of oil and gas. First, high frequency resolution time derivative or space derivative of the amplitude and phase spectra of time-windowed signals are computed. Second, the derivatives are transformed into seismic attributes that are suitable for seismic data processing or interpretation. Applications for the method are illustrated with graphical screen 3D volume displays of dip and azimuth, curvature and faults. Aside from providing high resolution these displays may improve the productivity of a seismic interpreter or data processor.

1 . A method to estimate residual time delay and dispersion between seismic signals recorded after propagation between time-separated or space-separated, time-windowed signals that have been Fourier transformed with high frequency resolution, where said residual time delay is an intercept at a reference frequency and dispersion is the slope of a linear relationship of residual time delay with respect to frequency, the method comprising:
 (a) specifying a reference frequency (ωref);   (b) in a processor, computing amplitude and phase spectra of the recorded seismic signals within windows centered at specified times t 1  and t 2  wherein t 2 > t 1 , the seismic signals recorded by placing seismic sensors above an area of interest and actuating a seismic energy source;   (c) in a processor, computing normalized amplitude spectra A with respect to frequency (ω) namely, (A(t 1 , ω)) and (A(t 2 , ω)), such that:
     A ( t 1, ωref)= A ( t 2, ωref);
 
   (d) in a processor, computing frequency-by-frequency mean amplitudes
   Mean  A (ω)=0.5 *[A ( t 1, ω)+ A ( t 2, ω)]
 
   (e) in a processor, identifying frequency pass bands wherein Mean A(ω) amplitudes are above a specified threshold;   (f) in a processor, computing phase difference with respect to frequency;
     d φ(ω)=φ( t 2, ω)−φ( t 1, ω),
 
   (g) in a processor computing residual time delay with respect to frequency;
     dt (ω)= d φ(ω)/ω,
 
   (h) in a processor, plotting dt(ω)—with respect to—ω scatter on a graph;   (i) in a processor, fitting a straight line that passes through points on said graph in   (h) that lie within said pass bands in (e) such that a Mean A(ω) weighted average of absolute difference between said points and said line is a minimum;   (j) In a processor, extracting a residual time delay, δt, as the value on said line at a user-specified frequency and dispersion as the slope of said line;   (k) in a processor, computing a final time delay;
   τ= t 2 −t 1 +δt  
 
   (l) at least one of storing in a computer readable storage medium and displaying on a computer graphics display the final time delay and dispersion parameter.   
     
     
         2 . The method of  claim 1 , to estimate the Earth's attenuation between reflectors by using only the amplitude spectra, the method further comprising:
 (m) a processor, performing (a) through (e) of  claim 1 , wherein the specified times   (t 1 , t 2 ) correspond to two different reflectors on a same seismic trace;   (n) in a processor computing In(A(t 1 , ω) and In(A(t 2 , ω) for data within the pass bands;   (o) in a processor computing an energy absorption time rate with respect to frequency
     E (ω)=2 *[In ( A ( t 1, ω)− In ( A ( t 2, ω)]/( t 2 −t 1);
 
   (p) in a processor, fitting a linear least squares line that is constrained to pass through zero at (ωref) and also through scatter of E(ω) data points within the pass bands;   (q) in a processor, storing the slope of the fitted line as an attenuation parameter called ‘Inverse Q’ for an interval between the reflectors at the specified times t 1  and t 2 ;   (r) in a processor repeating (m) through (q) for a plurality of specified times that belong to a same reflector pair in a plurality of seismic traces, wherein Mean A(ω) is computed for reflector pairs in the plurality of traces.   
     
     
         3 . A method to estimate wavenumber spectrum continuously at each point in a three dimensional seismic volume of traces associated with an area of Earth's subsurface, each trace comprising a time indexed record of signals recorded by a seismic sensor in response to actuation of a seismic energy source, the method comprising:
 (a) in a processor, computing high frequency resolution amplitude and phase spectra of time windowed signals obtained from said traces;   (b) specifying a lateral perimeter enclosing a plurality of traces;   (c) in a processor, placing said perimeter at a center point in said volume;   (d) in a processor, computing a mean amplitude with respect to frequency A(ω), over said perimeter at said center time and then computing an average mean amplitude for all frequencies within the seismic traces;   (e) defining a set of frequency passbands wherein a mean amplitude therein is greater than a specified multiplier of the average mean amplitude;   (f) initializing a first frequency within the first passband;   (g) in a processor, computing for current frequency in current passband the phase differences between the center trace and each other trace in said perimeter at the time of said center point:   (h) in a processor, fitting a plane through phase differences from (g) such that the plane is constrained to pass through zero at the center trace and minimizes squared phase differences over the scatter of points in said perimeter;   (i) in a processor, computing a root mean squared (rms) error (err(ω)), of phase difference scatter relative to the fitted plane;   (j) in a processor, comparing err(ω) with a specified threshold; if the error exceeds the threshold then reducing the size of the perimeter and repeating (h) and (i) for the reduced perimeter until either the error does not exceed the threshold or a minimum perimeter size is reached, in which case re-fitting the plane is performed as in (h) after removing any outliers;   (k) in a processor, storing a gradient of the final fitted plane that gives horizontal wavenumbers kx(ω), ky(ω), and associated err(ω), the mean amplitude A(ω) and variance, var[A(ω)], over the final perimeter,   (l) in a processor, incrementing to the next frequency in the passband until the end of that passband, then incrementing the passband, and repeating (g) through (j) until a last frequency in the last passband is processed,   (m) in a processor, incrementing the center time, resetting the perimeter to initial size and repeating the steps (e) through (m) until the end of data is reached.   
     
     
         4 . The method of  claim 3  further comprising:
 (a) in a processor, computing from the output in step (k) of  claim 3  the quantities, kx(ω)/ω and ky(ω)/ω; 
 (b) in a processor computing the amplitude, A(ω), weighted mean values of kx(ω)/ω and ky(ω)/ω; wherein 
 (c) the weighted mean of kx(ω)/ω gives the apparent time dip, dt/dx, and weighted mean of ky(ω)/ω gives the apparent time dip, dt/dy; wherein 
 (d) the true time dip=sqrt[(dt/dx)̂2+(dt/dy)̂2]and azimuth=arctan[(dt/dy)/(dt/dx) relative to the y-direction; and 
 (e) storing in a computer readable storage medium or displaying on a computer graphics display at least one of the apparent time dip vector and dip and azimuth vector in a medium. 
 
     
     
         5 . A method to estimate curvature of reflection time surfaces continuously in a three dimensional seismic volume, the method comprises:
 (a) obtaining a three dimensional seismic data volume by deploying seismic sensors above an area of the subsurface of interest, actuating a seismic energy source, and recording signals detected by the seismic sensors, then processing signals relative to a surface datum, and computing through  claim 4  the apparent time dips (dt/dx);   (b) specifying a lateral perimeter enclosing a plurality of unaliased seismic data traces;   (c) initializing time at a start of surface datum in (a) and placing said perimeter at a center point at a beginning of survey area in said volume;   (d) in a processor, computing (dt/dx) apparent time dip differences between the center trace and each other trace in said perimeter at the time of said center point;   (e) in a processor, fitting a plane through the scatter of said (dt/dx) differences over said perimeter such that the plane is constrained to pass through zero at the center trace and minimizes squared (dt/dx) differences with respect to the scatter of points in said perimeter;   (f) in a processor, computing root mean square (rms) error (err) of (dt/dx) difference scatter relative to the fitted plane;   (g) in a processor comparing err with a specified threshold; if the error exceeds the threshold then reducing the size of the perimeter and repeating (c) through (f) for the reduced perimeter until either err does not exceed the threshold or a minimum perimeter size is reached, in which case re-fitting the plane after removing any outlier is performed as in (e);   (h) classify the center point as a fault and save the center point coordinate as a fault in a computer readable storage medium if the err for the minimum perimeter size in   (g) still exceeds the threshold,   (i) in a processor, storing a gradient of the final fitted plane from (g) that gives horizontal second derivatives (d 2 t/dx 2 ), (d 2 t/dydx), and err, over the final perimeter,   (j) repeating (d) through (i) for all time and space points in the seismic volume to provide two sub volumes, (d 2 t/dx 2 ) and (d 2 t/dydx);   (k) replacing the volume of time dips (dt/dx) with the volume of (dt/dy) and repeating (a) through (j) to provide two additional subvolumes, (d 2 t/dy 2 ) and (d 2 t/dxdy), and   (l) in a processor, computing and storing K+ and K− measures of curvature as defined by equations (2) and (3) in paragraph [0050] and where coefficients (a, b, c) are given by equations (15), (17) and (19) in paragraphs [0139] and [0140].   
     
     
         6 . The method of  claim 5  further comprising displaying the dip and azimuth or K+ curvature and K− curvature measures as two-dimensional images on an interactive computer graphics screen.