Method of generating seismic wavelets using seismic range equation

A method in accordance with claim 2, wherein said radiated energy density is derived from a number of said source array elements (N), said frequency (f), said seismic velocity of first layer traversed (.alpha..sub.1), said density of the first layer transversed (.rho..sub.1), and from the illumination factor.

A method in accordance with claim 2, wherein said source directivity is derived from the ratio of said radiated energy density per unit solid angle radiated in a particular direction (.theta..sub.s,.phi..sub.s) to said radiated energy density E(f).

A method in accordance with claim 2, wherein said capture area is derived from the multiplication of the capture area along the acoustic axis and the transmitting pattern of the hydrophone array.

A method in accordance with claim 2, wherein said target's reflection coefficient is derived from the said angle of incidence (.theta..sub.i), said seismic velocities (.alpha..sub.i,.alpha..sub.i+1,.beta..sub.i and .beta..sub.i+1), and said densities (.rho..sub.i and .rho..sub.i+1) of layers at the interface.

A method in accordance with claim 2, wherein said divergence is derived from said thickness (h.sub.i) of the beds transversed by the ray and said ray angle (.theta..sub.i) in each bed, and said offset X, between source and receiver.

A method in accordance with claim 2, wherein said loss factor includes transmission loss (L.sub.t).

A method in accordance with claim 2, wherein said loss factor includes Q-loss (L.sub.Q).

A method in accordance with claim 2, and including the phase spectrum (.phi..sub.p (f)) of said model voltage waveform, taking the total travel time through the layers into account, which comprises determining the phase components of the electromotive force (.phi..sub..epsilon. (f)) generated by the incident primary pulse, deriving the value of any phase contributions of said load and hydrophone array impedance, and summing the components of said electromotive force and said load and hydrophone array impedance.

A method in accordance with claim 2, and including the contribution of the interbed multiple loss to said loss factor, which comprises selecting the maximum number of interfaces (J.sub.max) that a reflected pulse traveling toward a receiver will transverse before being reflected back downward, assuming a downgoing secondary ray path beginning at the source at ray angle (.theta..sub.d), at frequency (f), through a predetermined number of subsurface layers, to layer (i), up through a predetermined number of interfaces (J), down to the said target layer at said depth (d), up through the subsurface layers and water to the receiver and assuming an upgoing secondary wavelet path beginning at the source at ray angle (.theta..sub.u), at a frequency (f), down to said target layer at said depth (d), up to a predetermined subsurface layer (i), down a predetermined number of interfaces (J), then back up through the subsurface layers and water to the receiver, determining the source directivity for a given offset and target depth, for said upgoing and downgoing secondary pulses, for a selected J, calculating the capture array along the incident direction at the hydrophone array, for both said upgoing and downgoing secondary pulse, for said selected J, determining the reflection coefficients for the upgoing secondary pulse at the interfaces between the layer i and i-1 (R.sub.u (i,i-1)) and between the layers i+J and i+J+1 (R.sub.u (i+J,i+J+1)) and the downgoing secondary pulse interfaces between the layers i and i+1 (R.sub.d (i,i+1)) and between the layers i-J and i-J-1 (R.sub.d (i-J,i-J-1)), determining said divergence for both the upgoing (D.sub.vu) and downgoing (D.sub.vd) secondary pulses, at a given offset and said selected J, calculating the loss factors L(f) associated with the upgoing and downgoing secondary pulses, dividing the product of said radiated energy density E(f) said source directivity for the downgoing secondary pulse, said capture area for the downgoing secondary pulse, said target reflection coefficient for the downgoing secondary pulse by said divergence for the downgoing secondary pulse (D.sub.vd), and said loss factor for downgoing secondary pulse, to form the receive energy density for the downgoing secondary pulse (E.sub.d (f)) for a given subsurface layer i, and said selected J, deriving the amplitude spectrum of said model voltage waveform (.vertline.A.sub.d (i,J,f).vertline.), corresponding to the downgoing secondary pulse reflected off the interface between layer i and layer i+1 and said selected J, for all frequencies across the seismic band, utilizing said received energy density E.sub.d (f) of the downgoing secondary pulse and said value of any load impedance (Z.sub.L (f) and Z.sub.H (f)), deriving the phase spectrum of the downgoing secondary wave, taking the travel time through the layers into account, by summing the phase spectrum of the electromotive force generated by the incident secondary pulse with the value of any phase components of said load and hydrophone array impedances, multiplying both said reflection coefficients (R.sub.d (i,i+1) and R.sub.d (i-J,i-J-1)) by said amplitude spectrum and using the phase spectrum of the downgoing secondary pulse, to form the frequency spectrum of the downgoing interbed multiple (A.sub.d (i,J,f)), dividing the product of said radiated energy density, E(f), said source directivity for the upgoing secondary pulse, said capture area for the upgoing secondary pulse, said target reflection coefficient for the upgoing secondary pulse by said divergence for the upgoing secondary pulse, and said loss factors for upgoing secondary pulse, to form the receive energy density for the upgoing secondary pulse (E.sub.u (f)) for a given subsurface layer i, and said selected J, deriving the amplitude spectrum of said model voltage waveform (.vertline.A.sub.u (i,J,f).vertline.), corresponding to the upgoing secondary pulse reflected; off the interface separating layer i and layer i-1 and said selected J, for selected frequencies across the seismic band, utilizing said received energy density E.sub.u (f) of the upgoing secondary pulse and said value of any load impedance (Z.sub.L (f) and Z.sub.H (f)), deriving the phase spectrum of the upgoing secondary wave (.phi.(u,i,J), taking the travel time through the layers into account, by summing the phase spectrum of the electromotive force generated by the incident secondary pulse with value of any the phase components of said load and hydrophone array impedances, multiplying both said reflection coefficients (R.sub.u (i,i-1) and R.sub.u (i+j,i+j+1) by said amplitude spectrum and using the phase spectrum of the upgoing secondary pulse, to form the frequency spectrum of the upgoing interbed multiple, A.sub.u (i,J,f), summing the ratio of the frequency spectrum of the downgoing secondary pulse (A.sub.d (i,J,f)) to the frequency spectrum of the primary pulse (A.sub.p (f)) for each subsurface layer (i) above the target for 0.ltoreq.J.ltoreq.J.sub.max, and summing the ratio of the frequency spectrum of the upgoing secondary pulse (A.sub.u (i, J, f)) to the frequency spectrum of the primary pulse A.sub.p (f) for each subsurface layer (i) above the target for O.ltoreq.J.ltoreq.J.sub.max, to produce the interbed multiple loss factor at frequency (f), dividing said received energy density E.sub.p (f) by interbed multiple loss factor to form the received energy density E.sub.r (f) including the interbed loss factor, deriving the amplitude spectrum (.vertline.A (f).vertline.) of said model voltage waveform, including the effects of the interbed multiples, for frequencies across the seismic band, utilizing said received energy density (E.sub.r (f)) and said value of load impedance (Z.sub.L (f)), and deriving the phase spectrum (.phi.(f)) of said model voltage waveform, by summing phase components of the primary's phase spectrum .phi..sub.p (f) with the phase spectrum for the interbed multiple filtering .phi..sub.iB (f).

A method in accordance with claim 31, for performing enhanced amplitude-versus-offset analysis on unprocessed seismic data, which comprises combining said model traces for specified offsets to develop an unprocessed model gather, and comparing variations in the amplitude versus offset of said seismic data to the variation in amplitude versus offset of the model gather.

A method in accordance with claim 31, for generating a corrected model gather over a frequency band of interest, which comprises processing said model traces of unprocessed data, for a given source to receiver offset, and combining said processed model traces for each offset to produce a model gather.

A method in accordance with claim 46 wherein said transmission loss (L.sub.t) is the total loss with crossing an interface twice and is derived from the transmission coefficients associated with the corresponding layers traversed (T.sub.i,.sub.i+1, T.sub.i+1,.sub.i).

A method in accordance with claim 46, wherein said interface crossed include one of the following interfaces: solid-to-solid, fluid-to-solid, and solid-to-fluid.

A method in accordance with claim 49, wherein said Q-loss is derived from the frictional attenuation constant (Q.sub.i) of the subsurface layers, said P-wave velocity (.alpha..sub.i) of each transversed layer, said width of each transversed layer (h.sub.i), said frequency (f), and said ray angle (.theta..sub.i).

A method in accordance with claim 53, wherein said illumination factor (I.sub.n (f)) is derived from said amplitude spectrum (A.sub.n (f)) of the waveforms radiated, the value of any firing delay (.delta..sub.n), and said frequency (f).

A method in accordance with claim 56, wherein said capture area along the direction of the acoustic axis, said axis being normal to the surface, is derived from said hydrophone array sensitivity S.sub.H (f), said value of any load and hydrophone array impedances (Z.sub.L (f) and Z.sub.H (f)), said density of the first transversed layer, said P-wave velocity of the first transversed layer, and array depth.

A method in accordance with claim 56, wherein said transmitting pattern is defined by the ratio of said hydrophone directivity D(.theta..sub.H,.phi..sub.H,f) along the incident ray direction to the directivity of hydrophone along the acoustic axis D(O,.phi..sub.H,f), said axis being normal to the surface.